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COMPRESSIVE SENSING IMAGE FUSION BASED ON PARTICLE SWARM OPTIMIZATION ALGORITHM
In order to solve the problem that the spatial matching is difficult and the spectral distortion is large in traditional pixel-level image fusion algorithm. We propose a new method of image fusion that utilizes HIS transformation and the recently developed theory of compressive sensing that is called HIS-CS image fusion. In this algorithm, the particle swarm optimization algorithm is used to select the fusion coefficient ω. In the iterative process, the image fusion coefficient ω is taken as particle, and the optimal value is obtained by combining the optimal objective function. Then we use the compression-aware weighted fusion algorithm for remote sensing image fusion, taking the coefficient ω as the weight value. The algorithm ensures the optimal selection of fusion effect with a certain degree of self-adaptability. To evaluate the fused images, this paper uses five kinds of index parameters such as Entropy, Standard Deviation, Average Gradient, Degree of Distortion and Peak Signal-to-Noise Ratio. The experimental results show that the image fusion effect of the algorithm in this paper is better than that of traditional methods.
PREFACE *
Image fusion is an optimization method for spatial information and spectral information, which eliminates suppression and redundant information, highlights the information needed, and provides a more targeted and accurate images in various research fields (Wang X, 2015).Currently, the fusion methods include weighted average fusion, HSI transform algorithm, Brovey transform, principal component analysis algorithm, Gram-Schmidt Spectral Sharpening, Pan-Sharpening, wavelet fusion algorithm etc..Among these methods, HIS is one of the most widely used image fusion algorithms (Yang J, 2014).The traditional HIS image fusion algorithm can improve the spatial resolution of the fusion image to a certain extent, but it also causes spectral distortion because of the loss of the spectral information (Jianwei Liu, 2013).So the traditional HIS transform algorithm can't get the ideal fusion effect in spectral information and spatial resolution at the same time (TU Te-ming,2001, Zhang Y, 2012).In recent years, some scholars have proposed the fusion methods based on compressive sensing (CS) (Guo J, 2013).Alin Achim (2008) proposed a new image fusion algorithm in the compressive domain by using an improved sampling pattern; the study demonstrates that CS-based image fusion has a number of perceived advantages in comparison with image fusion in the * Address all correspondence to: Jingguo Lv, E-mail<EMAIL_ADDRESS>(MR) domain (Wan T, 2008).Then Atul Diveker et al. improves the compression-aware image fusion algorithm by creating a dictionary that relates high resolution image patches from a panchromatic image to the corresponding filtered low resolution versions.Any pair of co-occurring high and low resolution patches with similar statistical properties to the patches in the dictionary is sparse with respect to the principal component bases.The result shows that it can reduce the spectral distortion of the fused image and produces results superior to standard fusion methods such as the Brovey transform and principal component analysis (Atul. Divekar, 2009).Yang (2015) proposed an image fusion method based on block-based compressed sensing (BCS) that can reduce the storage requirements and reconstruction cost to a certain extent (Senlin Yang, 2015).Considering the advantages and disadvantages of HIS transform and compressive sensing (CS), we propose the HIS-CS image fusion algorithm.The key problem in HIS-CS algorithm is how to choose the appropriate fusion coefficient ω.In this paper, we use the particle swarm optimization algorithm to select the appropriate coefficient ω.
In the iterative process of particle swarm optimization algorithm, the image fusion coefficient ω is used as the particle, and the information entropy and the average gradient function are used as the optimization objective function.The goal is to make the fusion measurement value maximize the information entropy and the average gradient value so as to achieve the optimal value of the fusion coefficient under the function.In the iterative process of particle swarm optimization algorithm, the image fusion coefficient ω is used as the particle, and the functions of entropy and the average gradient are taken as the optimization objective function.The goal is to get one ω, which can maximize the value of functions of entropy and the average gradient.Then we take this optimal value as a weight coefficient during the use of weighted fusion rules for image fusion.This method can not only ensure the optimization of the fusion effect, but also make the fusion algorithm have a certain degree of adaptability.
Compressive Sensing(CS)
Candes and Donoho put forward CS theory in 2006 (Donoho D, 2006).And then it had a rapid development on the bases of the existing theories such as signal reconciliation analysis, time-frequency analysis, statistical probability theory, matrix analysis, functional analysis, statistical probability theory and so on (Gesen Zhang, 2012).Compressive Sensing can achieve compression at the same time as sampling.
The flow chart of compressive sensing is as shown in Figure 1.
Compressible signal Sparse transformation
M-dimensional Measurement
Reconstruct the signal Step 1 Step 2 Step 3 Sparse transformation Compressive sensing explores the essential structure of the signal from the overall situation, which can get rid of the links between signal frequency and other physical measurement (Zhang Y, 2012).As long as the signal has a compressible sparse domain, it can be linearly projected onto a low-dimension observation vectors using a measurement matrix that is non-coherent with the transformation matrix.The sample value in projection space contains enough information.So we can use the sparse optimization theory to accurately reconstruct the original signal from a small number of sample values with high probability.The theory of compression sensing mainly includes the sparse representation of the signal, the measurement matrix design and reconstruction algorithm selection.One of the advantages is that it gathers the steps of data collection and data sample into one.The data is compressed at the same time as the signal acquisition, and the cost in the signal acquisition and processing is greatly reduced.The process of compressive sensing is as follows: Step 1: If the signal . is the equivalent or approximation representation of signal X in the space domain.
Step 2: We design a MN measurement matrix , which has no relevance with the orthogonal basis .Then we can obtain the measurements Step 3: The sparse signal x can be recovered using measurements to solve (1) if the projection matrix satisfies the restricted isometry property (RIP).
The superiority of CS is that the sampling quantity is far less than the amount of data obtained by the traditional Nyquist sampling method, breaking through the limitation of the Nyquist sampling theorem.
Particle Swarm Optimization Algorithm
Particle swarm optimization (PSO) is an evolutionary computation.The basic thought is to find the optimal solution through the cooperation and information sharing among the individuals in the swarm (Yujie Xu, 2013).In this algorithm, the bird is abstracted as a point (particle) without volume and mass, and is extended to the N-dimensional space.The position vector of the particle i in the N-dimensional space is expressed as , and the vector of the flight velocity is expressed as . Each particle has a fitness value determined by the objective function, and also knows it's current position and the best position has been found.This process can be seen as the particle's own flight experience.In addition, each particle knows the best position gbest (which is the best value of all pbest), which is currently found by the whole group.This process can be seen as the flight experience of the swarm.Particles in the swarm determine the direction and velocity of the next step by the best experience of their peers in the group.In this process, the Particle Swarm Optimization (PSO) algorithm is first initialized into a group of random particles (random solutions), and then obtained the optimal solution by iteration.In each iteration process, the particles update their position and velocity through two extreme (pbest, gbest).
() ( )
In formulas ( 2) and (3), N is the total number of particles in the swarm; i V is the velocity of the particle; () rand is the random number between 0 and 1; i X is the current position of the particle; Step 1: Initialize a group of particles (the size is N), including random positions and velocities; Step 2: Evaluate the fitness of each particle; Step 3: The current fitness value of each particle is compared with its best position (pbest) ever found, if the current fitness value is better, then its current fitness value will be the best position (pbest); Step 4: The current fitness value of each particle is compared with the swarm's best position (gbest) ever found, if the current fitness value is better, then its current fitness value will be the swarm's best position (gbest); Step 5: Adjust every particle's position and velocities according to the formula (2), (3) Step 6: Check it out whether the results meet the end condition, if so then finish, or turn to step 2; The iteration termination condition is selected according to the specific problem.Generally we select the maximum number of iterations k G , or the optimal position to meet the minimum adaptation threshold currently found by the particle swarm(Jianyong Li, 2004).
HIS -CS Fusion Algorithm Based on Particle Swarm Optimization Algorithm
The advantage of HIS image fusion is that it can improve the spatial resolution obviously, and Compressive sensing (CS) can remain the spectral information better.In this paper, HIS-CS image fusion algorithm based on particle swarm optimization (PSO) is proposed utilizes the advantages of the two algorithm.The particle swarm optimization algorithm is used to determine the image fusion weight coefficient ω in the proposed method, which can avoids the problem that the experience value used in traditional methods can't be adjusted adaptively with different characteristics of different images.In this method, the particle swarm optimization algorithm is used to select the fusion parameter ω.In the iterative process, the image fusion coefficient ω is used as particle; the functions of information entropy and the average gradient are taken as the optimization objective function, which goal is to get the maximum values of the information entropy and the average gradient.So we can get the optimal value under the defined optimization objective function.The optimal value is taken as the target fusion weight coefficient used in the weighted fusion rule in HIS-CS image fusion.The method can guarantee the optimization of the fusion effect and make the fusion method have a certain degree of adaptability.
The process of HIS-CS image fusion based on the particle swarm optimization algorithm is as shown if Figure 3: Step 1: Raw image processing: The high resolution image is meshed with the multi-spectral image, we can obtain two images with high spatial information matching.Then reshape the image according to the specific research area.
Step 2: The multi-spectral image with registration is transformed by HIS transformation, then we can get Three relatively independent components H (Hue), I (Intensity), S (Saturation).
Step 3: Then we get the measurement matrix 1 y and y of panchromatic image PAN and I component got
Evaluation and Analysis of Image Fusion Results
By comparing the fusion image of different methods of Figure 4, we can find out that there is obvious improvement of the spatial resolution of each method, but there are differences between the improvement degrees of various algorithms.The common feature of the fusion images is that the spectral information has been changed, but the methods of this paper and the CS image fusion have the smallest spectral changes, the color information is mostly consistent with the original images.So in terms of spectral information retention, the methods of this paper and CS image fusion is better than the traditional methods.But the method of this paper has a better spatial resolution improvement than the method of CS image fusion.1, the value of AG, EN, PSNR, STD of the method in this paper are larger than that of other methods, so the method in this paper has the optimal evaluation indicators.The value of DD of this method is larger than CS image fusion, but is smaller than the other traditional methods.So we can see that the spectral information retention of the proposed method is better than the other traditional methods, but not as well as CS image fusion.Overall, the proposed method has a better performance than the traditional methods.
Conclusion
In this paper, particle swarm optimization algorithm is used to improve the HIS-CS image fusion algorithm.
In the proposed method, we combine a series of fusion weight coefficients ω as particle swarm, and find the optimal value among them to be the optimal fusion weight coefficient ω, which can make the proposed method have certain self-adaptability.In addition, by controlling the step size, we can get a more optimized result, which can balance the improvement of the spatial resolution and spectral information retention.So that by adjusting the step size, we can make the results to meet our requirements.Overall, the proposed method can improve the fusion effect to a certain extent.
But the proposed method has shortcomings ether.The proposed method performs slightly worse in spectral information retention than that of CS image fusion, though it has shown a great advantages in subjective and objective evaluation indices.In addition, in order to make the fusion weight coefficients ω more optimal, it will lead to a large computation by setting the step size too small.This needs to be further optimized and improved in the lasting research.
matrix .The process can also be expressed as the adaptive observation of signal X under the matrix the information operator of Compressive Sensing.
Figure 2
Figure 2 The flow chart of Particle Swarm Optimization algorithmThe process of Particle swarm optimization (PSO) is as follows:Step 1: Initialize a group of particles (the size is N), including random positions and velocities;Step 2: Evaluate the fitness of each particle;Step 3: The current fitness value of each particle is compared with its best position (pbest) ever found, if the current fitness value is better, then its current fitness value will be the best position (pbest);Step 4: The current fitness value of each particle is compared with the swarm's best position (gbest) ever found, if the current fitness value is better, then its current fitness value will be the swarm's best position (gbest);Step 5: Adjust every particle's position and velocities according to the formula (2), (3)Step 6: Check it out whether the results meet the end condition, if so then finish, or turn to step 2; The iteration termination condition is selected according to the specific problem.Generally we select
Figure 3
Figure 3 The flow chart of HIS -CS image fusion algorithm based on particle swarm optimization algorithm The process of HIS-CS image fusion based on Particle swarm optimization (PSO) is as follows:Step 1: Raw image processing: The high resolution image is meshed with the multi-spectral image, we can obtain two images with high spatial information matching.Then reshape the image according to the specific research area.Step 2: The multi-spectral image with registration is transformed by HIS transformation, then we can get Three relatively independent components H (Hue), I (Intensity), S (Saturation).
Fig 4 The results of different fusion methods
.
As we can see from data of Table | 3,495.8 | 2017-09-13T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Controlling the Limit-Cycle of the Ziegler Column via a Tuned Piezoelectric Damper
This paper is about the nonlinear analysis of a piezoelectric controlled Ziegler column. The piezoelectric controller, here referred to as Tuned Piezoelectric Damper (TPD), possesses evanescent characteristics and, moreover, it is tuned to the first natural frequency of the mechanical system, thus resembling the well-known Tuned Mass Damper. This means that the flow of energy between mechanical and electrical subsystems is driven by the resonance (Den Hartog principle) and magnified by the singularity of the evanescent electrical characteristics. Numerical simulations, showing how the proposed control strategy is effective in increasing the linear stability domain and decreasing the amplitude of the limit-cycles in the postcritical range, are presented.
Introduction
Structures subjected to follower forces exhibit rich and interesting dynamic features.Among these latter, the most studied are the loss of stability and the onset of several paradoxes (e.g., related to the damping).Moreover, it is interesting to remark that control strategies that are optimal for reducing vibrations can have a detrimental effect on stability (see, e.g., [1]).Indeed, developing a unified control strategy optimized for damping vibrations in the linear and postcritical regimes, and at the same time increasing the stability zone, is a challenging task.
Since their first introduction in the early 1990s, piezoelectric based controllers have attracted the interest of researchers and their industrial applications have increased over the past years.These controllers are usually divided into two main categories: active and passive controllers.The distinction is based on whether or not the controller is able to pump energy into the mechanical system.As it is well known, active controllers can be really effective but also suffer from stability issues.Examples of active controllers can be found in [2,3].This is why our choice is to focus our attention on passive controllers of the type firstly introduced in [3].As they are usually implemented by tuning the resonance(s) of the electric circuit to one (or more) natural frequency(ies) of the mechanical system, they can represent a valid alternative to the classic Tuned Mass Dampers (TMDs) [4][5][6][7][8].Their advantage is mostly due to the fact that they are more versatile, simpler to tune, and in most configurations lighter than classic TMD.Moreover, piezoelectric controllers can be used also in microdevices [9].
In our previous studies [10,11], we focused our attention on several kinds of piezoelectric control strategies, applied to discrete linear structures.In these papers, mechanical and electrical subsystems were studied in their linear and nonlinear dynamics, respectively.In [10], three different controllers were proposed and it was proved that, at various extents, they all have a beneficial effect on stability.In [11], attention was focused on a two-DOF system, namely, the nonlinear Ziegler column, which was taken as case study, and the amplitude of the limit-cycle was investigated with and without the piezoelectric controller: in particular, in that paper we used one of the three controllers defined in [10], namely, the SNRC (Singular Nonresonant Controller), which remembers the Nonlinear Energy Sink (see, e.g., [12,13]) even if, differently from the NES, the coupling between the mechanical system and the controller is linear and of gyroscopic type.
The objective of this paper is to study the behavior of the nonlinear Ziegler column equipped with another one of the three controllers introduced in [10], which is called the SRC (Singular Resonant Controller), which resembles the working mechanism of the TMD, since it is resonant and possesses evanescent electric properties.This type of controller, therefore, can be also referred to as Tuned Piezoelectric Damper (TPD).It is important to remark that we include into the category of TPD only passive circuits, that is, circuits that cannot pump energy into the mechanical systems.Few examples of controllers having these characteristics can be found in [14,15] for collocated control and in [16][17][18][19][20][21][22][23][24] for distributed control; moreover, if the circuit parameters are well optimized, good damping results can be obtained even without resonant elements (see, e.g., [25]).
The paper is structured as follows.In Section 2, the discrete model of a piezoelectric controlled nonlinear Ziegler column is recalled.Section 3 is devoted to the presentation of the numerical results.Finally, in Section 4 some conclusions and a summary of the main results are exposed.
The Model
The system under study is a piezoelectric controlled upward double-pendulum, shown in Figure 1.The equations of motion for this system are derived in [11] for finite rotations and will be here briefly recalled.The system consists of a two hinged weightless rigid bars of equal length ℓ, carrying two concentrated masses, 1 := 2 at the common hinge (point in the figure) and 2 := at the tip (point in the figure).The bars are viscoelastically constrained at the hinges by (a) linear springs of stiffness 1 := and 2 := and (b) linear dashpots having viscosity coefficients 1 and 2 , respectively.The system is loaded at the free end by a follower force of intensity , which keeps its direction parallel to the upper bar.Moreover, the pendulum is equipped with a piezoelectric device of stiffness (here considered negligible with respect to the stiffness of the springs), capacitance , and coupling coefficient , which is placed at the ground hinge, and it is connected to a one-node LR resonant circuit, of inductance and resistance (sketched in Figure 1), and to the ground.When considering infinitesimal rotations of the two bars, the system reduces (except for the masses values adopted here) to that analyzed in [10]; moreover, when the controller is removed, the system degenerates into the well-known Ziegler column [26].
The state of the system is described by taking as Lagrangian coordinates the rotations of the two bars, 1 () and 2 (), and the flux linkage () associated with the piezoelectric actuator.We recall here that the flux linkage is defined as the time integral of the voltage ; that is, = ∫ .
The equations of motion for the coupled system are obtained by following these steps: (1) The internal dissipation (due to damping) and nonconservative action (due to the follower force) are neglected, so that we can describe the system in terms of its Lagrangian, which is the sum of three components: (a) the mechanical Lagrangian , concerning the structure without any control devices, (b) the electrical Lagrangian , relevant to the electrical circuit, and (c) the piezoelectric Lagrangian , referred to as the piezoelectric device.
(2) The internal dissipation and the nonconservative action are accounted for through the Extended Hamilton Principle.
For more details about this process, the reader can refer to [10,11].The obtained nondimensional system of equations has the following form: where the superposed dot denotes a time derivative and where we introduced the following quantities (accounting for 1 = 2, 2 = , and 1 = 2 = ) for nondimensionalization: in which 0 and 0 are scaling capacitance and flux linkage, respectively.Here, 0 < ∈ R is the load parameter (taken as bifurcation parameter); 0 < ∈ R is the electromechanical coupling parameter; ] , , and (all positive and reals) are electrical parameters, here referred to as the "electrical mass," "electrical damping," and "electrical stiffness," respectively.
Numerical Results
Numerical results, relevant to the uncontrolled and controlled Ziegler column, in both linear and nonlinear regimes are discussed in this section.It should be remarked that all the bifurcation diagrams discussed in the following have been obtained via a numerical continuation procedure, which has been directly applied to system (1), in order to compute the amplitudes of the limit-cycles occurring in the postcritical regime.
3.1.Uncontrolled Column.This section is devoted to briefly resume the critical and postcritical behavior of the uncontrolled Ziegler column with the aim of preparing the discussion on the effects of the controller, given in the next section.
The linear stability domain of the uncontrolled column, that is, when = 0, can be exactly determined by making use of the Routh-Hurwitz criterion on the (complete degree-4) characteristic equation of the algebraic eigenvalue problem associated with the linearized equations (1) (see, e.g., [27]).The criterion leads to the finding of a critical locus in the (, 1 , 2 )-space, known in the literature as the "Whitney's umbrella" surface [28,29], whose equation reads as follows: where := 7/2 − √ 2 ≃ 2.09 is the critical load of the undamped system at which a circulatory Hopf bifurcation occurs.
The linear bifurcation diagram of the uncontrolled Ziegler column is displayed in Figure 2. In particular, Figure 2(a) shows the critical surface, given by (3), in the 3D domain (, 1 , 2 ); it separates the stable states (the region marked with in the figure) from the unstable ones (the region marked with in the figure).The points on the surface represent the Hopf bifurcation states, that is, except for those on the -axis that, indeed, are regarded as marginally stable (undamped) systems for which a circulatory Hopf bifurcation occurs at = (see, e.g., [30]).In Figure 2(b), the contour lines = const are displayed: it is apparent that the effect of damping is mostly detrimental in the whole ( 1 , 2 )-plane, since, except for a small region (filled in gray in the figure) close to an "optimal direction" (dashed line in the figure), the critical load of the damped system is lower with respect to .Moreover, it can be shown that on the left side of the optimal direction the stability is governed by the first mode, while on the right side it is governed by the second one.
The postcritical behavior of the uncontrolled Ziegler column is now discussed.In particular, we will refer to two systems, marked with a black dot and a label I or II in Figure 2(b), respectively, far and close enough to the critical load of the circulatory system, namely, (i) case study I: 1 = 0.05 and 2 = 0.2, entailing ≃ 0.80, for which damping has a strong destabilizing effect (−62%); (ii) case study II: 1 = 0.3 and 2 = 0.15, entailing ≃ 1.81, for which damping has a moderate destabilizing effect (−13%).
In Figures 3 and 4 large amplitudes limit-cycles manifest themselves.This is the consequence of the destabilizing effect of damping yet discussed with regard to the linear behavior of the column, which persists also in the postcritical regime.As a matter of fact, when the increment of the load with respect to the critical value, := − , is equal, for example, to = 0.3, we found max | 1 | ≃ 1.03 rad, max | 2 | ≃ 1.62 rad in case I and max | 1 | ≃ 0.52 rad, max | 2 | ≃ 1.13 rad.Therefore, the higher the destabilizing effect of damping on linear stability, the higher the amplitude of the limit-cycle (for the same increment of load with respect the critical one).
Controlled Column.
In this section, we analyze the behavior of the Ziegler column equipped with the SRC (Singular Resonant Controller) issued from the paper [10].As it was proved there through a perturbation technique, the energy flow between mechanical and electrical subsystems is driven, in this controller, by the resonance (Den Hartog principle [31]) and magnified by the singularity of the evanescent electrical characteristics.Thus, according to this control strategy we need to have = O(), ] = O(), = O( 3/2 ), and = O(), being a small parameter; moreover, in order to render the electrical oscillator resonant to the mechanical one, the tuning /] = 2 , where is one of the two column's frequencies at = , must be performed.It is important to remark that such a controller resembles the wellknown Tuned Mass Damper [4][5][6][7][8] even if the coupling is here linear and is of gyroscopic type; thus, the controller discussed in the present paper can be regarded as a Tuned Piezoelectric Damper (TPD).
According to this strategy, the following electrical parameters have been fixed: ] = 0.1 and = 0.03; moreover, has been chosen in order to tune the electrical frequency to the first mechanical one since, in both case studies, the first mode is the candidate to become unstable, namely, = 0.02 ( ≃ 0.447) for case study I and = 0.0375 ( ≃ 0.612) for case study II.The coupling parameter has been considered variable, with the aim of estimating the sensitivity of the controller's performances with respect to an increase of the electromechanical coupling and, in particular, it has been fixed to = 0.05 or = 0.1.
Concerning the linear stability of the controlled system, the effects of the controller on the critical load can be evaluated in Figures 5 and 6 where the bifurcation diagrams of the controlled (black curves) and uncontrolled (gray curves) Ziegler column, for cases I and II, respectively, are represented.It is apparent that, in both case studies, the controller is able to shift forward the uncontrolled bifurcation diagrams, thus entailing an increase of the stability region; in particular, we found the following in the two cases: (I) ≃ 1.23 (+54%), when = 0.05, and ≃ 1.58 (+98%), when = 0.1; (II) ≃ 1.90 (+5%), when = 0.05, and ≃ 1.98 (+9%), when = 0.1.Therefore, the controller is much more efficient in case study I where, remarkably, the damping has a strong destabilizing effect.
It is important to remark that, as a result of the shift, the controller reduces the amplitude of the limit-cycle occurring at the same level of load.This effect is displayed in Figure 7 where, for case study I, when = 1.7, and for the two considered values of , the time histories, relevant to uncontrolled (light gray curves in the figure) and controlled (dark gray curves in the figure) systems, show the benefits of the control.Finally, the flattening of the curves can be seen in Figure 8 where numerical integrations relevant to the uncontrolled system (first column in the figure) and the controlled system (second column in the figure), obtained for two different values of , at the same distance from the respective critical loads, are displayed, for case study I, when = 0.3 and = 0.1.In Figures 8(a), 8(b), and 8(c) the projections of the trajectories onto phase planes are plotted, showing the contraction of the amplitude of the limit-cycle.
Conclusions
In this paper, the effects of a TPD controller on the critical and postcritical behavior of the Ziegler column have been addressed.
The nonlinear equations of motion, for the coupled Piezo-Electro-Mechanical (PEM) system, have been recalled.The adopted control strategy first introduced in [10] is the SRC, namely, the Singular Resonant Controller, and its effects on the nonlinear dynamics of the system have been deeply investigated.
The main results can be summarized in the following points: (i) The analysis of the postcritical scenario shows that the controller is able to shift forward the bifurcation diagrams of the uncontrolled system.
(ii) The controller induces a contraction of the limit-cycle amplitudes.
(iii) Both previous effects are much more evident when increasing the value of the electromechanical coupling.
The obtained results are satisfying and show that the proposed control strategy has a beneficial effect on the stability of the system.Nevertheless, to evaluate the real performances of this controller, a further optimization of the parameters is required.This will be the object of forthcoming papers.
Figure 7 :
Figure 7: Time histories 1 and 2 for the case study I, when = 1.7, for the uncontrolled (light gray curves) and the controlled (dark gray curves) systems when (a) = 0.05 and (b) = 0.1.
Figure 8 :
Figure 8: Numerical phase portraits for the case study I, when = 0.1 and = 0.3, for the uncontrolled (first column, ≃ 1.105) and the controlled (second column, ≃ 1.88) systems. | 3,619 | 2015-09-10T00:00:00.000 | [
"Engineering",
"Physics"
] |
Unsteady Radiative Natural Convective MHD Nanofluid Flow Past a Porous Moving Vertical Plate with Heat Source/Sink
In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO2) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and TiO2-based nanofluids is graphed.
Introduction
In recent times, nanotechnology is promptly influencing scientists and researchers for its significant role in industrial sciences. For instance, in the pharmaceutical field, patients of cancer are treated via nanoliquids based operators, comprises of different radiations and medicines. Some cooling and heating processes like minimizing receivable heat from computer processors, controlling the temperature of nuclear reactors, calming down the radiators in vehicles and handling of thermal flows in heat valves involve the nanoliquids. These key features, along with several industrial and domestic applications, nanofluids have fascinated investigators and scientists in modern days. Nanofluids immersed in regular fluids have a tendency to elevate their thermal performance.
A nanofluid consists of particles with a size scale in nanometers, named nanoparticles. This idea was initiated by Choi [1], when he dropped nano-sized solid particles in a base fluid, and called the new fluid a nanofluid. The formation of nanoparticles involves metals, carbides and carbon nanotubes. Nanoparticles have significant industrial applications such as sunscreens of vehicles are more resistive to radiations, bumpers of cars have lighter weight, synthetic bones are stronger, more stain repellent clothing and enhanced durability of balls for several sports. Extensively, in the age of nanotechnology, where every object is reducing in size and their features are enhancing, nano-catalysts have effective utility in various processes such as composite solid rocket propellants, purification of water, production of bio diesel, delivery of drugs and manufacturing of carbon nanotubes [2]. A nanofluid has a higher thermal conductivity in contrast to a regular fluid, because of additional thermal conductivity of combined nanoparticles, but certainly, it has relatively different structure as compared to regular fluid due to different sizes and shapes of nanoparticles [3]. Masuda et al. [4] presented that it is a characteristic of nanoparticles to elevate the thermal conductivity of fluids. It was found that the dispersion of carbon nanotubes in oil can enhance its thermal conductivity up to 50% [5]. Currently, the mangneto-nanofluids have become very significant due to the presence of favorable features regarding energy processes, materials engineering and medical operations. Many processes take place at very high temperature and preparation of equipment demands a deep knowledge of heat transfer. Satellites, space aircrafts, missiles, turbines and nuclear plants lie in the category of those processes. This fact draws the attention of many researchers to find such suitable combinations that have a maximum heat transfer rate. From the vast and different ranges of base fluid and nanoparticles, this work comprises of Copper (Cu) and Titanium oxide (TiO 2 ) as nanoparticles and water as base fluid to find out the difference of heat enhancement and transfer rates.
The study of flows under the influence of many factors like magneto-hydrodynamics and thermal radiation is of deep concern due to its role in industries, physics, nuclear plants and chemical reactions. Das [6] provided a detailed analysis of natural convective flow along radiation effects for magneto-nanofluid. Das [7] investigated the motion and thermal behavior of nanofluids in a rotating frame. Ellahi et al. examined the importance of activation energy and chemical reaction for nanofluid peristaltic blood flow [8]. Theoretical aspects of unsteady magneto-hydrodynamics free convection flow were analyzed for some nanofluids by Hussanan et al. [9]. Ullah et al. [10] studied unsteady thin-film motion of nanofluid together with entropy generation. Wakif et al. [11] numerically analyzed the contribution of thermal radiation in time-dependent magneto-hydrodynamic (MHD) free convection couette flow of Cu-water with the help of single and two-phase models. Atif et al. [12] conducted a study to observe the impacts of Joule heating, viscous dissipation, internal heating and thermal radiation on MHD micro-polar Carreau nanofluid. Effects of the slip condition and magnetic field on natural convection in a vertical channel with water/alumina nanofluid were investigated by Malvandi et al. [13]. Mostafazadeh et al. [14] examined the influence of radiation on free convective laminar flow of nanofluid in a vertical enclosure employing single and two-phase models.
Another significant factor for fluid flow is heat generation/absorption. It has essential applications in the field of food industry, thermal engineering, mechanical engineering and physics like processes named as heat treatment, ventilation, and air conditioning. Food processing operations also involve cooling and heating processes [15]. Soomro et al. [16] investigated the heat generation/absorption and radiation effects on stagnation point flow of nanofluids. Heat generation/absorption effects on MHD free convection flow of a nanofluid were studied by Chamkha [17]. A detailed study covering the ion-slip and hall effect influence on CNTs along with heat control for porous surface was conducted by Ameen et al. [18]. Alzahrani et al. provided an in-depth analysis of heat consumption/generation of a Darcy flow for a rotating frame [19]. Hayat et al. investigated the flow and heat transfer behaviors for nanofluids in a rotating frame [20]. Performance of an Oldroyd-B fluid under the influence of thermal stratification and heat absorption/generation for mixed convection flow was examined by Hayat et al. [21]. Ebrahimi et al. [22] provided details of entropy generation and heat transfer in a micro-channel incorporating nanofluids. The influence of damped heat flux on natural convection flow of nanofluid past infinite vertical plate was studied by Nisa et al. [23].
In modern days, cavities filled with porous medium and fluid together are attracting the researchers and scientists. This kind of cavities has wide environmental and industrial utilities named nuclear fuel cooling, solidification, solar collectors, thermal insulation and so many others. These cavities can be divided either vertically [24][25][26] or horizontally [27][28][29]. A porous material means a medium whose structure has pores [30]. Umavathi [31] analyzed the characteristics of flow and heat transfer of composite porous medium saturated in nanofluid. Amhalhel et al. discussed the problems related to modeling of flow and heat transfer in porous medium [32]. Boundary layer flow of a permeable surface immersed in a porous medium regarding nanofluid was examined by Umar et al. [33]. Raju et al. [34] studied MHD flow of nanofluid over moving vertical plate in porous material under Soret and radiation impacts. AbdEl-Gaied et al. [35] reported the effect of a permeable moving flat plate on forced MHD laminar flow comprised of convective boundary conditions. Some other significant outcomes regarding thermal radiation and porous media were reported by [36][37][38][39][40].
The above literature review is the motivation behind the main emphasis of this article which is to examine the influence of porous material and heat sink on unsteady, MHD natural convection flow of nanofluid past a moving infinite vertical plate. The fluid motion occurs due to the impulsive movement of the plate and it is considered that flow is laminar. Water is considered as a base fluid and it contains two types of nanoparticles named Copper (Cu) and Titanium oxide (TiO 2 ). The nonlinear function of thermal radiation is linearized with the aid of Taylor series and the closed-form solutions of modeled partial differential equations are derived by means of Laplace transformation. Furthermore, the influence of various pertinent parameters is illustrated through graphs.
Statement of Problem
Suppose the natural convection based unsteady flow and shifting of heat for water-based nanofluid past a vertically infinite plate immersed in a porous material. Initially, the plate is static at t * = 0 with temperature T * ∞ . Later on, the plate starts an instinctive motion with velocity λU 0 in its own plane at t * > 0. Consequently, the temperature of the plate is enhanced or reduced to T * w . The considered geometry in the Cartesian plane is described as that y-axis is along the flow direction and x-axis is considered parallel to the plate. Moreover, the plate is saturated in a porous medium and it is assumed to be at y * = 0 and flow is restricted to y * > 0. As the vertical plate chosen in this work is infinitely long, temperature and velocity equations only depend on t and y. A uniform magnetic field of magnitude B 0 is acting along y-axis. The resulting magnetic field due to the flow of fluid along with the pressure gradient is neglected in contrast to the imposed magnetic field so that we consider the magnetic field as B = (0, 0, B 0 ). This supposition is valid, since the magnetic Reynolds number is small enough for partially ionized fluids and metallic liquids [41] . Furthermore, to neglect the polarization effect of fluid, no external electric field is acting. It is assumed that in mass equation density is a linear function of thermal buoyancy forces. This assumption is sufficient for dropping both liquid and gases when temperature difference has small values. A radiative heat flux q r is also taken into account and it is considered that this heat flux in the x-direction is negligible against radiative heat flux in y-direction. A combination of base fluid water and nanoparticles named Copper (Cu) and Titanium Oxide (TiO 2 ) is chosen and additionally, thermal equilibrium is assumed between these particles and base fluid water. It is also assumed that nanoparticles have a uniform size and shape. Lastly, a heat sink is also added to the considered system. The geometrical interpretation is provided in Figure 1. In presence of all above assumptions, natural convection flow past a moving vertical plate embedded in porous medium incorporating heat sink, thermal radiation and magnetic field is presented by the given equations [42] where u * is the velocity of fluid along the x-direction, T * is the temperature of fluid during flow, µ n f is the dynamic viscosity, β n f is the thermal expansion coefficient, ρ n f is the density, σ n f is the electrical conductivity, k n f is the thermal conductivity, g is gravitational acceleration, q r is the radiative heat flux, (ρc p ) n f is the heat capacitance and the term Q 0 with negative sign shows that a heat sink is added to system under observation. The physical quantities µ n f , ρ n f , (ρc p ) n f and (ρβ) n f are deduced by manipulating the expressions provided by [43] where φ is solid volume fraction of nanoparticle, ρ f is the density of base fluid, ρ s is the density of nanoparticle, σ f is the electrical conductivity of base fluid, µ f is the dynamic viscosity of base fluid, (ρc p ) f is the heat capacitance of base fluid, (ρc p ) s is the heat capacitance of nanoparticle. To deal the thermal conductivity of nanofluid, model given by Hamilton and Crosser, followed by Kakac [44] and Oztop [45] is utilized as where k s and k f represent the thermal conductivity of nanoparticle and base fluid respectively.
The associated initial and boundary conditions of considered problem are presented as: where λ = 0 shows the static plate and λ = ±1 represents the forth and back movement of the plate. The radiation heat flux, after using Rosseland approximation comes out to be [46] where the Stafan-Boltzman constant and adsorption coefficient are represented by σ * and k 1 , respectively. The term q r can be linearized by expansion of T * 4 using Taylor series about T * ∞ , keeping the supposition in mind that temperature differences are small enough to neglect the higher-order terms. After normalizing, T * 4 comes out to be T * 4 ≈ 4T * 3 ∞ T * − 3T * 4 ∞ . On using this linearization in Equation (2) The non-dimensional quantities are introduced as: On using above non-dimensional quantities, Equations (1) and (7) turn out to be as follows where and non-dimensional parameters are defined as Here, the Grashof number is denoted by Gr, the radiation parameter is denoted by Nr, the magnetic parameter is denoted by M 2 , the Prandtle number is denoted by Pr, the parameter of permeability is denoted by K and lastly Q is the heat sink parameter.
The associated initial and boundary conditions takes the following form after the introduction of dimensionless parameters:
Analytical Solution of Problem
To generate the solution of this problem, Laplace transform [47] is convenient tool because of non uniform boundary conditions. The other convenient methods like Adomian decomposition, homotopy analysis method, perturbation method and separation of variables do not serve the purpose here due to boundary conditions. we formulate the Laplace transform pair for the sake of results of current problem as an integral of the following form where R ∈ {u, θ}. The above integral is convergent for Re(s) > γ 0 , and s = Ψ + jΩ, γ o is some positive real number and j = √ −1.
On using Laplace transform, Equations (9) and (10) obtain the following form The initial and boundary conditions in Laplace domain are gives as: u(y, s) → 0,θ(y, s) → 0, for y → ∞, The solution of Equations (18) and (19) according to Conditions (20)- (22) are evaluated as where The implementation of inverse Laplace transform provides the following relation for velocity and temperature in real time domain with where the complementary error function is defined as The Nusselt number is given as follows: where error function is defined as
Numerical Case Studies
To deeply understand the physics of the current problem, a parametric study is conducted and obtained outcomes are delineated with the help of graphs. The physical features of dimensionless fluid temperature and velocity as a result of variation in most significant substantial factors like Grashof number (Gr), magnetic parameter (M 2 ), porosity parameter (K), radiation parameter (Nr), heat sink parameter (Q) and solid volume fraction of nanoparticles (φ) are presented in Figures 2-16. The values of the volume fraction of nanoparticles belongs to the interval [0, 0.2]. The case λ = 1 corresponds to the upward motion of vertical plate, λ = −1 corresponds to the downward motion of the vertical plate and λ = 0 for static plate. Moreover, Q = 0, Nr = 0 and φ = 0 corresponds to the absence of heat sink parameter, radiation parameter and nanoparticles respectively. Figure 2 presents the velocity profile of both nanofluids Cu-water and TiO 2 -water with the same volume fraction of both nanoparticles. It is revealed that Cu-water has a thinner boundary layer which results due to an increase in its dynamic viscosity because of the relatively higher density of Cu. From Figure 3, an exact agreement between velocity solution of current work and Das [6] can be observed for Q = 0 and 1 K → 0. This agreement verifies the velocity solution for our current work. Figure 4 interprets the variation of velocity profile for various values of Gr. In the physical sense, Gr deals with the fraction of thermal buoyancy force to viscous force. Increase in Gr implies that buoyancy force together with the aid of allied forces is getting stronger and eventually it is suppressing the viscous forces. This factor justifies the decrease in resistance and ultimately fluid gets accelerated. A similar kind of behavior is witnessed for both λ = 0 and λ = ±1 as well. Furthermore, On free stream surface, away from the plate buoyancy force weakens and fluid attains the zero velocity. Physical justification of this fact is that increment in K, decreases the resistance offered by a porous medium which in turn enhances the momentum development of the regime and consequently, the velocity of the fluid is increased. Enhancement in fluid velocity is spotted for both stationary (λ = 0) and moving vertical plate (λ = ±1). Figure 6 depicts the variation in velocity, when the strength of the imposed magnetic field is increased (i.e., M 2 increases). It is witnessed that dimensionless velocity has higher values when M 2 increases, for static plate (λ = 0) and moving plate (λ = ±1) as well. This enhancement in momentum boundary layer thickness is certified by the physical fact that when the magnetic force lines past the vertical plate, they give a sudden push to decelerated fluid and as a result fluid overcomes the viscous forces. Consequently, the velocity of the fluid faces a rise when the value of M 2 increases. This sudden push is featured by instinctive peaks immediately near the plate and as the fluid moves away from the plate, it calms and these peaks slowly decrease. Figure 7. It is noticed that for both static plates (λ = 0) and moving plate (λ = ±1), thermal radiation is a cause of enhancement in fluid velocity as an increase in values of Nr is resulting in elevation of velocity profiles. The physical justification of this increment is the higher rate of energy transport to the fluid. This higher rate results in a reduction of viscous force because the bonds between fluid components get weaker due to the higher energy transport rate. Finally, fluid gets accelerated. Figure 8 covers the effect of solid volume fraction on dimensionless velocity of fluid. It is noticed that fluid flow gets accelerated following an increase in the volume fraction. It is also observed that momentum boundary layer thickness enhances with an increase in φ for static (λ = 0) and moving (λ = ±1) plate. This is due to the factor that increases in φ, weakens the viscous forces which leads to a raise in the velocity profile of the fluid. Moreover, Figure 9 demonstrates that for static plate (λ = 0) case and moving plate (λ = ±1) case, the velocity of the fluid increases with an increase in time t. This behavior also explains the transient nature of flow. In Figure 10, the thermal profile of two types of nanofluids Cu-water and TiO 2 -water are plotted. It is witnessed that the temperature of Cu-water is slightly higher than TiO 2 -water. This difference is supported by the fact that Cu nanoparticles have relatively higher thermal conductivity against TiO 2 nanoparticles, therefore suspension of Cu in base fluid water enhances the thermal conductivity of Cu-water and eventually temperature of nanofluid rises. It is also observed that the thermal boundary layer thickness is greater in the case of Cu-water. The thermal conductivity of the fluid augmented with Nanoparticle's addition. These Nanofluids can be considered heat transmission fluids in heat transfer applications. From these temperature profiles, it is anticipated that Cu-water and TiO 2 -water can be used as alternatives in heat exchange processes, under specific conditions. Combination of thermal conductivity and other desirable features such as corrosion resistance and creep rupture strength enable copper to be specified for heat exchangers in industrial field, however, it is expensive and precious when it comes to locating it. Figure 11 demonstrates the behavior of dimensionless temperature for increasing values of Nr. An expected behavior is noticed as the radiation parameter Nr defines the relative contribution of conduction heat transfer to thermal radiation transfer. Hence, it is clear that the temperature will be increased by enhancing the thermal radiation parameter. Physically, k 1 faces a decay because of elevation in divergence of radiative heat flux ∂q r ∂y . This results in an enhancement in the amount of radiative heat transfer to the fluid, and consequently, the temperature of the fluid rises. Effect of variation in values of Pr on dimensionless temperature is revealed in Figure 12. It is spotted that nanofluid temperature faces a decay corresponding to increment in Pr. The physical verification of this decay is that fluid with high Pr value has relatively lower thermal conductivity, which, decreases the amount of heat transfer and as a result, temperature reduces. Furthermore, the thickness of the thermal boundary layer decreases. Figure 13 incorporates the influence of heat sink parameter (Q) on the temperature of nanofluid. As expected, an increase in Q results in a decrease of temperature. This is because of the fact that the increase in Q corresponds to more amount of consumed heat which certainly implies that temperature is decreasing function of Q. It can be remarked that heat transfer can be controlled very effectively by including some heat sink in the system. Figure 14 exhibits the impact of solid volume fraction (φ) on thermal profile. Enlargement in φ implies enhancement in temperature. It is seen that the temperature of pure water (φ = 0) is less than the temperature of Cu-water. Moreover, the suspension of nanoparticles in some regular fluid boosts the thermal conductivity of fluid under observation. This physical phenomenon justifies the appreciation in nanofluid's thermal conductivity corresponding to increasing values of φ. Hence, the temperature of fluid increases. It also reveals the meaningful influence of nanofluids in engineering as the processes involving heating and cooling face changes in mass and thermal behaviors due to change in volume fraction of nanoparticles. Figure 15 describes that temperature enhances as the time increases. Physically, plate with relatively higher temperature is exposed to fluid for longer duration, therefore fluid absorbs more amount of heat which leads to enhance the velocity of fluid. Hence, the average kinetic energy of fluid increases and consequently, the temperature of fluid rises. This phenomenon explains the transient effect on heat transfer. Heat transfer augmentation in the attendance of nanoparticles in the base fluid is observed. The convective heat transmission of nanoparticles is dependent on coolant and fluid flow rate. The temperature profile also depicts that near the wall, the temperature is high but it goes to zero gradually as fluid moves far away from the wall. For the validity of the temperature solution of the current problem, a comparative analysis is conducted with [6] in Figure 16. It is clearly observed that both the solutions are in good agreement when the heat sink is removed from the system (Q = 0). Figure 17 reveals that enlargement in Nr values results in the enhancement of the heat transfer rate. This can be justified as the temperature gradient has strong dominance when thermal radiation Nr has higher values. This dominance of temperature gradient increases the rate of heat transfer. Moreover, it is witnessed that with addition in value of φ along the x-axis, the heat transfer rate slightly increases. This behavior is supported by the fact that the maximization of solid volume fraction φ enhances thermal conductivity and decreases thermal boundary layer thickness. As a result, the greater value of nanoparticle's volume fraction leads to elevate the rate of heat transfer. The negative sign of the rate of heat transfer shows that the plate is at the receiving end in the process of heat transfer. The reason is that heat is generated near the plate and temperature of fluid may overcome the temperature of the plate. This results in the transfer of heat from fluid to plate.
Velocity distribution for various values of Nr is drawn in
The control of Pr on the heat transfer rate is graphed in Figure 18. It is noted that heat transfer rate is low for higher Pr values due to the fact that fluid with high Pr values have relatively smaller thermal conductivity, therefore conduction of heat for such fluids is low. This reason concludes that the transfer of heat is low for fluids with greater Pr values. Figure 19 illustrates the heat transfer rate for several values of Q. It is found that the heat transfer rate decreases as the value of Q rises. This behavior is obvious since the heat sink added to the system will absorb the heat, therefore the amount of heat transfer from fluid to plate will be lower. At the end, variation in heat transfer rate regarding different nanofluids are witnessed in Figure 20. It is shown that the rate of heat transfer for Cu-water is higher than that of TiO 2 -water. The fundamental reason behind this comparatively greater rate of heat transfer is the higher thermal conductivity of Cu. The addition of Cu in some base fluid such as water in the current work enhances the thermal conductivity of that fluid, which leads to a greater rate of heat transfer. Table 1 encloses all the values used in plotting and graphing. Table 1. Thermophysical properties of nanoparticles and water [45].
Conclusions
The aim behind this study is to calculate the exact solutions of time-dependent free convection MHD flow of some nanofluids close to a moving vertical plate, saturated in porous medium incorporating radiative heat flux and heat sink. The non-linear thermal radiation term is linearized by Rosseland approximation. The fundamental partial differential equations along with suitable initial and boundary conditions are made dimensionless first and later Laplace transformation is employed to convert them in ordinary differential equations and solutions are derived in closed form. The meaningful physical contribution of associated parameters in momentum and energy profiles is interpreted with the help of graphs. The expression for Nusselt number is also evaluated to observe the influence of pertinent factors on the process of heat transfer.
The significant results of this study are • For both nanofluids, the increase in the porosity parameter, magnetic parameter and Grashof number leads to an increase in the velocity of the fluid.
• Temperature of both nanofluids gets elevation with an increase in radiation parameter, while an opposite behavior is noted for increasing values of heat sink parameter.
•
Cu-water has greater momentum boundary layer thickness than TiO 2 -water nanofluid.
•
Rate of heat transfer increases as the radiation parameter increases, while the increase in values of heat sink parameter reduces the rate of heat transfer. • TiO 2 -water has a lower rate of heat transfer at the wall in contrast to Cu-water.
Author Contributions: Conceptualization, T.A., Z.S. and P.K.; methodology, T.A. and P.T.; software, T.A. and W.W.; validation, P.K. and P.T.; formal analysis, T.A., Z.S. and W.W.; investigation, P.K., W.W. and P.T.; resources, P.K. and W.W.; writing-original draft preparation, T.A. and Z.S.; writing-review and editing, T.A., P.K. and Z.S.; visualization, P.K. and W.W.; supervision, P.K. and W.W. All authors have read and agreed to the published version of the manuscript. We are obliged to the respectable referees for their important and fruitful comments to enhance the quality of current article.
Conflicts of Interest:
The authors declare no conflict of interest. | 6,375.6 | 2020-02-01T00:00:00.000 | [
"Engineering",
"Materials Science",
"Physics",
"Environmental Science"
] |
Lidar research activities in Potenza, Southern Italy
The lidar group in Potenza has almost 10 years’ experience in the fi eld of lidar research. Important results have been accomplished both in aerosol and water vapour research. The lidar system in Potenza has acquired different confi gurations during the years, always preserving the capability to accomplish two wavelength aerosol and water vapour Raman measurements. An important up-grade was the introduction of a water vapour DIAL channel in 1997. The lidar system in Potenza has been involved in several aerosol and water vapour measurement campaigns: stratospheric aerosol measurement campaign (1994-1995); LITE correlative measurement campaign (September 1994); Water Vapour Intensive Observation Period (January-February 1997); EARLINET project (since February 2000). A second lidar system, primarily dedicated to water vapour Raman measurements, is under development and starting January 2002 will go through an intensive observation period dedicated to the validation of sensors on-board ENVISAT (principally GOMOS, MIPAS and SCIAMACHY). This paper summarises some of the major results accomplished, as well as expected results from the forthcoming campaigns. Mailing address: Dr. Paolo Di Girolamo, Dipartimento di Ingegneria e Fisica dell’Ambiente (DIFA), Università della Basilicata, C.da Macchia Romana, 85100 Potenza, Italy; e-mail<EMAIL_ADDRESS>
Introduction
Atmospheric water vapour and aerosols play a crucial role in the Earth climate, being a key element in the global radiation budget, in atmospheric circulation, as well as in the microphysical processes leading to cloud formation and development.The role of atmospheric water vapour and aerosols in the climate system is only partially understood at present, as a result of their highly variable time and space distribution on the global scale.Global coverage measurements of aerosol and water vapour with high accuracy, and high spatial and temporal resolution are needed throughout the troposphere up to the lower stratosphere.
In spite of the recent improvements in their performances, passive remote sensors from space provide global coverage of aerosol and H 2 O distribution with accuracy and a vertical resolution still insuffi cient for climate studies, primarily in the middle and upper troposphere.
The lidar system based both on the Raman and DIAL techniques can provide accurate measurements of atmospheric water vapour, as well as aerosols, with high space and time resolution.Ground-based and airborne lidar systems operational spread around the globe, as well as the Shuttle-based experiment LITE, have demonstrated the technological maturity of the lidar technique for operational space-borne application.
In this paper we review the major results accomplished by one of these systems, namely the lidar system in Potenza.We intend to illustrate the performed measurement campaigns in terms of aerosol and water vapour measurements.The EARLINET project, mentioned in the abstract, is not included in the present work since a specifi c paper within this special issue is devoted to this effort.
The aerosol /water vapour system
The lidar system in Potenza is located within the scientifi c laboratories of IMAA (40°50' N, 14°10' E, 820 m a.s.l.) and was developed in co-operation with the Physics Department of the «Federico II» University of Naples.The system has been operated throughout the years by personnel from Instituto di Metodologie per l'Analisi Ambientale (IMAA) -Consiglio Nazionale delle Ricerche and University of Basilicata.It started to take measurements in July 1993.Figure 1 shows the block diagram of the system.The Potenza lidar system was originally developed around a Nd:YAG laser source, including second and third harmonic generation crystals (532 and 355 nm) and providing pulses at a repetition rate up to 20 Hz.More recently, a second laser source was added, namely a dye laser, tunable within a spectral region of major absorption for water vapour (690-730 nm) (Ambrico et al., 1997;Di Girolamo et al., 1999).The dye laser source is pumped by a portion of the 532 nm beam.
As the laser pulses propagate through the atmosphere, part of their energy is backscattered to the instrument by particles -typically aerosols or hydrometeors -and by the molecules of the gas species comprising the atmospheric mixture.Laser beams at 355 nm and 532 nm are used to monitor aerosol and clouds.The 355 nm laser beam is also used to stimulate vibrational Raman scattering by water vapour and nitrogen molecules, at 407.5 and 386.6 nm, respectively.
The dye laser is exploited for the application of the DIAL technique to water vapour monitoring.This laser source is able to transmit two laser beams at two different wavelengths (l on and l off), the fi rst one falling on a water vapour absorption line center and the second falling on the line shoulder.For the measurements illustrated in the present paper, l on is set to 723.59, while l off is 723.71 nm.
The receiver consists of a vertically pointing cassegrainian telescope (0.5 m diameter primary mirror, 5 m combined focal length).The presence of a series of dichroic mirrors split the collected radiation into four portions (355 nm, 386 nm, 407 nm, 532 nm).Interference fi lters or single/double grating monochromator are used as spectral selection devices.The introduction of a fused-silica beamsplitter transmits 50% of the collected radiation into the old section of the receiver, and deflects the remaining 50% into the DIAL channel.This particular partitioning is considered in order to obtain comparable performances for the Raman and DIAL techniques for the reported water vapour measurements.Detection is accomplished by means of photomultipliers.Detected signals are sampled by means of both analog-to-digital conversion and photon counting.
Water vapour DIAL measurements were supported by a photoacoustic apparatus, used to perform high-resolution measurements of the water vapour absorption spectrum and to check the dye laser tuning on the selected absorption line during the DIAL measurement.The photoacoustic experiment was developed around a vacuum cell equipped with fused silica windows; distilled water is contained in a small tanker inside the cell.Pressure variations inside the cell, resulting from water vapour absorption, are detected by a condenser microphone, whose signals are amplifi ed and processed by an analog integrator and acquired by means of a digital oscilloscope.
Cal/ val lidar system
A second lidar system, primarily dedicated to water vapour Raman measurements, is under development at IMAA.This system will mainly be used to validate ENVISAT data products.This system is based on a Nd:YAG laser equipped with third harmonic generation crystals (repetition rate up to 100 Hz).The third harmonic is transmitted into the atmosphere in a coaxial mode.The receiver is developed around a vertically pointing telescope in Cassegrain confi guration with a 0.5 m diameter primary mirror and a combined focal length of 5 m.The collected radiation is split into three channels by means of dichroic mirrors.Interferential fi lters are used to select the elastic backscattered radiation at 355 nm, the N2 Raman shifted signal at 386.6 nm and the water vapour Raman shifted signal at 407.5 nm.Each wavelength is then split into 2 different channels for both low and high range signals.Photomultiplier tubes are used as detectors.Low range signals are sampled in analog mode by means of a digital oscilloscope (500 MHz).High range signals are acquired in photon counting mode using a Multi Channel Scaler (MCS) board with a dwell time of 100 ns.Lidar measurements will be performed simultaneously with radiosonde launches to calibrate lidar measurements of water vapour.
Stratospheric aerosol measurement
campaign (1994)(1995) Lidar measurements of stratospheric aerosol were made in Potenza on a routine basis in the period 1994-1995(Di Girolamo et al., 1995, 1996).This measurement campaign is the continuation of the one started in Naples in September 1991.Measurements cover the history of the aerosol cloud produced by the eruption of Mount Pinatubo (June 1991, Philippines).The eruption of Mount Pinatubo in June 1991 determined a large increase in the stratospheric aerosol load on a global scale.This eruption is considered to be the most important of the century in terms of both volcanic material injected into the stratosphere and effects on the global climate (Zhao et al., 1995).Apart from the Pinatubo eruption, the period 1991-1995 was characterized by minor volcanic eruptions (Hudson, etc.) which produced negligible effects in the stratosphere on the global scale.This allowed aerosol sensors to observe the restoration of pre-volcanic constant background conditions and thus allowed to clearly distinguish and isolate the effects on a single eruption event.
Figure 2 shows the evolution with time of the stratospheric aerosol load.Data are expressed in terms of aerosol backscattering coeffi cient at 351 and 355 nm.A large increase in aerosol load is observed starting September 1991, but maximum load is observed in December 1991 and decay started immediately afterwards.Integrated Backscattering (IB) is obtained by integrating the aerosol backscattering coeffi cient throughout the stratosphere.IB (fi g. 3) reached its maximum value in December 1991, displaying a subsequent decay with an e-folding times of 237 ± 25 days.Figure 4 shows the evolution with time of the aerosol optical thickness tA.tA reached its maximum in December 1991, then decaying with an e-folding times of 250 ± 111 days.tA is obtained from the elastic signal assuming an aerosol-free region above an below the stratospheric aerosol layer (Di Girolamo et al., 1996).While an aerosol free region is always present above the stratospheric aerosol layer, cirrus and upper tropospheric clouds can sometime prevent from locating an aerosol-free region below the stratospheric layer.Therefore, the number of data points for tA in fig. 4 is smaller than the number of data points of IB in fi g. 3. Furthermore, the considered approach is particularly effi cient for values of tA in excess of 0.3.Thus, in the second half of the data record (period 750-1500 days after eruption), when values of tA are often smaller than 0.3, the number of data points in fi g. 4 with respect to fi g. 3 is further reduced.
Approximately 20 Mtons of SO2 were injected into the lower stratosphere within the fi rst few days after the eruption (Bluth et al., 1992), and by late July 1991 the resulting aerosol cloud was diffused on a global scale (McCormick and Veiga,1992).The presence of a massive long-lasting stratospheric aerosol layer leads to an in-crease in the planetary albedo, resulting in a lower energy fl ux at surface level, as well as in an absorption enhancement within the aerosol layer.The latter leads to a temperature increase in the lower stratosphere, together with an enhancement of diffuse sky radiation.Effects of stratospheric aerosols of volcanic origin on the global radiation budget are dependent on the amount, height and lifetime of the material injected (Pollack et al., 1976).Observed values of the aerosol optical thickness (fig.4) are consistent with a local increase in stratospheric temperature of 4-6 K.
Figure 5 shows the evolution with time of the aerosol layer center of mass height, together with theoretical descent curves for different particle sizes as obtained from Kasten (1968).Theoretical data account just for sedimentation of aerosol particles, while vertical eddy diffusion is not considered.The fi gure clearly shows that data in the period 400-1000 days following the eruption follow the 0.3 mm particle size curve, while data in the period 1000-1500 days after the eruption follow the 0.1 mm particle curve.
LITE correlative measurement campain (September 1994)
LITE (LIdar in space Technology Experiment), flying on the Space Shuttle in the period 10-19 September 1994, represented the fi rst attempt to perform global coverage lidar measurements from space (McCormick et al., 1993).The lidar system in Potenza was involved together with another 60 lidar ground stations in the validation of LITE measurements.Thus, in conjunction with the LITE mission an intensive lidar measurement campaign was carried out in Potenza.
Because of the relative distance between LITE ground tracks and the validation station for all passes, measurements carried out in Potenza were primarily aimed to the validation of LITE stratospheric measurements (Cuomo et al., 1997(Cuomo et al., ,1998;;Pappalardo et al., 1997).LITE accomplished 6 overpasses within 1500 km from Potenza.The minimum distance between LITE ground track and Potenza was 600 km. Figure 6a,b shows the comparison between simultaneous LITE and Potenza lidar measurements at both 355 (fi g. 6a) and 532 nm (fi g. 6b), in coincidence with Shuttle orbit 33.Data are expressed in terms of the aerosol backscattering ratio RA(z).Each LITE profi le is averaged over 300 laser shots, with a vertical resolution of 150 m, while each Potenza lidar profi le is averaged over 90 min, with a vertical resolution of 300 m.Data are reported with their error bars.
Assuming that data at different altitudes are uncorrelated for both Potenza lidar and LITE, it is possible to make a statistical analysis of the two data sets to quantify the degree of agreement between the LITE and Potenza lidar measurements.Potenza lidar measurements of RA,532(z) (R LITE (z) are reported together with their error bars.Also reported is the best fi t linear function.
Even if both R
Pz A,532(z) and R A ,532 LITE (z) are affected by a non negligible uncertainty, only the error on R Pz A, 532(z) was considered in the fi tting procedure.Fitting lines are presented in fi g. 7a-e.The correlation coeffi cient of the fi t, R, equal to 1 in case of perfect correlation, quantifi es the degree of correlation between LITE and Potenza lidar data.If data analysis is properly performed, values of the fi tting parameter c are expected to be equal to 0. The parameter m gets the signifi cance of a normalization coeffi cient to calibrate data: (z).The fi tting procedure was applied to data at both 532 (fi g. 7a-e) and 355 nm (fi g. 8a-e).Results can be summerized as follows.At 532 nm, values of R are in the range 0.88-0.93(average value of 0.90 ± 0.02).Such high values of R imply a very good correlation between LITE and Potenza lidar data in terms of RA,532(z).Values of m are in the range 0.96-1.08,with an average value of 1.02 ± 0.07.At 355 nm, values of R are in the range 0.72-0.81(average value of 0.77 ± 0.04) and values of m are in the range 0.79-1.19(average value of 0.92 ± 0.19).This latter result implies that LITE measurements at 355 nm are slightly underestimating Potenza lidar measurements.
Water vapour intensive observation period (January-February 1997)
Water vapour measurements in the troposphere up to approximately 10 km a.s.l.have been performed by means of a ground-based lidar system through the simultaneous application of the Raman and DIAL techniques.
Water vapour absorption lines were carefully selected to minimise DIAL measurement uncertainty.In particular, l on was selected to limit interferences by molecular species different from the investigated one, to minimise the temperature variability of the water vapour absorption line strength and to meet the requirements in terms of optimal optical depth (Ambrico et al., 2000).The dependence on temperature and pressure of the water vapour absorption cross-section, as well as laser line alteration due to water vapour absorption and the effects of the limited laser spectral purity, have been carefully accounted for in the estimate of the altitude variability of the effective absorption cross-section, with particular attention to boundary layer measurements.Selected values for l on and l off are 723.59 and 723.71 nm, respectively.
In early 1997 (20 January-20 February), an intensive observation period was devoted to the simultaneous application of the Raman and DIAL techniques for water vapour measurements.As an example of the performed measurements, fi g. 9 shows the Raman measurement of the nH 2 O(z) vertical profi le carried out on February 18, 1997 (22:20-00:20 GMT).The fi gure also shows the simultaneous humidity profi le measured by the DIAL technique (22:20-00:20 GMT) and by a radiosonde launched at 22:55 GMT.Measurements are expressed in terms of specifi c humidity (g/kg) and are reported with their error bars.Raman measurements extend up to approximately 9 km, while DIAL measurements display large error values above 7 km and have not been reported above this height.
The calibration coeffi cient for Raman data is obtained on the basis of an extended comparison between Raman measurements and simultaneous and co-located radiosonde measurements, the accuracy of Raman measurement being strictly related to the reliability of radiosonde humidity measurements used for the calibration.Since the DIAL technique is self-calibrating, water vapour density measurements can be performed in the troposphere by the DIAL technique with an uncertainty which is primarily limited by the DIAL signal statistical error.
Raman, DIAL and radiosonde measurements appear to be in good agreement up to approximately 8 km AGL, with a relative deviation which does not exceed 20% up to 7 km (fi g. 9).
In the same period, measurements were also performed to characterize the boundary layer structure (Di Girolamo et al., 1999).Aerosols and moisture tend to be trapped within the PBL and can be used as tracers for the study of the boundary layer vertical structure and time variability (Pappalardo et al., 2001).Figure 10 shows the comparison between simultaneous lidar and radiosonde data for 11 February; lidar data are expressed in terms of aerosol backscattering coeffi cient at 723 nm, while radiosonde data are expressed in terms of potential temperature and relative humidity.The potential temperature profi le appears to be anti-correlated with both the relative humidity and the aerosol backscattering, the aerosol layer top being associated with a maximum in potential temperature and a minimum in relative humidity.
Forthcoming measurements
The lidar system described in Section 2.2 will go through an intensive observation period (starting January 2002) dedicated to the validation of the sensors on-board ENVISAT, primarily AATSR, GOMOS, MIPAS, MERIS and SCIAMACHY.AATSR will provide, among others, measurements of cloud top height.The lidar system will be used to validate these measurements, primarily in the vertical interval 0.5-20 km.MIPAS will provide measurements of several atmospheric constituents in the height region 8-53 km.The lidar system will be used to validate MIPAS measurements of the water vapour profi le in the vertical region 8-10 km.Validation above this height (up to approximately 20 km) will be provided by radiosondes.GOMOS measurements of stratospheric aerosol will be validated by lidar system up to approximately 20 km.The system will also be used to validate MERIS and SCIAMACHY measurements of aerosol optical thickness.SCIAMACHY will also provide, among others, measurements of precipitable water to be validated by lidar.The stratospheric aerosol profi le and cloud top height can be retrieved from SCIAMACHY limb measurements and such measurements can be validated by the lidar system.A complete list of validated and validating sensors is given in table I. Calibration and validation measurements (cal/val) will be carried out on a routine basis for the fi rst 6 months after the launch, but will continue afterwards with a reduced schedule for all the duration of the mission.
Fig. 2 .
Fig. 2. Vertical profi les of the aerosol backscattering coeffi cient at 351 and 355 nm for 61 selected nights of measurements in the period September 1991 -June 1995.Data are expressed in units of 10 -6 m -1 sr -1 .
Fig. 3 .
Fig. 3. Time evolution of integrated backscattering IB for the period 1991-1995.Also reported is the exponentially decreasing function fi tted to the data.
Fig. 4 .
Fig. 4. Time evolution of the aerosol optical thickness tA for the period 1991-1995.Also reported is the exponentially decreasing function fi tted to the data.
Fig. 5 .
Fig. 5. Time evolution of zc for the period 1991-1995.Also reported are the theoretical descent curves for 1 mm, 0.3 mm and 0.1 mm diameter particles.
Fig. 6 .
Fig. 6.Simultaneous LITE (thin line) and Potenza (solid line) lidar measurements of the aerosol scattering ratio at 355 nm (a) and 532 nm (b) for orbit 33.Data area reported with their error bars Fig. 7a-e.R A ,532 LITE (z) versus R Pz A,532 (z) for all data points within the stratospheric aerosol layer: a) orbit 33; b) orbit 34; c) orbit 128; d) orbit 129 and e) orbit 145.Values of R A ,532LITE (z) are reported together with their error bars.Also reported is the best fi t linear function.
Fig
Fig. 8a-e.R z A,355 LITE ( )versus R A Pz ,355 (z) for all data points within the stratospheric aerosol: a) orbit 33; b) orbit 34; c) orbit 128; d) orbit 129 and e) orbit 145, together with the best fi t linear function.
Fig. 10 .
Fig. 10.Vertical profi les of aerosol backscattering coeffi cient at 723 nm for 11 February 1997 (bold line) and simultaneous radiosonde profi les of potential temperature (open up triangles) and relative humidity (solid dots). | 4,687.2 | 2003-12-25T00:00:00.000 | [
"Environmental Science",
"Physics"
] |
Perception Sensors for Road Applications
New assistance systems and the applications of autonomous driving of road vehicles imply ever-greater requirements for perception systems that are necessary in order to increase the robustness of decisions and to avoid false positives or false negatives [...].
Introduction
New assistance systems and the applications of autonomous driving of road vehicles imply ever-greater requirements for perception systems that are necessary in order to increase the robustness of decisions and to avoid false positives or false negatives.
In this sense, there are many technologies that can be used, both in vehicles and infrastructure. In the first case, technology, such as LiDAR or computer vision, is the basis for growth in the automation levels of vehicles, although its actual deployment also demonstrates the problems that can be found in real scenarios and that must be solved to continue on the path of improving the safety and efficiency of road traffic.
Usually, given the limitations of each of the technologies, it is common to resort to sensorial fusion, both of the same of type sensors and of different types.
Additionally, obtaining data for decision-making does not only come from on-board sensors, but wireless communications with the outside world allow vehicles to offer greater electronic horizons. In the same way, positioning in precise and detailed digital maps provides additional information that can be very useful in interpreting the environment.
The sensors also cover the driver in order to analyze their ability to perform tasks safely. In all areas, it is crucial to study the limitations of each of the solutions and sensors, as well as to establish tools that try to alleviate these issues, either through improvements in hardware or in software. In this sense, the specifications requested of sensors must be established and specific methods must be developed to validate said specifications for the sensors and to complete the systems.
In conclusion, this Special Issue aims to bring together innovative developments in areas related to sensors in vehicles and the use of the information for assistance systems and autonomous vehicles.
Papers in the Special Issue
As assistance and automation increase in road vehicles, the requirements of perception systems rise significantly and new solutions emerge in research and the market. Reference [1] presents a systematic review of the perception systems and simulators for autonomous vehicles. This work has been divided into three parts. In the first part, perception systems are categorized as environment perception systems and positioning estimation systems. In the second part, the main elements to be taken into account in the simulation of a perception system of an AV are presented. Finally, the current state of regulations that are being applied in different countries around the world, on issues concerning the implementation of autonomous vehicles, is presented.
As previously mentioned, the number of small sophisticated wireless sensors that share the electromagnetic spectrum is expected to grow rapidly over the next decade and interference between these sensors is anticipated to become a major challenge. In Reference [2], the interference mechanisms in one such sensor, automotive radars, is studied, and the results are directly applicable to a range of other sensor situations.
One of the most common applications of perception systems in vehicles is obstacle detection. In this field, several technologies have been used for years and new algorithms have tried to obtain more robust and efficient results under complex scenarios.
A robust Multiple Object Detection and Tracking (MODT) algorithm for a non-stationary base is presented in Reference [3], using multiple 3D LiDARs for perception. The merged LiDAR data is treated with an efficient MODT framework, considering the limitations of the vehicle-embedded computing environment. The ground classification is obtained through a grid-based method, while considering a non-planar ground. Furthermore, unlike prior works, a 3D grid-based clustering technique is developed to detect objects under elevated structures. The centroid measurements obtained from the object detection are tracked using an Interactive Multiple Model-Unscented Kalman Filter-Joint Probabilistic Data Association Filter.
Reference [4] presents an efficient moving object detection algorithm that can cope with moving camera environments. In addition, a hardware design and the implementation results for the real-time processing of the proposed algorithm are presented. The proposed moving object detector was designed using hardware description language (HDL) and its real-time performance was evaluated using an FPGA based test system.
A computationally low-cost and robust detecting and tracking moving objects (DATMO) system, which uses as input only 2D laser rangefinder information, is presented in Reference [5]. Due to its low requirements, both in sensor needs and computation, the DATMO algorithm is meant to be used in current autonomous guided vehicles to improve their reliability for the cargo transportation tasks at port terminals, advancing towards the next generation of fully autonomous transportation vehicles.
A continuous waveform radar is widely used in intelligent transportation systems. There are several waveforms and the chirp sequence waveform has the ability to extract the range and velocity parameters of multiple targets. Reference [6] proposes a new waveform that follows the practical application requirements, high precision requirements, and low system complexity requirements. Theoretical analysis and simulation results verify that the new radar waveform is capable of measuring the range and radial velocity simultaneously and unambiguously, with high accuracy and resolution even in multi-target situations.
Another classical use of perception systems is the characterization of the scenario and the road. An Extended Line Map (ELM)-based precise vehicle localization method is proposed in Extended Line Map [7], and is implemented using 3D Light Detection and Ranging (LIDAR). A binary occupancy grid map in which grids for road marking or vertical structures have a value of one and the rest have a value of zero was created using the reflectivity and distance data of the 3D LIDAR.
Furthermore, vision-based lane-detection methods provide low-cost density information about roads. A robust and efficient method to expand the application of these methods to cover low-speed environments is presented in Reference [8].
Moreover, perception sensors are also used for driver and other passenger detection and characterization. Perhaps the least intrusive, physiology-based approach is to remotely monitor driver drowsiness by using cameras to detect facial expressions. A multi-timescale drowsiness characterization system composed of four binary drowsiness classifiers, operating at four distinct timescales and trained jointly, was developed in Reference [9].
Finally, the information retrieved by perception sensors can be used for decision-making systems. The first step for decision-making in an autonomous vehicle or an assistance system is the understanding of the environment. Reference [10] presents three ways of modelling traffic in a roundabout, quite a critical scenario, based on: (i) The roundabout geometry; (ii) mean path taken by vehicles inside the roundabout; and (iii) a set of reference trajectories traversed by vehicles inside the roundabout.
Reference [11] presents a machine learning-based technique to build a predictive model and to generate rules of action to allow autonomous vehicles to perform roundabout maneuvers. The approach consists of building a predictive model of vehicle speeds and steering angles based on collected data that are related to driver-vehicle interactions and other aggregated data intrinsic to the traffic environment.
Reference [12] presents a path-planning algorithm based on potential fields. Potential models are adjusted so that their behavior is appropriate to the environment and the dynamics of the vehicle and they can face almost any unexpected scenarios. The response of the system considers the road characteristics (e.g., maximum speed, lane line curvature, etc.) and the presence of obstacles and other users.
Funding: This work received no external funding. | 1,740.2 | 2019-12-01T00:00:00.000 | [
"Computer Science"
] |
Optical/X-ray/radio view of Abell 1213: A galaxy cluster with anomalous diffuse radio emission
Context. Abell 1213, a low-richness galaxy system, is known to host an anomalous radio halo detected in data of the VLA. It is an outlier with regard to the relation between the radio halo power and the X-ray luminosity of the parent clusters. Aims. Our aim is to analyze the cluster in the optical, X-ray, and radio bands to characterize the environment of its diffuse radio emission and to shed new light on its nature. Methods. We used optical data from the SDSS to study the internal dynamics of the cluster. We also analyzed archival XMM-Newton X-ray data to unveil the properties of its hot intracluster medium. Finally, we used recent data from LOFAR at 144 MHz, together with VLA data at 1.4 GHz, to study the spectral behavior of the diffuse radio source. Results. Both our optical and X-ray analysis reveal that this low-mass cluster exhibits disturbed dynamics. In fact, it is composed of several galaxy groups in the peripheral regions and, in particular, in the core, where we find evidence of substructures oriented in the NE-SW direction, with hints of a merger nearly along the line of sight. The analysis of the X-ray emission adds further evidence that the cluster is in an unrelaxed dynamical state. At radio wavelengths, the LOFAR data show that the diffuse emission is ~510 kpc in size. Moreover, there are hints of low-surface-brightness emission permeating the cluster center. Conclusions. The environment of the diffuse radio emission is not what we would expect for a classical halo. The spectral index map of the radio source is compatible with a relic interpretation, possibly due to a merger in the N-S or NE-SW directions, in agreement with the substructures detected through the optical analysis. The fragmented, diffuse radio emissions at the cluster center could be attributed to the surface brightness peaks of a faint central radio halo.
Introduction
Radio halos are diffuse, low-surface-brightness synchrotron sources (∼0.1 µJy arcsec −2 at 1.4 GHz) hosted in the central volume of a fraction of massive and unrelaxed galaxy clusters.They extend up to spatial sizes of 1−2 Mpc, roughly following the distribution of the intracluster medium (ICM) and have no evident counterparts in the optical band.Their steep spectrum (S (ν) ∼ ν −α ; with α > 1) indicates the existence in the ICM of ultra-relativistic electrons (γ 1000) moving in weak (∼µG) magnetic fields (see, e.g., Feretti et al. 2012;van Weeren et al. 2019
for reviews).
A strong correlation has been found between the total power of radio halos at 1.4 GHz (P 1.4 GHz ) and the X-ray luminosity (L X ) of the ICM (Feretti et al. 2012;Cassano et al. 2013;Yuan et al. 2015;Cuciti et al. 2021), but there are notable outliers.In fact, anomalous radio halos have been observed with a radio power larger than expected from the P 1.4 GHz −L X, 0.1−2.4kev correlation shown by the majority of radio halos, with the halo in Abell 523 among of the most frequently studied of this type (Girardi et al. 2016;Vacca et al. 2022a,b).
Another controversial case is the diffuse source in the galaxy cluster Abell 1213.This is a poor (Abell richness class = 1; Abell et al. 1989) cluster at z ∼ 0.047 dominated in its central region by the FR II radio galaxy 4C29.41 and two more cluster members identified as radio galaxies.
Very notably, NE of 4C29.41,data of the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) and observations with the Very Large Array (VLA) at 1.4 GHz by Giovannini et al. (2009;hereafter G09) revealed the presence of a diffuse extended emission that does not seem due to the discrete radio sources in the cluster central region.Indeed, G09 classified it as a small-size radio halo, concluding that the radio morphology and power of this diffuse source are linked to the physical properties of the cluster as a whole and not to the activity of cluster radio galaxies.However, if this source is a radio halo, it would be really peculiar.In fact, it appears well off-centered with respect to the ICM distribution inferred from ROSAT/HRI data and overluminous when compared to the ICM X-ray luminosity (see Fig. 17 of G09).Moreover, the low X-ray luminosity (L X = 0.10 × 10 44 erg s −1 in the ROSAT 0.1−2.4keV band; Ledlow et al. 2003) and poor optical richness of A1213 suggest that it is not massive in comparison with typical clusters known to host a radio halo.An analysis based on redshift data from the Sloan Digital Sky Survey (SDSS) DR6 by Hernández-Fernández et al. (2012) supports this hypothesis.In fact, they measure a member galaxies velocity dispersion of ∼560 km s −1 (see their Table 1).This is quite a low value, bearing in mind that massive clusters with radio halos often exhibit velocity dispersions 1000 km s −1 .
In this intriguing context, we performed an exhaustive study of A1213 in the optical, X-ray, and radio bands.In particular, we used SDSS photometric and spectroscopic information to extend the analysis of Hernández-Fernández et al. (2012) by searching for optical substructures, which are an indicator of the dynamical state of the cluster (e.g., Girardi & Biviano 2002).Then, we complemented the optical analysis with public X-ray data from XMM-Newton to draw a multiband picture of A1213 and use this information to study the environment of its extended radio emission.Finally, we used archival radio data from the LOw Frequency ARray (LOFAR) and the VLA data by G09 to derive the spectral properties of the diffuse radio source.
The paper is organized as follows.We describe the analyzed optical data and select the members of the cluster in Sect. 2. We estimate the global properties and analyze the optical substructures in Sects.3 and 4. In Sect.5, we discuss the large-scale structure around the cluster, while in Sect.6, we present the analysis and results of the XMM-Newton X-ray data.In Sect.7, we show the radio data from LOFAR.Section 8 is devoted to the summary and discussion of our results.In this work, we use H 0 = 70 km s −1 Mpc −1 in a flat cosmology with Ω m = 0.3 and Ω Λ = 0.7.In the assumed cosmology, 1 corresponds to ∼55.2 kpc at the cluster redshift.We recall that the velocities we derive for the galaxies are line-of-sight velocities determined from the redshift, V = cz.Unless otherwise stated, we report errors with a confidence level (c.l.) of 68%.
Redshift data and spectroscopic cluster members
From SDSS DR13, we extracted 402 galaxies with a redshift z ≤ 0.2 within a radius R = 60 , corresponding to 3.31 Mpc in the cluster rest frame, from the position RA = 11 h 16 m 40 s .00,Dec = +29 • 16 00 .0 (J2000).
To select cluster members among the 402 galaxies in the spectroscopic catalog, we used the two-step method known as Peak+Gap (P+G), which was previously applied by Girardi et al. (2015).The first step is the application of the adaptive-kernel DEDICA method (Pisani 1993(Pisani , 1996; see also Girardi et al. 1996).Using this method, A1213 is identified as a peak at z ∼ 0.04658 consisting of 144 galaxies in the range 0.041989 ≤ z ≤ 0.052006, that is, 12588 ≤ V ≤ 15591 km s −1 for the line-ofsight velocity V = cz (see Fig. 1).Of the non-member galaxies, 53 are foreground and 205 are background galaxies.The histogram with the thick red line highlights the 144 galaxies that are assigned to A1213 using the 1D-DEDICA reconstruction method.
The inset shows the final 143 member galaxies, with the redshifts of the BCG and the pair of bright close galaxies BG1 and BG2 shown.
In a second step, we combine the space and velocity information by using the "shifting gapper" method (Fadda et al. 1996;Girardi et al. 1996).Of the galaxies that lie within an annulus around the center of the cluster, this procedure rejects those that are too far away in terms of velocity from the main body (i.e., farther away than a fixed velocity gap).The position of the annulus is shifted with increasing distance from the center of the cluster.The procedure is repeated until the number of cluster members converges to a stable value.Following Fadda et al. (1996), we used a gap of 1000 km s −1 in the cluster rest frame and an annulus size of 0.6 Mpc or more to include at least 15 galaxies.In determining the cluster center, we considered the position in right ascension (RA) and declination (Dec) of the brightest cluster galaxy in our sample (BCG) [RA = 11 h 16 m 22 s .70,Dec = +29 • 15 08 .3 (J2000)].With this procedure, one galaxy is discarded and we confirm 143 cluster members.The distribution of member galaxies is shown in the redshift space and in the projected phase space in Figs. 1 and 2, respectively.To highlight the region of cluster members, we also plot in Fig. 2 the escape velocity curves obtained with the mass estimate calculated below (see Sect. 3), assuming a Navarro et al. (1997) mass-density profile and adopting the prescription of den Hartog & Katgert (1996).
Table 1 lists the velocity catalog for the prominent member galaxies.Instead, Fig. 3 shows the central region of the cluster with, superimposed, the VLA radio (from G09) and XMM-Newton X-ray contours obtained from our analysis (see Sect. 6).
The cluster galaxy population is dominated by the brightest cluster galaxy (BCG) ID 422, which is ∼70 far from the centroid of the X-ray emission (see Sect. 6).It is also a bright radio source.However, our catalog lists several galaxies with magnitude r ≤ r BCG + 1.Indeed, A1213 is a typical "core" cluster, as classified by Rood & Sastry (1971).
A199, page 2 of 12 Fig. 2. Projected phase space of the galaxies of A1213, where the rest frame velocity V rf = (V − V )/(1 + z) versus the projected clustercentric distance R is plotted.Only galaxies with redshifts in the range ±3000 km s −1 are shown (black dots).The red and blue circles show the 143 members of the cluster (red and blue galaxies, as defined in the text).The giant and large red squares refer to the BCG and the pair of bright galaxies BG1 and BG2, respectively.The green curves contain the region where |V rf | is smaller than the escape velocity (see text).
In the central region, the most interesting galaxies are the couple IDs 467+468 (see Fig. 3), very close in the sky and separated by only 400 km s −1 in radial velocity.Notably, they show an excess of intracluster light likely due to interaction, thus we treat them as the bright couple BG1+BG2 (see Table 1).If we sum their fluxes we obtain a magnitude r ∼ 13.75.They have an higher velocity with respect to the average and act as a counterpoint to the BCG (see Fig. 1).We note that ID 467 = BG1 is the optical counterpart of the FR II radio galaxy 4C29.41 (see G09 and Sect.1).
In Fig. 3, we highlight more notable galaxies.At ∼4.6 NNE of the BCG, ID 441 is a star-forming spiral galaxy.∼2 S of ID 441, ID 442 is an head-tail radio galaxy oriented toward NE.More bright galaxies in Fig. 3 are IDs 408 and 531.
Far from the cluster center, at ∼23 NW of the BCG (not shown in Fig. 3), ID 274 is a prominent cluster member with a close bright companion.We do not have a spectroscopic redshift for the latter, but the photometric redshift estimate from the SDSS (z phot ∼ 0.050 ± 0.009) suggests it is also a likely cluster member.
Global properties and galaxy population
The analysis of the velocity distribution of the 143 cluster members was performed using the biweight estimators for location and scale included in ROSTAT (statistical routines of Beers et al. 1990).Our measurement of the mean redshift of the cluster is z = 0.0469 ± 0.0001 (i.e., V = 14052 ± 39 km s −1 ).We estimate the velocity dispersion, σ V , by applying the cosmological correction and the standard correction for velocity errors (Danese et al. 1980).We obtained a value of σ V = 463 +41 −31 km s −1 , where the errors are estimated by a bootstrap technique.
To derive the mass 1 M 200 , we used the theoretical relation between the mass M 200 and the velocity dispersion in clusters presented and verified with simulated clusters by Munari et al. (2013;their Eq. (1) and Fig. 1).We took a recursive approach to this step.To obtain a first estimate of the radius R 200 and M 200 , we applied the relation of Munari et al. (2013) to the global value of σ V obtained above.We considered the galaxies within this first estimate of R 200 to recalculate the velocity dispersion.The procedure is repeated until a stable result is obtained.We estimated σ V,200 = 573 +52 −38 for 81 galaxies within R 200 = 1.20 +0.11 −0.08 Mpc, in good agreement with the estimate by Hernández-Fernández et al. (2012).The mass is M 200 = 2.0 +0.4 −0.6 × 10 14 M .The uncertainty for R 200 is calculated using the error propagation for σ V (R 200 ∝ σ V ), while the uncertainty for M 200 is computed considering that M 200 ∝ σ 3 V and adding an uncertainty of 10% due to the scatter around the relation of Munari et al. (2013).The global properties of the cluster are shown in Table 2.
Figure 4 shows the distribution of member galaxies in the (r − i vs. r) and (g − r vs. r) color-magnitude diagrams.The (g − r vs. r) color-magnitude relation indicating the location of early-type galaxies is seen down to faint magnitudes of r ∼ 17.5 mag, about 2.5 mag fainter than the m * r value.Following Boschin et al. (2012) we use a 2σ rejection procedure to obtain r − i = 0.671−0.019× r and g − r = 1.378−0.037× r.We used the (g − r vs. r) relation to classify red and blue galaxies (107 and 36, respectively).Blue galaxies are defined as galaxies that are 0.15 mag bluer than the color expected for their magnitude in the red sequence (i.e., the dashed blue line in Fig. 4, lower panel; e.g., Boschin et al. 2020).Other galaxies are defined as red galaxies.
Analysis of optical substructure
We analyzed the presence of substructures using the velocity distribution of galaxies, their projected positions on the sky, and the combination of these two pieces of information (1D, 2D, and 3D tests, respectively).
Using a set of indicators such as kurtosis, skewness, tail index, and asymmetry index (Bird & Beers 1993), the analysis of the velocity distribution shows no evidence of any possible deviations from the Gaussian distribution.The BCG has a lower velocity than the mean velocity of the cluster, and Fig. 1 (inset) shows how much this velocity is peculiar within the velocity distribution.According to the Indicator test by Gebhardt & Beers (1991), the BCG velocity is peculiar at the >99% c.l.; the same result is obtained when considering the sample of galaxies within R 200 .For the BCG, we calculate |V rf /σ V,200 | = 0.80, placing A1213 in the upper range of |V rf /σ V | distribution, since only about 10% of the clusters have such a high value (see Fig. 8 of Lauer et al. 2014).
Then, we analyzed the spatial 2D distribution of the 143 member galaxies (see Fig. 5).First, we computed the ellipticity ( ) and position angle of the major axis (PA, measured counterclockwise from north) using the method based on moments of inertia (Carter & Metcalfe 1980; see also Plionis 2002, where weight equals one).We obtained = 0.24 +0.06 −0.10 and PA = 119 +11 −10 .The low value of the ellipticity is due to the complex structure of the cluster rather than a round, homogeneous distribution of galaxies, as shown below.We also used the 2D-DEDICA method (Pisani 1996, see also Girardi et al. 1996).Our results are shown in Fig. 5 and Table 3.For each detected galaxy clump with a c.l. greater than 99% and a relative density (with respect to the densest peak) ρ 0.2, Table 3 lists the number of member galaxies, the position of the 2D density peak, and ρ. Figure 5 shows the main peak in the cluster core (2D-CORE in Table 3) and two peaks in the NW and NE (2D-NW and 2D-NE) external regions of the cluster (at R ∼ R 200 ).The BCG is contained in the cluster core, while the NW peak is dominated by the luminous galaxy ID 274 and a close bright likely cluster member (see Sect. 2).The NE peak follows the direction of the main elongation of the X-ray isophotes (see Sect. 6).For all groups, Table 3 also lists the mean velocities, which do not significantly differ taking into account the relative uncertainties.We note that the velocity of the BCG is peculiar with respect to the velocity distribution in the 2D-CORE clump at the 99% c.l.
In the full 3D analysis, we looked for a correlation between velocity and position data.The eventual presence of a velocity gradient is quantified by a multiple linear regression fit to the observed velocities with respect to galaxy positions in the plane of the sky (see also den Hartog & Katgert 1996).To assess the significance of this velocity gradient, we performed 1000 Monte Carlo simulations of galaxy clusters by randomly shuffling the velocities of the galaxies and determining, for each simulation, the coefficient of multiple determination (RC 2 , NAG Fortran Workstation Handbook 1986).The significance of the velocity gradient is the fraction of cases in which the RC 2 of the simulated data is smaller than the observed RC 2 .In A1213, the velocity gradient is not significant in the whole sample as well as within the R 200 region.Within the 0.5 R 200 region, the velocity gradient is significant at the 98% confidence level.In this case, the position angle on the celestial sphere is PA = 33 +12 −16 degrees, which means that the high-velocity galaxies are located in the NE region of the cluster (see Fig. 6).
We then used our modified version of the ∆-test of Dressler & Shectman (1988), which considers only the indicator of local mean velocity (hereafter DSV test, Girardi et al. 2016).This indicator is δ , where the local mean velocity V loc is calculated using the ith galaxy and its N nn = 10 neighbors.For a cluster, the cumulative deviation is given by the value of ∆, which is the sum of the |δ i,V | values of the individual N galaxies.As in the calculation of the velocity gradient, the significance of the ∆ (i.e., the presence of substructure) is based on 1000 Monte Carlo simulated clusters.In A1213, the significance of the substructure is 96.3%.In Fig. 6, we show the Dressler & Schectman bubble-plot resulting from the indicator of the DSV test for the whole sample.Larger circles indicate galaxies where the local mean velocity deviates more from the global velocity.The visual inspection of the bubble plot suggests the presence of poorly populated substructures in the core, in particular, a low-velocity substructure in the SW (large blue circles) and possibly a high-velocity substructure in the NE (large red circles).The relative position of these substructures is consistent with our estimate of the PA of the velocity gradient in the central cluster region.
As an attempt to detect substructure members, we resorted to the technique developed by Biviano et al. (2002).We compared the distribution of δ i,V values of the real galaxies with the distribution of δ i,V values of the galaxies of all the 1000 Monte Carlo simulated clusters (Fig. 7).The distribution of values of real galaxies shows a tail at low δ i,V values and possibly a tail at high δ i,V values.Looking at galaxies with |δ i,V | 3, we found five galaxies in the low tail and four galaxies in the high tail, with none of them being a luminous galaxy or a galaxy that belongs to the prominent galaxies (Sect.2).
Since the substructures seem to consist of few galaxies, we repeated the DSV test with N nn = 5 neighbors.The significance of the substructure is 96.6% for the whole sample.If we consider only red passive galaxies, which usually trace the most important structures and merger remnants, the significance increases to 98.3%.In Fig. 8, we show the Dressler & Schectman bubble-plot obtained for the sample of red galaxies.We confirm the presence of a low-velocity poorly populated substructure in the core.
Finally, we used the 3D-DEDICA method (Pisani 1996;Bardelli et al. 1998), which splits A1213 into more than ten groups.Since it is well known that the multidimensional application of the DEDICA algorithm could lead to spurious substructure (Bardelli et al. 1998), we also applied the alternative version of Balestra et al. (2016), based on the rule of thumb for the kernel size given by Silverman (1986).The goal here is to identify the most important substructures at the expense of losing some smaller substructures.Table 4 lists the properties of all the galaxy peaks detected with a probability higher than the >99% c.l. and a relative density ρ ≥ 0.2. Figure 9 shows the positions of the galaxies associated with the detected peaks.The galaxies assigned to the 3D-NW and 3D-SE peaks form the main system and have similar mean velocities, i.e., they are proba-A199, page 4 of 12 2).Thin blue contours show the (smoothed) X-ray emission of the cluster as derived from the XMM-Newton archival image ID 0550270101 (photons in the energy range 0.7−1.2keV).Labels denote galaxies discussed in the text.The arrow highlights the diffuse radio emission classified by G09 as a small-size radio halo.The black cross shows the position of the centroid of the X-ray emission (see Sect. 6).
bly split because of their different 2D positions.The 3D-CORE peak is a further confirmation of the existence of a group with low-velocity galaxies and projected onto the core.
Large scale structure around A1213
From our analysis of the redshift distribution (see Fig. 1), the second peak in relative density is at z ∼ 0.06 and it is populated by 47 galaxies.Using the 2D-DEDICA method, we find that part of its galaxy population (14 galaxies) clumps together at ESE around the coordinates RA = 11 h 19 m 35 s .00,Dec = +29 • 09 48 .7 (J2000; see Fig. 10).For this group of 14 galaxies, we estimate a velocity dispersion of σ V ∼ 300 km s −1 and z = 0.0601.
The redshift difference between A1213 and this group may be interpreted as a luminosity distance of 61 Mpc or that the group is moving at V rf ∼ 4000 km s −1 with respect to the A1213 cluster frame.This speed is of the order of the core-core falling speed in massive clusters.Since A1213 is a poor cluster, we think they are not gravitationally interacting.Moreover, the group is located at 42 from the center of A1213, i.e. at a projected distance >2 Mpc.Also, we note that the color g − r of the group galaxies is slightly redder than the color of red-sequence galaxies of A1213 (see Fig. 4), which is another hint that the group is in the background with respect to A1213.
According to NED2 , the center of the background group coincides with WHL J111934.5+291100(also MSPM 02054), at z ∼ 0.059.We note that at ∼40 SSW of A1213, an handful of galaxies (see Fig. 10) defines the galaxy group MSPM Notes. (a) As an optical center, we list the position of the BCG.
Fig. 4. PanSTARRS magnitude diagrams: r − i vs. r (upper panel) and g − r vs. r (lower panel) of member galaxies of A1213 (green points) and the background eastern group (red squares, see Sect. 5).Large green squares show the BCG and the pair of bright galaxies: BG1 and BG2.Black lines show the color-magnitude relations obtained for the A1213 member galaxies.The blue dashed line in the lower panel is used to separate red galaxies from blue ones.
Analysis of the X-ray data
A1213 was observed by the European Photon Imaging Camera (EPIC, Turner et al. 2001) instrument on board the XMM-Newton satellite.EPIC is formed of three detectors MOS1, MOS2, and pn that simultaneously observe the same target.The archival observation was pointed on the radio galaxy 4C29.41,whose optical counterpart is ID 467 = BG1 (obs.ID 0550270101).We reprocessed the dataset using the Extended-Science Analysis System (ESAS, Snowden et al. 2008) embedded in SAS version 16.1 following the analysis described in detail in Ghirardini et al. (2019).After the soft protons cleaning procedure (with the mos-filter and pn-filter ESAS tasks; NE NW Fig. 5. Spatial distribution in the plane of the sky of the cluster members (black dots) with the corresponding isodensity contour map obtained with the 2D-DEDICA method (red contours).The black cross shows the position of the BCG, which is considered to be the center of A1213.
The diagram is centered on the center of the cluster.A circle with a radius of 21 , i.e., approximately R 200 , is drawn.The labels refer to the two peripheral 2D-DEDICA peaks listed in Table 3. Snowden et al. 2008), the total available clean exposure time is 16.5 ks for MOS1, 14.8 ks for MOS2, and 4.3 ks for pn.We extracted, for each EPIC detector, the photon-count images in the 0.7−1.2keV band, which is the energy band that maximizes the source-to-background ratio in galaxy clusters (e.g., Ettori et al. 2010), and co-added them to obtain a total EPIC image.With the ESAS tool eexpmap, we produced the EPIC exposure map folding the vignetting effect.We used the ESAS collection of closed-filter observations to produce a map of the non-X-ray background (NXB), which we rescaled to our observations by comparing the count rates in the unexposed corners of the field of view.Figure 11 shows the resulting vignetting-corrected, NXB-subtracted, count rate image of A1213.A Gaussian filter smooths the image for visual purposes only.
X-ray properties of A1213
We performed a spectral analysis of A1213 following the analysis described in Ghirardini et al. (2019).For each region, we extracted spectra and response files using the ESAS tasks mosspectra and pn-spectra.From the spectra we filtered out the point A199, page 6 of 12 sources detected in the field of view by running the SAS wavelet detection tool ewavdetect (see Fig. 12).
Since the surface brightness of cluster A1213, apart from some bright point sources, appears to be very shallow, following Leccardi & Molendi (2008) and Ghirardini et al. (2019) we preferred to model the background instead of subtracting it.This approach models the background with different spectral components: (a) the NXB component and (b) the sky-background component, estimated from the region shown in red in Fig. 11 (see Ghirardini et al. 2019 for a detailed explanation of both components).
To estimate the global properties of A1213 we extracted a spectrum from a circle with 5 arcmin radius (shown in white in Fig. 11) centered on the centroid of the X-ray emission (RA = 11 h 16 m 26 s .40,Dec = +29 • 14 46 .8) within a 5 (∼0.4 R 500 ) radius.We modeled the diffuse source emission with the thinplasma emission code APEC (Smith et al. 2001) in XSPEC v12.9.1, leaving temperature, metal abundance, and normalization as free parameters (the solar abundances were taken from Asplund et al. 2009) and redshift fixed to the optical value of z = 0.0469 (see Sect. 3).This component is absorbed by the Galactic hydrogen column density along the line of sight, which we fixed to the HI4PI Map value (N H = 1.19 × 10 20 cm −2 ; Ben Bekhti et al. 2016).We found a best-fit temperature T X = 2.02 ± 0.09 keV and a metal abundance Z = 0.26 ± 0.05 in solar units (C-Statistic = 1699.93using 1659 PHA bins and 1653 d.o.f.).
From the scaling relation reported in Arnaud et al. (2005, their Eq.( 2)) and the computed mean cluster temperature, we estimated the masses M 500 = (1.12 ± 0.15) × 10 14 M and M 200 = (1.54 ± 0.25) × 10 14 M , from which we derived R 500 = 0.72 ± 0.03 Mpc ∼12.7 and R 200 = 1.09 ± 0.07 Mpc ∼19.2 .The The histogram with the solid line shows the observed galaxies.The histogram with the dashed line shows the galaxies of the simulated clusters, normalized to the number of observed galaxies.The blue vertical lines indicate the |δ i,V | > 3 regions where we expect to find substructure members.values of R 200 and M 200 estimated from the X-ray measurements are in agreement within errors with those derived from the optical properties (see Tables 2 and 5).
Finally, we extracted the surface brightness (SB) profile of the cluster up to 14 and then we fitted the profile with a single β-model, 13.This result allowed us also to reconstruct the X-ray luminosity of the cluster.In particular, using the pyproffit.deprojectmodule (Eckert 2016(Eckert , 2020)), we computed the luminosity within R 500 .We obtained L X [0.1−2.4 keV] = (1.53 ± 0.08) × 10 43 erg s −1 .By using the pyproffit.deprojectmodule, we also reconstructed the proton density profile (n p ) of the ICM.Remembering that n p is related to the electron density profile by n e = 1.17 n p (Ghirardini et al. 2019), for the central electron density, we obtained a value of n e,0 = 1.19 +0.43 −0.26 ×10 −3 cm −3 .Govoni et al. (2017) found a scattered correlation between n e,0 and the mean central magnetic field strength B 0 (see their Fig. 15,right panel).This allows us to provide a rough estimate of the magnetic field in the central region of the cluster.We find B 0 ∼ 2−3 µG.
MSPM 02299 MSPM 02054
Fig. 10.Spatial distribution of the 47 galaxies populating the redshift peak at z ∼ 0.06 (red symbols).The galaxies highlighted by red circles are assigned to the eastern clump by 2D-DEDICA, while red stars put in evidence galaxies belonging to the group MSPM 02299 (see text).Black points are the 143 members of A1213, whose BCG is indicated by a black cross.A circle with a radius of 21 (∼R 200 ) is also drawn.
The group at NNW
Figure 11 also shows an extended X-ray emission at ∼9 NNW of A1213 and centered on the SDSS galaxy CGCG 156-041 (RA = 11 h 16 m 14 s .33,Dec = +29 • 23 06 .9).The galaxy is at z = 0.02929, so it is the main member of a foreground system, not related to A1213.We extracted a spectrum from a circular region of 1.5 around this galaxy (plotted in magenta in Fig. 11) to estimate the physical properties of this foreground source.For the source emission, we used again the APEC model fixing the metal abundance at Z = 0.25 (solar units), z = 0.02929, and N H = 1.22 × 10 20 cm −2 .The temperature of the source is 0.83 ± 0.06 keV, corresponding to a small group of galaxies with a mass M 500 ∼ 0.2 × 10 14 M (from the M 500 −T X relation in Lovisari et al. 2021).
LOFAR radio data
The field of A1213 is covered by the LOw-Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS-DR2; Shimwell et al. 2022).These data are public (Mosaic Field: P168+30) and provide a picture of the cluster region at 144 MHz, a lower frequency with respect to the VLA data of G09.As shown first by Hoang et al. (2022), the LOFAR images confirm the existence of the diffuse emission observed in NVSS and VLA data.In particular, at 144 MHz the radio emission extends toward the east, with a projected size of ∼510 kpc, quite longer than the size of the emission seen by G09 at 1.4 GHz (see Fig. 14).However, we also point out that some fragmented diffuse emission is detected at the cluster center at the 3.3σ level.In particular, there are hints of faint diffuse structures toward NW and SE of the BCG, to the N of the tailed radio galaxy (ID 442) and to the SSE of 4C29.41.
The existence of data sets at two different frequencies allowed us to produce a spectral radio index map.Indeed, A199, page 8 of 12 Fig.11.Smoothed, vignetting-corrected XMM-Newton/EPIC count-rate image of A1213 in the 0.7−1.2keV band.The circles show the regions used to estimate the global X-ray properties of A1213 (white) and of the extended source located NNW of the cluster (magenta, see text).Instead, the red region was used to estimate the local background components.The black cross marks the centroid of the X-ray emission.Black labels highlight galaxies that are also X-ray point sources.11.The circle has a radius of 5 .Black points are MOS1, red points MOS2, and green points pn detector data.The lines are the bestfit sky background and source models for the three EPIC detectors.The data around 1.5 keV and 7 keV are excluded from the analysis to avoid strong instrumental line emissions (see Ghirardini et al. 2019).The bottom panel shows the data divided by the folded model.spatially resolved spectral index mapping of diffuse sources can provide useful information on their nature and origin (e.g., van Weeren et al. 2019).
To produce the spectral index image, we retrieved the LoTTS-DR2 image at the resolution of 20 from the Mosaic Field P168+30 (see above) and compared it with the image Fig. 13.X-ray surface brightness profile of A1213 (black dots).The blue curve represents the best fit, using a single β model, as described in the text.The particle background (shown as the green curve) has already been subtracted from the X-ray surface brightness profile.The bottom panel shows the contribution of each bin to χ2.
Table 5. Global properties of A1213 as inferred from the analysis of the X-ray data.obtained from the VLA data of G09.In particular, the VLA image was obtained combining C and C/D configuration data (see G09 for more details) using the same cell-size and resolution of the LOFAR image.The two images were put on the same reference frame using the AIPS3 task HGEOM and convolved to the resolution of 40 to have a better signal-to-noise ratio in the faint diffuse emission regions.The noise level in the 144 MHz image is 0.28 mJy beam −1 and at 1.4 GHz is 0.25 mJy beam −1 in the region of A1213.A clip at the 3σ level was applied in producing the spectral index image to avoid large uncertainties.
Our map (see Fig. 15) has small uncertainties on the spectral index, mainly in the range 2−12% across the source and indicates a steepening of the radio spectrum from the north to the south of the diffuse emission.In particular, a slice in N-S of this region shows that the spectral index drops from −1.0 ± 0.04 to −1.4 ± 0.04.This steepening is further highlighted by comparing the average values of the spectral index in the northern and southern regions of the diffuse emission.We are aware that the LOFAR data provide a better coverage in the short spacing range than the VLA data.However, we note that in the VLA configuration adopted by G09 there are 10 inner antennas in D configuration and the largest structure that can be imaged at high sensitivity is 16.2 in size.The diffuse emission detected with LOFAR is ∼13 × 9 in size, significantly smaller than 16.2 .Moreover, the size of the structure where we derived the spectral index distribution is even much smaller.Therefore, we are confident that the spectral comparison is not affected by the different uv-coverage (for a similar case see, e.g., Feretti et al. 2004).
The steepening of the radio spectrum in the N-S direction suggests that this source, rather than a radio halo, could be a radio relic.In fact, this spectral behavior has been observed in confirmed radio relics for which spectral index maps are available (e.g. in the cluster CIZA J2242.8+53.01;van Weeren et al. 2010).
It is known that the properties of relics are related to the X-ray properties of their parent clusters (e.g., Feretti et al. 2012).This fact offers a way to compare the suspected relic of A1213 with the radio relics known in the literature.The comparison is shown in Fig. 16, which reports the power of radio relics at 1.4 GHz versus the X-ray luminosity of the parent clusters in the energy range 0.1−2.4keV.Blue dots are radio relics from the literature (see Feretti et al. 2012;van Weeren et al. 2019), while the red square shows the location of A1213 in the diagram considering the new X-ray luminosity derived in this work.The figure shows that the diffuse source of A1213 is in agreement with the relic power-cluster X-ray luminosity correlation.
Summary and discussion
The mass estimates based both on the optical and the X-ray data confirm that A1213 is a poor galaxy cluster (M 200 ∼ 2 × 10 14 M ).Moreover, we collected convincing evidence that this cluster is far from being dynamically relaxed.
From the optical point of view, despite the fact that the velocity distribution of member galaxies does not deviate significantly from the Gaussianity, a compelling argument in favor of a disturbed dynamics in A1213 comes from the very significant peculiar velocity of the BCG.This is quite unusual in reg- ular clusters, where the brightest galaxy is located at the peak of the velocity distribution (see, e.g., the case of CL1821+643; Boschin & Girardi 2018).
With regard to the 2D analysis of the galaxy distribution, we can see that the cluster is only slightly elliptical and roughly oriented in the NE-SW direction.Our analysis of optical substructures suggests that A1213 is composed by several galaxy groups.In particular, we detected two external (at R ∼ R 200 ) groups: 2D-NW and 2D-NE (see Table 3).2D-NW is the densest one A199, page 10 of 12 and exhibits a dominant galaxy (ID 274) and several galaxies all around, thus maybe it has not yet crossed the central region of A1213.On the contrary, 2D-NE seems elongated in the same direction as the X-ray emission (see below).It could be a group in a recent, post-merger phase occurring in the plane of the sky.
About the central cluster region, both the velocity gradient and the DSV test suggest the existence of two substructures oriented in the NE-SW direction.The one with lower radial velocity is detected also by the 3D-DEDICA test (3D-CORE in Table 4).Indeed, the core of A1213 is quite intricate.The existence of the BCG and the bright couple BG1+BG2, which differ substantially in terms of radial velocity ( 1000 km s −1 ), could suggest that these galaxies trace a merger almost along the line of sight.In fact, during a merger of two groups, the external galaxies are usually swept away and only the dense cores survive (see simulations by, e.g., González-Casado et al. 1994;Vijayaraghavan et al. 2015).However, if the groups did not have compact cores but rather their luminosity was concentrated in a bright dominant galaxy (or a couple of bright galaxies), the merger is not visible as a double peak in the velocity distribution and it is traced only by the brightest galaxies.
Another important piece of evidence is the fact that blue, star-forming galaxies (e.g., galaxy ID 441 in Table 1) are not restricted to the peripheral regions of the cluster, as shown from the projected phase space of cluster galaxies (Fig. 2).This is not what is commonly found in galaxy clusters, where blue galaxies usually tend to avoid the core regions (e.g., Girardi et al. 2015;Mercurio et al. 2021) and is consistent with the scenario of an assembling cluster through accretion of several poor groups rich in late-type galaxies.Another explanation could be that in A1213, which is a poor cluster, the ram-pressure by the ions of the ICM (see Boselli et al. 2022 for a recent review) is not efficient to quench the star formation in blue galaxies falling into the cluster core.
As for the X-ray properties of A1213, it displays a patchy, shallow X-ray emission on scales of ∼700 kpc (see Fig. 11) in the presence of various point sources.A comparison with Fig. 3 shows that several of these sources coincide with the most prominent optical galaxies in the field, such as BCG, BG1, and ID 442.None of these bright galaxies coincide with the centroid of the X-ray emission.Once the point sources detected in the image are excised, the diffuse X-ray emission appears almost regular, slightly elongated in the NE-SW direction, with an ellipticity of ∼ 0.1 and PA ∼ 35 • within 0.5 R 500 .
To describe the morphological state of A1213 in the X-ray band, two parameters are useful: the surface brightness concentration c SB and the centroid shift w (see Santos et al. 2008;Poole et al. 2006;Maughan et al. 2008 for details).Since a central surface brightness excess is a primary indicator of the presence of a cool core (Fabian et al. 1984), then the c SB parameter is a useful indicator of the dynamical state of the cluster.On the other hand, the w parameter is sensitive to the presence of bright substructures.For A1213, we derive c SB = 0.14 and w = 0.025, a clear indication of this cluster to be unrelaxed.In fact, typical values for disturbed clusters are c SB < 0.19 and w > 0.01, as found by Campitiello et al. (2022).
In summary, the diffuse X-ray emission overlaps with the optical galaxy distribution and is slightly elongated in the same NE-SW direction.Moreover, the X-ray morphology, the absence of well-defined emission peaks and the above-defined dynamical indicators strengthen the evidence that A1213 is in an unrelaxed dynamical state.We also note that although the diffuse X-ray emission within R 500 is clumpy (Fig. 11), its large-scale shape appears only slightly elongated.This indicates that if the cluster core had a recent interaction it probably did not occur on the plane of the sky.
About the X-ray luminosity of A1213, it was previously proposed that the cluster is underluminous to explain the discrepancy with the power of the radio halo (G09, Giovannini et al. 2011).Considering our new estimate of the luminosity within R 500 , together with the value of the gas temperature derived through the spectral analysis (see Sect. 6.1), we can now claim that A1213 is not an underluminous cluster (e.g., Lovisari et al. 2021, their Fig. 3).Instead, we determine that it is quite a typical poor cluster.
The purpose of our work was to characterize the optical/ X-ray/radio properties of A1213 in order to study the environment of the diffuse radio emission discovered by G09 in this cluster and shed new light on its nature.The SDSS and XMM-Newton data show a good agreement in the cluster central region, including the fact that both data sets indicate an elongation in the NE-SW direction.Instead, the observed radio emission does not coincide with the diffuse X-ray emission (see Fig. 3), as occurs generally in unrelaxed clusters with radio halos (e.g., Govoni et al. 2001), because of its offset with respect to the ICM distribution and its extension toward the NE, the same direction traced by the galaxy distribution from the core to the cluster periphery (at R ∼ R 200 ).
Indeed, recent LOFAR images at 144 MHz of the LoTSS-DR2 confirmed the presence of the diffuse emission observed in A1213 at higher frequencies (see Hoang et al. 2022, their Fig. 4, as well as our Fig.14).However, since the radio emission does not follow the X-ray emission, (Hoang et al. 2022) infer that this extended source is not a radio halo, but it is the tail of the central radio galaxy 4C29.41 (our ID 467 = BG1) bent by the interaction with the ICM (see their Fig. 4).This would explain why A1213 is an outlier in the normal scale relations between X-ray and radio properties of radio-halo clusters (e.g., Cassano et al. 2013).But the scenario could be even more complicated.In fact, (Hoang et al. 2022) detect an excess of diffuse emission on the easternmost region of the emission seen with LOFAR (see their Fig. 4, left panel).Since there is no obvious optical counterpart of this source, its origin is unclear and these authors propose that it could be associated to a merger occurring in the NE-SW direction.
Our VLA 1.4 GHz/LOFAR 144 MHz spectral index map rejects the hypothesis of the radio galaxy tail and supports a different explanation.In fact, the spectral index distribution (Sect.7 and Fig. 15) is compatible with a radio relic interpretation, where "fossil" electrons of the radio galaxy 4C29.41 (but also of the head-tail galaxy ID 442) are reaccelerated by shock(s) due to a merger.The radio relic is elongated from the cluster center toward the cluster periphery, therefore it is located either in front or behind the cluster.This is consistent with a merger in the N-S or NE-SW directions, in agreement with the results of our optical analysis.A relic with a similar structure is detected in the cluster Abell 115 (Govoni et al. 2001;Botteon et al. 2016), although the latter is much larger in size.The relic hypothesis is also supported by the plot shown in Fig. 16, where the diffuse source of A1213 fits the empirical correlation between the power of radio relics and the X-ray luminosity of the parent clusters.
Finally, Fig. 14 shows some evidence of fragmented diffuse radio emissions at the cluster center whose nature is uncertain.They could be related to the relic, or could be the tip of the iceberg of very low-surface-brightness emission permeating the cluster center.Indeed, our estimate of the central magnetic field strength, B 0 ∼ 2−3 µG (Sect.6.1), is compatible with the possible presence of a faint radio halo in the A199, page 11 of 12 cluster core (e.g., van Weeren et al. 2019).Also, recent works (e.g., Hoang et al. 2021;Botteon et al. 2021) reported the discovery with LOFAR of radio halos in low-mass (M 500 5 × 10 14 M ) galaxy clusters.Thus, the existence of a faint halo in A1213 (M 500 ∼ 1 × 10 14 M ), while quite uncommon, would not be so extraordinary.
In conclusion, A1213 represents an interesting target to investigate the connection between optical (galaxy population) and X-ray (ICM) cluster properties and diffuse radio emissions in a low-mass regime that is still mostly unexplored.In this context, new deeper X-ray observations of this cluster could be decisive to test the proposed relic scenario.In fact, the eventual detection of X-ray surface brightness discontinuities (associated with shocks in the ICM) in correspondence to the suspected radio relic would strengthen our interpretation.Instead, dedicated LOFAR LBA observations (e.g., de Gasperin et al. 2021) could be crucial in characterizing the very low-surfacebrightness diffuse emission detected in the center of the cluster.
Fig. 1 .
Fig.1.Distribution of redshifts of galaxies with z ≤ 0.2.The histogram refers to all galaxies with spectroscopic redshifts in the region of A1213.The histogram with the thick red line highlights the 144 galaxies that are assigned to A1213 using the 1D-DEDICA reconstruction method.The inset shows the final 143 member galaxies, with the redshifts of the BCG and the pair of bright close galaxies BG1 and BG2 shown.
Fig. 3 .
Fig. 3. SDSS g-band image of the galaxy cluster A1213 with, superimposed, the contour levels of the VLA 1.4 GHz radio image by G09 (red thick contours, HPBW = 35 × 35 , first contour level at 1 mJy beam −1 , the others spaced by a factor √2). Thin blue contours show the (smoothed) X-ray emission of the cluster as derived from the XMM-Newton archival image ID 0550270101 (photons in the energy range 0.7−1.2keV).Labels denote galaxies discussed in the text.The arrow highlights the diffuse radio emission classified by G09 as a small-size radio halo.The black cross shows the position of the centroid of the X-ray emission (see Sect. 6).
Fig. 6 .
Fig. 6.Dressler & Schectman bubble plot for the DSV test.Spatial distribution of the 143 cluster members, each indicated by a symbol: the larger the symbol, the larger the deviation |δ i,V | of the local meanvelocity from the global mean-velocity.The blue thin and red thick circles indicate where the local mean velocity is smaller or larger than the global mean velocity.Here the bubble size is less enhanced than the standard size for better readability (size equal to exp(w/3), with w = |δ i,V |).The green arrow indicates the position angle of the velocity gradient that is calculated within 0.5 R 200 .The diagram is centered on the BCG.
Fig. 7 .
Fig. 7. Distribution of δ i,V values of the deviation of the local mean velocity from the global velocity (according to the DSV test, see text).The histogram with the solid line shows the observed galaxies.The histogram with the dashed line shows the galaxies of the simulated clusters, normalized to the number of observed galaxies.The blue vertical lines indicate the |δ i,V | > 3 regions where we expect to find substructure members.
Fig. 8 .
Fig. 8. Dressler & Schectman bubble plot for the DSV test (see also Fig.6) applied to the red galaxy population only and looking for small substructures (N nn = 5).Here, the bubble size follows the traditional exponential scale (size equal to exp(w), with w = |δ i,V |).
Fig. 9 .
Fig. 9. Spatial distribution of the 143 cluster members in the sky, with the groups discovered with the 3D-DEDICA method marked by different symbols.Red circles and squares show the galaxies of 3D-NW and 3D-SE peaks, respectively.Blue triangles indicate the galaxies of the 3D-CORE peak, which are characterized by low velocities.The green central cross indicates the position of the BCG.
Fig. 12 .
Fig. 12. EPIC spectrum of A1213 extracted from the white circle shown in Fig.11.The circle has a radius of 5 .Black points are MOS1, red points MOS2, and green points pn detector data.The lines are the bestfit sky background and source models for the three EPIC detectors.The data around 1.5 keV and 7 keV are excluded from the analysis to avoid strong instrumental line emissions (seeGhirardini et al. 2019).The bottom panel shows the data divided by the folded model.
Fig. 15 .
Fig. 15.VLA 1.4 GHz/LOFAR 144 MHz spectral index map of the radio emission of A1213 at the angular resolution of 40 × 40 .As a reference, we also plot in black the contours of the LOFAR image at the same resolution.Contour levels are at 0.84, 3.36, 13.44, 53.76, and 215.04 mJy beam −1 .
Fig. 16 .
Fig. 16.Monochromatic radio power of relics at 1.4 GHz versus the cluster X-ray luminosity of the parent clusters (energy band 0.1−2.4keV).Blue dots are radio relics from the literature (see text), while the red square refers to A1213.
Table 2 .
Global properties of A1213 as inferred from the analysis of the optical data. | 11,824.4 | 2023-03-04T00:00:00.000 | [
"Physics"
] |
CYCLOSTATIONARITY APPLIED TO ACOUSTIC EMISSION AND DEVELOPMENT OF A NEW INDICATOR FOR MONITORING BEARING DEFECTS
cyclostationnarité, cyclostationnaire précoce Abstract The exploitation of cyclostationarity properties of vibratory signals is now more widely used for monitoring rotating machinery and especially for diagnosing bearing defects. The acoustic Emission (AE) technology has also emerged as a reliable tool for preventive maintenance of rotating machines. In this study, we propose an experimental study that characterizes the cyclostationary aspect of Acoustic Emission signals recorded from a defective bearing (40µm on the outer race) to see its efficiency to detect a defect at its very early stage of degradation. An industrial sensor (UE10 000) is used. An electrical circuit converts the high frequency signal into an audible signal by heterodyning. The cyclic spectral density, which is a tool dedicated that to put into evidence the presence of cyclostationarity, is used for characterizing the cyclostationary. Two new indicators based on this cyclostationary technique are proposed and compared for early detection of defective bearings.
Introduction
Most researches on machinery fault diagnosis can be classified in time, frequency or time-frequency domain.In time domain, the RMS value of vibratory signals, Crest Factor (CF), Skewness and Kurtosis are the most used statistical descriptors since they are scalar [1,2].Techniques advanced signal processing have been widely used in vibration.In the frequency domain, the envelope analysis, also known as amplitude demodulation, has been widely used and proved to be very effective in detecting bearing characteristic frequencies.
On the other hand, many research studies have been published on the detection and diagnosis of bearing defects by acoustic emission.Tandon and Choudhury [3] presented a detailed review of vibration and acoustic methods, noise measurements, shock waves and acoustic emission technique.They updated critical works [4] incorporating latest and advanced techniques.Yongyong et al. [5] presented a detailed review of the application of acoustic emission for monitoring bearings.There are few publications on the application of ultrasonic techniques for monitoring bearing condition [6,7].Kim et al. [8] focused on the diagnosis of bearings (defect about 100 μm) operating at low speeds.Kedadouche et al. [9] presented a a Corresponding author<EMAIL_ADDRESS>study between acoustic emission and vibration.This study was focused on the diagnostic of bearing which presents a defect at an early stage (40 μm).Chiementin et al. [10] used time domain indicators: RMS, Kurtosis, and proposed to improve the signal-to-noise ratio by applying denoising techniques (wavelet, spectral subtraction, sanc) on experimental acquired AE data.Liao et al. [11] used wavelet analysis and Zvokelj et al. [12] were interested in the application of empirical mode decomposition (EMD) applied to AE signals.Recently, Kilundu et al. [13] applied the cyclostationary on acoustic emission and showed the effectiveness of the spectral correlation and the ICS (integrated correlation spectral) indicator for monitoring bearing defect but with relatively big defect sizes.
The aim of this study is to investigate the effectiveness of acoustic emission techniques to detect bearing defects at a very early stage and compare the results with signals from vibration measurements, using an experimental approach.An artificially defect in the form of a scratch with a 40 microns size, induced on the outer ring of the bearing was used for this comparative study.It is the smallest bearing fault size that has ever been investigated in literature.The ultrasonic sensor (UE 10 000) is used with an electrical circuit that converts the high frequency signal into an audible signal EA by heterodyning.The ultrasonic signals from a normal bearing and those of the damaged
Cyclostationarity
A signal is cyclostationary at an order "n", if its statistical properties, at an order "n" are periodic.Antoni [14] presented a review of cyclostatinary processes and gives many examples.It is well known that the defects on the rolling bearing produce a series of shocks.These shocks are not perfectly periodic because of slips.Antony has suggested that these slips are non-stationary process and may be approximated as quasi-cyclostationary over only a limited period of time [15].Kilundu et al. [13] note that the acoustic emission is similar to vibrations and suggest the same cyclostationarity properties for AE signal arising from a defective bearing.An efficient method for testing cyclostationarity of a signal X(t) (residual part after extracting the deterministic part of the signal) is to compute the two-dimensional Fourier transform of its autocorrelation function R xx (t, τ ) i.e where f and α are, respectively, the spectral and cyclic frequencies.
The cyclic power spectral density of the signal is estimated by using Welch's averaged periodogram method.The parameters and the method are set based on the recommendations of Antoni [21,22].For this investigation the parameters employed for obtaining the averaged cyclic periodogram estimate were as follows: hanning window with 2/3 overlap; window length: 256; cyclic frequency resolution: 0.2 Hz.
Methodologies for processing cyclostationary signals
Antoni et al. [15] presented a review of some signal processing tools dedicated to cyclostationary signals (Fig. 1) when the signals are issued from rotating machines.Figure 1 presents an organization chart for different steps.
The technique consists in resampling the signal in the angle domain (Step 1) and extracting the angle periodic component using the synchronous average (Step 2).After that, the residual (2sd order) may be computed by extracting the periodic part (deterministic) from the original signal (Step 3).If we cannot resample the signal in the angle domain, other tools may be used which are dedicated to extract the deterministic part for any signal like Comb-filter, ALE, SANC and DRSep. . .etc.In the last decades, several blind algorithms were dedicated to the separation of mixtures of unobserved signals.Recently applied to mechanical systems and in particular to rotating machines that usually generate vibration signals exhibiting cyclostationarity, Bonnardot et al. [16] developed a multiple cyclic regression (MCR) technique for extracting the 2sd order of a signal.Boustany and Antoni [17] proposed a new method called SUBLEX which achieves to the same objectives under the same assumptions as [16], but using a different approach.After that, Boustany and Antoni [18] proposed a new effective method called RRCR (Reduced-Rank Cyclic Regression) that benefits from the respective advantages of the original MCR and SUBLEX methods but suppresses their drawbacks.All these technique may be used to study the cyclostationary of rotating machine (Fig. 2).In this paper, the last method (RRCR) is used for extracting the second order of the signal from the acoustic emission and from the vibration signal in order to compute their cyclic spectral density (CSD).
Experimental study
The test bench used in this study is shown in Figure 3a.A shaft is supported by two bearings and connected to a motor with a flanged coupling bolted rubber.Two systems were investigated, one with a healthy bearing (SKF, 1210 EKTN9) and the other with an artificially damaged bearing on the outer race (defect order: BPFO = 7.24).The default size is 40 microns as shown in Figure 3b.
The equipments for vibration data collection and ultrasound are shown in Figure 4a.They consist in an accelerometer with a sensitivity of 100 mV.g −1 and an ultrasound detector (UE Systems UltraProb 10 000).Both sensors are connected to an analogous digital converter (THOR Analyzer PRO: DT9837-13310) with a sampling frequency of 48 kHz.The latter is connected to a collectoranalyzer BETAVIB.The ultrasonic sensor used in this study operates in the lower ultrasonic spectrum from 20 kHz to 100 kHz.A heterodyne circuit converts the high frequency acoustic emission signal as detected by the transducer around a central frequency Fc into an audible signal (0-7 kHz) (Fig. 4b).The heterodyned signal may then be recorded through conventional data acquisition system at 48 kHz.The mechanical system is excited by an unbalance mass rotating.The acoustic emission signals from the two bearings (healthy and faulty) are recorded at the central frequency of 30 kHz which was found as the more sensitive to the defect when rotating at various speeds (300, 600 and 900 rpm).
Figures 5a and 5b show, respectively, the vibration signal of the damaged bearing when operating at 300 rpm and its second order obtained by RCRR. Figure 5c shows the spectrum of the original signal (Blue line) and its 2nd order (Red line) for the defective bearing while Figure 5d exhibits the spectrum for the healthy bearing.A zoom around [0-300 Hz] reveals that the frequency related to the rotation of the shaft (deterministic part) exists only in the original signal, while we can observe the bearing frequency (BPFO) in the 2nd order spectrum in both cases (healthy and faulty), but with a very small amplitude.All other deterministic peaks were filtered in the 2nd order spectrum.Figure 6 compares the cyclic spectral density (CSD) between the healthy and defective bearing.Figure 6b clearly exhibits BPFO and its harmonics around the resonance of bearing which are located between [500-1500 Hz] and [4000-5000 Hz], with a level of energy definitely larger than for the healthy bearing (Fig. 6a).
Acoustic emission signal
Figures 7a and 7b show, respectively, the ultrasonic signal of the damaged bearing when operating at 300 rpm and its second order obtained by RCRR.We note that the second order is the same as the original signal when a defect is present.The acoustic emission doesn't detect information related to the rotational frequency (deterministic part), but we observe a decrease of noise.Figure 7c shows the spectrum of the original signal (Blue line) and its 2nd order (Red line) for the defective bearing while Figure 7d exhibits the spectrum for the healthy bearing.A zoom around [0-300 Hz] reveals that the spectrum of the 2nd order is the same as the spectrum of the original signal when a defect is present while its amplitude is lower when there is no defect.At this speed we can consider that the original signal recorded by acoustic emission is at order 2. It is in fact the main advantage of acoustic emission measurements.However, the contribution of the deterministic part is lost.
Similarly to vibration analysis, Figure 8b clearly highlights the CSD of ultrasonic signal of the defective bearing, showing the manifestation of BPFO and its harmonics around the resonance [500-1500 Hz] with a level of energy of the CSD definitely larger than for the healthy bearing (Fig. 8a).
Comparison between vibration and acoustic emission
Figures 9-11 represent the CSD of vibration and acoustic measurements for the defective bearing at speeds of 300 rpm, 600 rpm and 900 rpm, respectively.It can be noticed that acoustic emission detects BPFO and its harmonics for all speeds.However, the vibration measurements show only the manifestation of BPFO when operating at low speed (300 rpm) but only an increase of the energy at high frequencies around the resonance can be noticed for the two other speeds.In conclusion, it is clear that the acoustic emission measurement is more efficient to detect a defect than vibration measurements when the defect is very small (40 μm) for an early stage of degradation when increasing the speed.
New indicator of cyclostationary
In order to track the defect evolution, Kilindu et al. [13] proposed a new indicator called Integrated Spectral Correlation denoted ICS, to evaluate energy at the defect frequency (Eq.( 2)) from the CSD.The indicator is computed by integrating the magnitude of the spectral correlation between α 1,2 = f bearing (1 ± 1%) along α-axis, and for all the values along f -axis (Eq.( 2)).
where f s is the sample frequency.If the defect is applied to outer race, the bearing frequency BPFO appears: where Bd is the diameter of the balls; P d is the diametral pitch; θ is the contact angle; N b is the number of balls and w is the rotational speed.However, it is well known that the increase of degradation of a faulty bearing not only causes an increase in the amplitude of the vibration frequencies of bearings, but also generates vibration harmonics of these frequencies as well as modulation frequencies.Consequently, the key of diagnostic relies on the number of harmonic of the bearing frequency and of their modulation frequencies [19,20].
We have tried to develop two new indicators like ICS that are denoted ICS 1 and ICS 2 which take into account the amplitude modulation of the defects and the frequency resonance of the bearing: -For the first one, the ICS is computed by integrating the magnitude of the cyclic spectral density between (BPFO − 2.2 × F r and BPFO + 2.2 × F r) along α-axis, and for all the values f around the resonance (Eq.( 4)).
where a = n × BPFO − (2.2 × f r ) and b = n × BPFO + (2.2 × f r ) and f r is frequency of rotational speed.-For the second one, the ICS is computed by integrating the magnitude of the cyclic spectral density between (BPFO − 2.2 × F r, BPFO + 2.2 × F r) along α-axis, and for all the values along f -axis (Eq.( 5)).
Figure 12 shows the indicators (ICS, ICS 1 and ICS 2 ) computed for the healthy bearing (Blue bar) and the defective bearing (Red bar) at different speeds.When rotating at 300 rpm, all the three indicators may distinguish between the healthy and defective bearing and it can be noticed that the two new indicators (ICS 1 and ICS 2 ) are more sensitive than the ordinary ICS.However, at higher speeds (600 and 900 rpm), all these indicators are not efficient.We suppose that the problem may be due to the fact that when the defect size is very small, the amplitude of the healthy bearing is equivalent to the amplitude of the defective bearing due to the effect of other excitations that act in the high frequency domain (friction, lubricant, etc.).
For enhancing these indicators, we have investigated three new indicators.We propose to normalize the previous indicators by dividing them by time descriptors of the original signal.The new indicators (ICSN: Integrated Cyclic Spectral Normalised) are normalized relative to their RMS, Skewness, and kurtosis given by Equations ( 6)- (8).Table 1 presents the values of the temporal descriptors of the healthy bearing and the defective one.It is well known that the Kurtosis and Skewness are so sensible to random chocks.Due to the effect of excitations, that act in the high frequency domain (friction, lubricant, etc.), the healthy bearing produces random chocks.For this reason we note that the Kurtosis and Skewness of the healthy bearing are greater than for the defective bearing.-When rotating at low speed (300 rpm), all the indicators normalised are efficient and the ICSN 2 is the best compared to others indicators.-When rotating at 600 rpm, only ICSN 2 makes a difference between the healthy and the defective bearing, for all the indicators.-However, when rotating at higher speed (900 rpm), only ICSN 2 normalised by Skewness (Fig. 15) allows for making a difference between the healthy and the defective bearing.Figure 15 shows that all these indicators normalized by skewness were able to distinguish a defective bearing from a healthy one, whatever the rotating speed.However, the indicator ICSN 2 normalised by Skewness revealed to be more sensitive than the two others by making a large difference between the healthy and the defective bearing for all the speeds (Fig. 15).Consequently, we propose to adopt this indicator (ICSN 2 ) for the monitoring of acoustic emission signals applied to bearing diagnosis.
Conclusion
This study focused on the potential of cyclostationary tools applied to the acoustic emission to detect a very small defect (40 microns) compared with the vibration measurement.Two bearings (defective and healthy) were investigated on a test bench at different speeds.This study highlights the cyclostationarity character of acoustic emission measurements.The cyclic spectral density (CSD) is computed for all acoustic emission and vibration signals and the results show that the acoustic emission measurement is more efficient than the vibration measurement for an early detection of degradation even when defect is very small (40 μm) especially when increasing the speed.A new indicator (called ICSN 2 ) is developed for the monitoring of acoustic emission signal.This indicator is based on the amplitude of the cyclic spectral density computed into a bandwidth close to bearing frequencies and its harmonics and normalized by the Skewness of the time signal.It must be noticed that this study is the first one able to detect a so small defect on bearings (40 microns).Further tests are planned with several defects of different sizes to explore the full potential of this method; the results will be confirmed later.
Fig. 7 .
Fig. 7. (a) Ultrasonic signal of the defective bearing, (b) second order after applying the RRCR method of the defective bearing, (c) spectrum of (a) and (b) of the defective bearing, (d) spectrum of the healthy bearing.
Figures 13 -
15 show the indicators normalised by RMS, Kurtosis and Skewness, respectively, and computed for the healthy bearing (Blue bar) and the defective bearing (Red bar).
Table 1 .
Temporal descriptors for the healthy and the defective bearing at different speeds.
Fig. 13.Indicators of cyclostationarity normalized by RMS for different speeds, healthy bearing, defective bearing. | 3,911.6 | 2014-01-01T00:00:00.000 | [
"Materials Science"
] |
An Overview of Ecopreneurship, Eco-Innovation, and the Ecological Sector
: Given the current trend toward a more sustainable and environmentally-friendly economy, the overlap between entrepreneurship and sustainability has become a key research area. Part of this trend is the emergence of ecopreneurial businesses. These businesses are pioneers in using innovation to achieve sustainable growth by exploiting market opportunities. This article presents an overview of the concepts of ecopreneurship, eco-innovation, and the ecological sector. A rigorous review of the literature in this area is presented. The results of this review show the key values and principles that are central to this new stream of research and shed light on opportunities for further research. The primary conclusion is that there is a need for collective collaboration between ecopreneurs, consumers, and producers to achieve long-term sustainability.
Introduction
Concern for the environment and the preservation of natural resources has increased in recent years [1].According to several studies, firms should orient their business activity toward providing value across three dimensions: economic, social, and environmental [2][3][4].The focus on these three dimensions is referred to as the triple bottom line.
A new stream of research has recently appeared in the entrepreneurship literature.This new stream of research explores corporate strategies that focus on the environmental dimension [5].This focus does not overlook other dimensions (social and economic).However, priority is given to addressing the effect of the negative externalities of firms' economic activity on these firms' immediate surroundings.The goal is, therefore, to build a business model that is sustainable in the long run [6,7].Ecopreneurship and the ecological sector contribute to achieving this goal.The concept of ecopreneurship is based on three pillars: innovation, caring for the environment, and long-term sustainability [8].
The term ecopreneurship is a portmanteau word formed from combining the form eco (as in ecological) and entrepreneurship.The term eco comes from the Greek work eikos, which literally translates as home.Ecology is the branch of science that studies how our home functions in the sense of our environment and surroundings.People's interest in taking care of and preserving biological resources has increased in response to a model of production that consumes natural resources more quickly than they can recover.Under such a model, resources are depleted more quickly than they are replenished [9].
Entrepreneurship, on the other hand, is generally defined as the discovery of gaps in the market in which entrepreneurs are capable of spotting and exploring new business opportunities [10][11][12].Thus, ecopreneurship is the search for new opportunities that help protect the environment in pursuit of environmental sustainability [13].Chopra defines ecopreneurship as "entrepreneurship through an environmental lens" [14] (p. 1).
In light of this situation, the popularity of environmentalism and ecologism is increasing from a practical perspective as well as from a purely theoretical or academic perspective [15].A production model that minimizes the negative externalities affecting the planet is needed [16].Therefore, studying how key actors such as consumers, distributors, and producers respond to this transition toward a more sustainable and ecological model is of interest [17].
Ecological consumers are primarily characterized by their adoption of environmentally responsible behaviors.Studying the profile of ecological consumers is a key task in the design and execution of an organization's competitive strategy [18,19].Today, social, political, and technological changes do not take place gradually as the result of a steady trend [20].Instead, disruptive changes occur over a short period.These rapid, drastic changes cause discontinuities.A new production model has been developed to address this environmental turmoil and ensure long-term well-being [21].The ecological sector is considered a strategic way of adapting to change [22,23].
Doma ńska et al. [4] reported that, for firms to strike a balance between value creation across the social, economic, and environmental dimensions, there must be certain incentives at the national level.Accordingly, it is argued that the main challenge for government institutions is to decide on the right level of incentives in the form of subsidies to ensure that firms are green-oriented.Therefore, there is a research gap in the analysis of the role of institutions with respect to ecopreneurship.
In addition, most studies on ecopreneurship have focused on defining the concept in theoretical terms [7,13,14,23].We, therefore, believe it is important to adopt a real-world focus on creating environmentally-friendly businesses through an alternative commercialization system such as the ecological sector.
This article offers extensive analysis of the current state-of-the-art ecological entrepreneurship and presents an integrative framework.It describes the link between ecopreneurship as a new way to sustainably generate economic activity and the ecological sector as a system that complements ecopreneurship in the pursuit of environmental-friendliness.This article highlights the synergies that arise from collaboration between all actors involved in production, distribution, and commercialization in this business alternative.The aim of this research is to compare previous studies to define and establish the principal features of ecological entrepreneurship as a subcategory of entrepreneurship.This study responds to calls from numerous scholars to further analyze the relationship between environmentalism and entrepreneurship in the business setting [7,23,24].This study also contributes to advancing the growing literature on ecopreneurship by presenting ideas for future lines of research.
This study is organized into three main sections.Section 2 presents a review of the literature on ecopreneurship and the key factors and features of ecological consumers.In this section, we also describe the status of the ecological sector and the actors that operate within this sector.Section 3 presents the main conclusions of the study.We end the study by discussing implications, contributions, and ideas for further research.
Theoretical Framework
A systematic literature review was conducted to develop an integrative framework for ecopreneurship.The Web of Science (WoS) scientific database, which is compiled by Clarivate Analytics, was used.A high level of rigor, quality, and reliability were the main drivers of this decision.Because there is still no consensus in academia concerning environmentally sustainable entrepreneurial activity, various keywords were used to refer to the same concept: ecopreneurship, green entrepreneurship, sustainable entrepreneurship, and environmental entrepreneurship.Emulating the systematic review by Parida et al. [25], the filter was applied only to scientific articles and book chapters.
The following bar chart [Figure 1] shows that ecopreneurship remains in its nascent stages despite following a positively increasing trend.The first articles date from 1992, although it was not until 2010 that the subject became more relevant to scholars.As environmental issues gain popularity among scholars and practitioners, sustainable ways of doing business become an increasingly prevalent subject of study.
among scholars and practitioners, sustainable ways of doing business become an increasingly prevalent subject of study.The first implication of an ecological transition is that solutions to today's environmental and social problems cannot be found by applying the same methods and processes that caused these problems in the first place.These solutions should be based on innovation that is aimed at sustainable growth and the efficient management of natural resources [26].Traditionally, natural resources have been in the hands of the government and other state institutions.However, under a new paradigm, it is argued that local actors such as social associations or business networks are becoming key elements in the advancement toward sustainable development through effective exploitation of local resources [27,28].Similarly, to generate knowledge at the local level, establishing interconnected networks that encourage the creation of new organizations is necessary [29,30].
Knowledge of co-creation is the antecedent to entrepreneurial learning [31,32].According to the resource-based view, specific resources can provide sustainable competitive advantages [33], and business success is based on obtaining economic rents that exceed those of competitors.Beyond this resource-based view, the adaptive management view and entrepreneurial learning offer the most suitable approach to deal with environmental issues.According to the adaptative management view, entrepreneurial learning takes place not only at the individual level within the firm but also as a result of cooperation and joint participation of the stakeholders in a given environment [27,34].
According to Cantino et al. [27], outperforming competitors in terms of income fails to offer a solution to the social and ecological threats faced by all firms.Therefore, entrepreneurial learning is a key element in the advancement toward the creation of sustainable firms that are capable of protecting the environment [27,35] as well as exploring new opportunities to create environmental value [36].
The negative effects of the economic development model of "take, make, dispose" [37,38] pose a grave threat to the progress of economies on a global scale and the long-term sustainability of natural resources.Social and environmental challenges cannot be solved using the same means of production that created them in the first place.Therefore, part of the process of entrepreneurial learning lies in the development of new business models [39].The key is to fundamentally break our dependence on the dominant production models.For example, agroecology enables producers to recover their social focus and autonomy.Similarly, the circular economy optimizes the free circulation of both raw materials and waste and firmly favors the local economy.The circular economy is a new business model that aims to achieve more sustainable and environmentallyfriendly development, with a particular focus on urban and industrial waste to "achieve a better balance and harmony between the economy, environment, and society" [37] (p.11) The circular economy, therefore, entails the adoption of production methods that are cleaner and more ethically The first implication of an ecological transition is that solutions to today's environmental and social problems cannot be found by applying the same methods and processes that caused these problems in the first place.These solutions should be based on innovation that is aimed at sustainable growth and the efficient management of natural resources [26].Traditionally, natural resources have been in the hands of the government and other state institutions.However, under a new paradigm, it is argued that local actors such as social associations or business networks are becoming key elements in the advancement toward sustainable development through effective exploitation of local resources [27,28].Similarly, to generate knowledge at the local level, establishing interconnected networks that encourage the creation of new organizations is necessary [29,30].
Knowledge of co-creation is the antecedent to entrepreneurial learning [31,32].According to the resource-based view, specific resources can provide sustainable competitive advantages [33], and business success is based on obtaining economic rents that exceed those of competitors.Beyond this resource-based view, the adaptive management view and entrepreneurial learning offer the most suitable approach to deal with environmental issues.According to the adaptative management view, entrepreneurial learning takes place not only at the individual level within the firm but also as a result of cooperation and joint participation of the stakeholders in a given environment [27,34].
According to Cantino et al. [27], outperforming competitors in terms of income fails to offer a solution to the social and ecological threats faced by all firms.Therefore, entrepreneurial learning is a key element in the advancement toward the creation of sustainable firms that are capable of protecting the environment [27,35] as well as exploring new opportunities to create environmental value [36].
The negative effects of the economic development model of "take, make, dispose" [37,38] pose a grave threat to the progress of economies on a global scale and the long-term sustainability of natural resources.Social and environmental challenges cannot be solved using the same means of production that created them in the first place.Therefore, part of the process of entrepreneurial learning lies in the development of new business models [39].The key is to fundamentally break our dependence on the dominant production models.For example, agroecology enables producers to recover their social focus and autonomy.Similarly, the circular economy optimizes the free circulation of both raw materials and waste and firmly favors the local economy.The circular economy is a new business model that aims to achieve more sustainable and environmentally-friendly development, with a particular focus on urban and industrial waste to "achieve a better balance and harmony between the economy, environment, and society" [37] (p.11) The circular economy, therefore, entails the adoption of production methods that are cleaner and more ethically responsible for the environment as well as promotes awareness among producers and consumers and uses renewable technologies and materials [40].
The terms ecopreneurship and environmental entrepreneurship are used interchangeably [16,23] to denote innovative behavior by individuals and organizations that operate in the private sector and that view an environmental focus as the main pillar of the business model and sustainable competitive advantage.According to Kirwook and Walton [41], ecopreneurship consists of creating new business ideas by stressing sustainability as a basic principle.
By showing the economic benefits of being more ecological and environmentally-friendly, ecopreneurs act as a pull factor that encourages other businesses to be ecologically proactive.This role contrasts with push factors such as government regulations and pressure by stakeholders and organizations such as NGOs [24,42].Ecopreneurship has also been identified as a new way of participating in the commercialization of ideas, products, and services where the outcome of the exchange between the provider of services and the consumer is positive for both parties as well as for the environment.
Ecopreneurship is related to the economic concept of the common good, which refers to fostering and imparting the human values of dignity, solidarity, sustainability, social justice, democracy, and transparency.The economy of the common good has a broad scope and covers principles that concern not only people but also the environment.The goal is for the firm to conduct its business activities without negatively affecting people and the environment.
According to stakeholder theory [43,44], companies must strive to meet all stakeholders' aims and, thereby, foster social and institutional sustainability.For firms, the application of this model means an increase in economic profitability [45] and even provides the opportunity to gain a competitive advantage by offering consumers a differentiated product.One important group of firms' stakeholders consists of governments and political leaders, who, in recent times, have implemented restrictive, demanding policies to encourage care for the environment.Organizations such as NGOs are playing an increasingly prominent role in a changing world made highly fragile by intensive consumption of natural resources that is exhausting biological reserves.
The opposite stance is the neoliberalism expounded by Milton Friedman [46].Under this approach, the maximization of economic profit should be the primary objective of all organizations.Accordingly, corporate social responsibility (CSR) would be thought to have a negative impact on financial profitability.Milton Friedman's approach relates to a neoliberal system and a conventional method of production, which is characterized by the pursuit of profit and competition.However, Gamble et al. [44] have argued that the effect of the negative externalities of firms on stakeholders must be reduced.Accordingly, it is essential to find a new economic and production model that responds to the economic, social, and environmental needs of the 21st century from an integral, holistic perspective.
The literature review shows that the terms ecopreneurship, environmental entrepreneurship, and ecological or green entrepreneurship are used interchangeably [16].The figure of the ecopreneur is limited to a single individual.This individual may be the creator of an organization in the environmental sector or an environmental intrapreneur.Environmental intrapreneurs are defined as employees of existing companies who revitalize and strengthen these companies [47].In contrast, according to virtually all interpretations, ecopreneurial companies base their behavior on ecological values and promote environmental entrepreneurs both inside and outside the company itself.Similarly, many authors argue that ecopreneurship is intricately linked to the implementation of innovations.Therefore, these two concepts go hand in hand [24,[48][49][50].
Depending on the focus and the way in which innovation occurs, there are different conceptual approaches to ecopreneurship.The most relevant approaches are presented in Table 1.
Approach
References Definition 1 Gerlach [50], Lober [51], Pastakia [52], Petersen and Schaltegger [53] Ecopreneurship is based on implementing innovations in the environmental sector.The ecopreneur is aware of the environmental impact that her or his business exerts on the surroundings and develops innovations that reduce this impact. 2 Volery [54], Azzone and Noci [55], Isaak [56], Larson [57], Porter and van der Linde [58], Holger [59] Ecopreneurship is a strategic tool.The application of sustainable policies has a twofold benefit: it improves profit prospects and is kind to the environment. 3 Anderson [60], Kÿro [61], Cantino et al. [27] Ecopreneurship is a tool to transform society.Ecopreneurs play a key role in the evolution and development of institutions.
Source: Compiled by the authors based on Gerlach [50].
According to Approach 1 [50][51][52][53], ecopreneurship is based on the successful implementation of innovations that result in new products or services.Petersen and Schaltegger [53] describe ecopreneurship in terms of recognizing, creating, and exploiting opportunities presented by the market using ecological innovations.The proponents of Approach 2 define ecopreneurship as a strategic tool [54][55][56][57][58][59].These authors' research shares one key principle: that the activities carried out in the ecopreneurial sector give the organization a competitive advantage [54].These scholars view environmental issues as one of the priorities of corporate strategy [55,56].Along these lines, Porter and van der Linde [58] argue that innovations that lead to an improvement in organizational productivity are associated with greater competitiveness.The logic behind this assertion is that these organizations have a much smaller negative impact on the environment but also have better cost structures.Furthermore, the quality of the products and services that they supply is higher.Approach 3 has a sociological focus [27,60,61].The proponents of this approach study how the origins of the environmental economy and the principles of ecology relate to the entrepreneurial and business spirit.The cited proponents of this approach have concluded that business and, thus, entrepreneurial spirit can be used to change society [60,61].Thus, this approach addresses the role of ecopreneurs in society and the way that ecopreneurship can be used as a vehicle for change in social structures [61].Based on the adaptative management approach, the learning processes of a social network are totally integrated into the social structure.Hence, the exploitation of new opportunities sometimes requires institutional changes [27,62].
Given these different approaches to ecopreneurship, it is important to highlight differences with respect to social entrepreneurship.Social entrepreneurship refers to innovative behavior by individuals or organizations in the private sector that place social goals at the center of their corporate strategy [63,64].Social entrepreneurs combine entrepreneurial activity with a social mission [65].They identify unexploited resources and create new services and products based on these resources to improve general well-being [66,67].Using the concept of social entrepreneurship in its broadest sense as concern for society, the term "social" implicitly encompasses environmental issues.Thus, from a certain perspective, social entrepreneurship includes environmental entrepreneurship [68,69].
Eco-Innovation
As explained earlier, ecopreneurship cannot be understood without considering innovation [70].Ecopreneurship and innovation are two distinct yet interrelated concepts that have a symbiotic relationship in the context of environmental development.The Environmental Technology Action Plan (ETAP), which was adopted by the European Commission (EC) to promote eco-innovation and the use of environmental technologies [71], defines environmental innovation as follows: "the production, assimilation, or exploitation of a novelty in products, production processes, services, or in management and business methods, which aims, throughout its life cycle, to prevent or substantially reduce environmental risk, pollution, and other negative impacts of resource use (including energy)." In 2004, the EC cited eco-innovation as one of the key factors to Europe's competitiveness: "Eco-innovation is any innovation resulting in significant progress toward the goal of sustainable development, by reducing the impacts of our production modes on the environment, enhancing nature's resilience to environmental pressures, or achieving a more efficient and responsible use of natural resources."In addition, ecological innovation helps reduce costs, take advantage of new development opportunities, and improve a company's image in the eyes of customers [72].
According to Tomás-Estrada [73], innovation that is applied to cities can be defined as the actions aimed at improving the functioning of the city in economic, social, and environmental terms.These three dimensions promote urban innovation.We focus on the environmental dimension, which refers to the practice of encouraging a reduction in the environmental impact of business.
Eco-innovation is a key element because it increases value for both producers and consumers while reducing negative impacts on the environment [73].In a global context, where change is increasing and innovation is disruptive [74], sources of competitive advantage must be created [75], and differentiation strategies must be developed through eco-innovation.Investment in eco-innovation enables firms not only to gain a privileged market position but also to maintain this position in the long term.If firms are unable to compete through cost, they can compete through innovation [33,76].The trend is positive and increasing, and the data reflect the tertiarization of the economy.Therefore, eco-innovation should not be overlooked in service sectors [77].In the ecological domain, these innovations may originate by viewing the environment as an engine for strategic change [78].Eco-innovations can take place in three business areas, as Table 2 shows [79].
Process innovations
These innovations relate to the production of goods and services.The goal is usually to enhance eco-efficiency.In most cases, these improvements are based on the use of more environmentally-friendly production technologies [80].
Organizational innovations
These innovations relate to restructuring within the firm.These innovations primarily concern employees and the organization of their work tasks.New forms of management such as the adoption of environmental management models also fall into this category.
Product innovations
These innovations refer to the development of a completely new product or service or the improvement of an existing product or service.For example, ecological design could offer a good alternative to producing products that use natural resources more efficiently.The use of recycled organic materials is an example of the improvement of an existing product.The development of long-term sustainable environmental technologies such as renewable energy technologies entails the development of new products in the market [2,80].
The evolution and development of eco-innovation and ecopreneurship would be impossible without the support of other key elements in the ecological transition [Figure 2].These elements include ecological consumers, whose consumption habits define a new lifestyle.
Characteristics of Ecological Consumers
The ecological consumer landscape is shaped by the values, norms, and habits of consumers in a given context.Peattie [81] argued that the development and evolution of production and consumption systems that seek a balance with the environment and long-term sustainability ultimately depend on the willingness of consumers to collaborate and encourage more ecological consumption practices [82].Consumers must, therefore, identify with this new production model and must be aware of the environmental impact of the production and consumption of the products they use.Accordingly, consumers who feel that their decisions have a significant environmental and social impact are more willing to behave sustainably.This is the only way to achieve a shift toward economies that are more viable in the long term and economies that are more environmentallyfriendly.
According to Pardave [83], ecological consumers avoid any product that is synonymous with unnecessary waste and threatens the environment.In other words, ecological consumers avoid products with production processes that harm the planet and that entail an abuse of biological resources [83].According to this definition, ecological consumers uphold not only a lifestyle but also a new model of understanding the way we live.This new model proposes local, non-excessive consumption and production of small quantities of goods and services [84].
Characteristics of Ecological Consumers
The ecological consumer landscape is shaped by the values, norms, and habits of consumers in a given context.Peattie [81] argued that the development and evolution of production and consumption systems that seek a balance with the environment and long-term sustainability ultimately depend on the willingness of consumers to collaborate and encourage more ecological consumption practices [82].Consumers must, therefore, identify with this new production model and must be aware of the environmental impact of the production and consumption of the products they use.Accordingly, consumers who feel that their decisions have a significant environmental and social impact are more willing to behave sustainably.This is the only way to achieve a shift toward economies that are more viable in the long term and economies that are more environmentally-friendly.
According to Pardave [83], ecological consumers avoid any product that is synonymous with unnecessary waste and threatens the environment.In other words, ecological consumers avoid products with production processes that harm the planet and that entail an abuse of biological resources [83].According to this definition, ecological consumers uphold not only a lifestyle but also a new model of understanding the way we live.This new model proposes local, non-excessive consumption and production of small quantities of goods and services [84].
Martínez [85] affirmed that such consumers tend to be aware of their practices in terms of the consequences of their consumption habits.These practices can contribute positively to sustainable development as well as the quality of life where they live and the surrounding area.The contribution is possible because these practices place less priority on the higher costs that must be borne to support this type of consumption in the long run.Therefore, ecological consumers are often associated with the Greek philosophy of stoicism.According to stoicism, life cannot be understood without a concern for others.It relates to the awareness that people have of the environment where they live.Thus, the main aim is to achieve a state of happiness and wisdom by constantly eliminating superfluous conveniences, material goods, and wealth.
Antonetti and Maklan [86], on the other hand, affirmed that feelings of guilt and responsibility, which are the fruits of consumption, encourage ecological consumers to alter their habits in pursuit of more environmentally-friendly practices.Thus, they argued that, when consumers experience these feelings, they view themselves as the main threat to the environment because of their consumption behaviors and, therefore, decide to alter their habits.Changing these habits means consuming more environmentally-friendly products that are produced using non-conventional production methods.Thus, in the context of ecopreneurship, the firm in its capacity as an organization also represents a key element of the ecological transition.
Ecological Companies and Products
Regarding ecological companies and products, we must first distinguish between ecological products, fair trade, and local consumption.Although these three concepts are intricately linked and are not promoted through conventional distribution channels, they have certain differences.In all three cases, consumers that seek ecological, fair trade, or local products show a willingness to shift toward a more sustainable model of production and consumption [87].In many cases, it is a question of consumer activism, which is synonymous with embracing certain values to fight against threats to the environment and social justice.The related lifestyles of vegetarianism and veganism also support the fight for animal welfare.Vegetarian consumers belong to the group of consumers who are aware of their surroundings and seek to build a model in which economic activity goes as far as possible not to harm the available natural and biological resources.In the search for a more sustainable and environmentally-friendly system, many stakeholders have the power and the responsibility to carry out this transformation in pursuit of the common good [88].This is so because achieving more sustainable practices requires the coordination and support of all parties involved in the production and consumption processes [Figure 3].
Martínez [85] affirmed that such consumers tend to be aware of their practices in terms of the consequences of their consumption habits.These practices can contribute positively to sustainable development as well as the quality of life where they live and the surrounding area.The contribution is possible because these practices place less priority on the higher costs that must be borne to support this type of consumption in the long run.Therefore, ecological consumers are often associated with the Greek philosophy of stoicism.According to stoicism, life cannot be understood without a concern for others.It relates to the awareness that people have of the environment where they live.Thus, the main aim is to achieve a state of happiness and wisdom by constantly eliminating superfluous conveniences, material goods, and wealth.
Antonetti and Maklan [86], on the other hand, affirmed that feelings of guilt and responsibility, which are the fruits of consumption, encourage ecological consumers to alter their habits in pursuit of more environmentally-friendly practices.Thus, they argued that, when consumers experience these feelings, they view themselves as the main threat to the environment because of their consumption behaviors and, therefore, decide to alter their habits.Changing these habits means consuming more environmentally-friendly products that are produced using non-conventional production methods.Thus, in the context of ecopreneurship, the firm in its capacity as an organization also represents a key element of the ecological transition.
Ecological Companies and Products
Regarding ecological companies and products, we must first distinguish between ecological products, fair trade, and local consumption.Although these three concepts are intricately linked and are not promoted through conventional distribution channels, they have certain differences.In all three cases, consumers that seek ecological, fair trade, or local products show a willingness to shift toward a more sustainable model of production and consumption [87].In many cases, it is a question of consumer activism, which is synonymous with embracing certain values to fight against threats to the environment and social justice.The related lifestyles of vegetarianism and veganism also support the fight for animal welfare.Vegetarian consumers belong to the group of consumers who are aware of their surroundings and seek to build a model in which economic activity goes as far as possible not to harm the available natural and biological resources.In the search for a more sustainable and environmentally-friendly system, many stakeholders have the power and the responsibility to carry out this transformation in pursuit of the common good [88].This is so because achieving more sustainable practices requires the coordination and support of all parties involved in the production and consumption processes [Figure 3].
Fair Trade
According to the World Fair Trade Organization (WFTO), fair trade is a trade system based on dialogue, transparency, and respect that seeks greater equality in international trade by focusing on social and environmental criteria.It contributes to sustainable development by offering better trade conditions and ensuring the rights of disadvantaged producers and workers.It is an alternative system of intermediary-free trade designed to support the development of people and fight poverty.The WFTO enables workers to enter an international market that they would, otherwise, be unable to access.
Ultimately, the decision lies with the consumer.It is, nonetheless, necessary to have an effective distribution network that works together and is capable of reaching the consumer through promotion and help from the government.Therefore, synergies between different groups affected by the ecological transition are necessary to achieve long-term well-being for everyone [89].These synergies are only possible with the alliance and cooperation of the producers and distributors as well as the demands of consumer activists.These consumers are aware of the need for environmental protection and a healthy diet free from toxic substances.
In different European countries, different stakeholders have promoted this kind of consumption and production.In Germany, the government has applied several trade policies in supermarkets and distributors, rewarding more environmentally-friendly products and encouraging the consumption of healthy, sustainable food [90].All producers in this industry have been affected by these new regulations and have had to adapt their strategies and products to meet the government's demands.In contrast, in France, external regulations have been unnecessary because the supermarkets already stock these new products [91].
In this review of the European ecological sector, the Nordic countries (Denmark, Finland, Sweden, Norway, and Iceland) deserve special attention.These countries are the major force in ecological consumption and production [92].For example, Denmark was the first country to regulate ecological products, which created a national logo for this type of market 25 years ago.Surveys show that 97% of the population is familiar with this industry.Pursuing this environmentally-friendly path, Denmark aspires to become the first country that only produces ecological food.In the Nordic countries, the government, consumers, and the business world have joined forces.Innate values and principles in the national culture and customs place Denmark in a leading position in terms of market share of ecological products and per capita consumption of ecological products [92,93].
In commercial terms, the ecology sector reflects a trend that resembles that of healthy restaurants or healthy living [94].As soon as consumers demand that supermarkets stock ecological products, these businesses will be the first to display them on their shelves.As of today, however, supermarkets do not consider this sector to be profitable.Thus, price should not be a determinant of whether to make this kind of purchase because the slightly higher price is justifiable on the grounds of quality, the value offered to the consumer, and the value received by the producer on the other side of the world [93].
Like many other institutions that support fair trade, Oxfam is fully aware that the satisfaction of Western customers is crucial to support the business model in the long term and to achieve the economic profitability it needs to continue.Thus, the aim of this type of organization consists of analyzing the current trends in Europe and studying how these trends can be met with the resources and capabilities in disadvantaged parts of the globe such as South America.
Local Consumption
Local consumption can be achieved by establishing sustainability policies in specific settings where this type of consumption is a key driver of the economy.Informal networks can also be established by purchasing products from producers who are known to consumers or cooperatives that sell their products in the local town or region.Local consumption is part of an ecosystem where the preference is for local goods and services as part of a social system that promotes environmental sustainability and a healthy diet.Consuming local products also reduces both companies' and consumers' carbon footprints because it reduces or even removes intermediaries from the interactions between the producer and the consumer.This reduction in the number of intermediaries decreases greenhouse gas emissions from transporting these products.
The fact that the number of intermediaries is lower also implies that products are fresher because the time that elapses between being collected and reaching the consumer is lower.Furthermore, artificial substances are unnecessary to keep the products fresh for longer.Therefore, local consumption usually refers to small-sized and medium-sized enterprises (SMEs) located in a particular area that promote ecological and sustainable values [94,95].
Shrivastava and Kennelly [96] as well as Cantino et al. [27] used the concept of the place-based enterprise in their research.For these authors, this concept refers to organizations that act on a local scale and that play a key role in the development and advancement of sustainability policies in their immediate surroundings.Through the adaptative management view and knowledge co-creation, this type of firm can follow the path toward sustainability [97].As mentioned earlier, the role of government institutions in the management of natural resources is gradually being taken by local organizations.Collaboration between all stakeholders and local organizations is necessary to ensure the success of adaptative management and knowledge of co-creation [98].
Organic Products
Lastly, organic products respect the environment through chemical-free production that is free from fertilizers, pesticides, and the like [99].However, if these products are not obtained locally, the carbon footprint of the product will be greater, which reduces its green value.Thus, it is easy to see how these three concepts (organic, fair trade, and locally grown) are interrelated.
Organic products and organic meat offer a production system that differs from conventional production to achieve a balance between the economy and nature.Furthermore, this is a profitable formula for sectors that produce natural products using organic methods, which eliminates the consumer-health and environmental risks associated with chemical products such as the fertilizers and conservatives used in conventionally produced food [100].
Another important instrument is the organic label.Regulations governing organic production are imposed by the European Union (EU) under the EU Organic Logo.Since its creation in 1992, this logo has provided a key tool to encourage environmental action by EU member states.It is one of the measures included in the EU's Sustainable Consumption and Production and Sustainable Industrial Policy Action Plan.
This logo is voluntary, so it depends fully on the seller's willingness to sell this type of product or, conversely, to use conventional methods.The advantages of this logo include enhancing customers' trust in the product by indicating the strict standards it must meet to be considered organic.Products are inspected annually, and the logo is recognized in all countries that form part of the agreement.The reputation of the firm is positively affected by showing a concern for the environment and social awareness [72].
Organic agriculture is defined by the European Commission as an "agricultural method that aims to produce food using natural substances and processes and tends to have a limited environmental impact" [101].The criteria used to determine whether a product is organic include the following: periodic crop rotation so that resources in a given location are not exhausted and are used efficiently, the limitation of pesticides, fertilizers, antibiotics, or any chemical product, the prohibition of transgenic and genetically modified organisms, the promotion of local species because of their capacity to adapt to local conditions, and organic feeding and free range rearing of livestock.
In Europe, the demand for organic production greatly outweighs the supply because the mechanisms to respond to the demands of increasingly environmentally-aware consumers are still insufficient.Therefore, although the preference is to consume locally produced products, organic consumption often relies on internationally sourced products.Accordingly, organic products that are commonly imported to the EU include coffee from Brazil, kiwi fruit from New Zealand, rice from Thailand, and coconuts from Peru.Producing this type of food is also strongly related to fair trade.In addition, the leaders of companies that produce organic food as well as crop and livestock farmers are much younger than the average worker in this sector of Europe [91].
Conclusions, Limitations, and Future Research
This article offers an integrative framework of the current state of a new stream of entrepreneurship: ecopreneurship.Our review of the literature on this concept identifies its key features.This study also contributes to the literature by exploring the links between ecopreneurship and eco-innovation.Both of these terms are based on the pursuit of environmental-friendliness.In this framework, it is crucial to note the key role of consumers in promoting green practices and choosing organic products.It is necessary to understand the importance of the long-term search for sustainability by entrepreneurs [102] as well as scholars [103] and to search for ways to encourage care for the environment, which is ultimately our home (eikos).
To achieve sustained and consistent progress in this sector, active collaboration between consumers, producers, distributors, and the government is necessary.The promotion of a more sustainable and environmentally-friendly production model will not work unless sustainable policies and initiatives are supported by all parties involved in the production and consumption processes.Consumers play a crucial role in this sense because they ultimately determine product value through their consumer habits [101].However, consumer activism achieves nothing unless the government supports this activism with laws and measures that ensure that consumers' demands are met and that production and distribution are compliant.The positive contribution of all actors can, therefore, foster operational synergies in the sector [104].Thus, both prevalence in the market and the ease of distribution will increase consumers' access to this type of product to benefit people's health and take better care of the environment [105].
In addition, introducing certain organic, fair trade, and local products in supermarkets reflects a change in mentality.There is a general trend toward increasing the range of products that are certified with the organic logo.However, a minimal rotation of these products is necessary to keep them on the supermarket shelves.Therefore, collaboration between producers, distributors, consumers, and public agencies is necessary to achieve this steady, consolidated growth [43].
Although ecopreneurship is in a phase of constant growth and progress, it also faces numerous difficulties that hinder its development and prevent it from being fully exploited.The main challenge is to achieve sustainable long-term growth.As mentioned earlier, the prosperity of this phenomenon ultimately depends on the concerted effort of all actors.Therefore, steady, consolidated growth is affected by the actions of all those involved.Another major challenge facing this sector is the lack of information and, particularly, the lack of visibility of this business model or products derived from this business model.As Brugarolas and Rivera [105] affirmed, ecological consumers would be prepared to consume goods with the organic logo.However, they feel that the information at their disposal is limited, and they know little about this new form of production.Therefore, the prominence of the sector in the market must be increased to promote and incentivize society to modify its consumption habits.The key element in resolving this issue is to find a place where supply and demand converge.This demand is growing and is driven by a growing concern for environmental issues [5].
Limitations and Implications
One of the limitations of this article is that it only analyzes the concept of eco-innovation as a determinant of ecopreneurship, overlooking other crucial factors such as environmental entrepreneurial orientation.This article offers a theoretical framework for ecopreneurship that is of interest for ecopreneurs as well as firms focused on innovation for environmental sustainability, organizations seeking to promote CSR policies, and governments that wish to contribute positively to the environment and society.
Future Research
Several potential lines of research on ecopreneurship and sustainability may be highlighted.First, the theory must be developed and broadened.Although numerous authors have studied this concept, a more solid theoretical grounding is necessary, and the concepts and definition related to ecopreneurship must be unified.It would be of interest to analyze ecopreneurship and eco-innovation initiatives through empirical testing to offer insight into the effects of ecopreneurs and their firms on communities and society [6,106].As mentioned earlier, ecopreneurship can be a source of a competitive advantage [53].Therefore, it is essential to understand how ecopreneurs create value beyond the economic or financial dimension, which contributes positively in both a social and ecological sense [107,108].It is also important to analyze the key factors of ecopreneurship that directly affect profitability in economic terms.Several authors, including Donaldson [45], have affirmed that applying this model can improve companies' economic profitability.Similarly, based on their theory of shared value, Porter and Kramer [109] have argued that creating social and environmental value has positive effects on financial performance.The main aim is, therefore, to analyze sustainability-derived financial effects on companies.Besides financial performance, it would be of major interest to study the effects of the environmental performance of these kinds of ecopreneurial firms on their immediate surroundings.For example, scholars could quantitatively measure whether the impact on the environment is as expected.There are, therefore, numerous lines of investigation to pursue in the area of measurement scales.Because this topic is in its early stages, measurement scales to evaluate constructs such as environmental performance are scarce.Lastly, the role of institutions is fundamental to move toward a more sustainable and environmentally-friendly world.Therefore, studying the role of institutions as moderators of the relationship between eco-innovation and environmental performance provides a major opportunity for further research.
Figure 1 .
Figure 1.Life cycle of the subject "ecopreneurship" in Web of Science.
Figure 1 .
Figure 1.Life cycle of the subject "ecopreneurship" in Web of Science.
Figure 2 .
Figure 2. Linkages between the main concepts covered by this study.
Figure 2 .
Figure 2. Linkages between the main concepts covered by this study.
Figure 3 .
Figure 3. Key elements of ecological transition.Source: Compiled by the authors.
Figure 3 .
Figure 3. Key elements of ecological transition.Source: Compiled by the authors. | 9,914.8 | 2019-05-22T00:00:00.000 | [
"Business",
"Economics"
] |
Ionosphere-Weighted Network Real-Time Kinematic Server-Side Approach Combined with Single-Differenced Observations of GPS, GAL, and BDS
: Currently, network real-time kinematic (NRTK) technology is one of the primary approaches used to achieve real-time dynamic high-precision positioning, and virtual reference station (VRS) technology, with its high accuracy and compatibility, has become the most important type of network RTK solution. The key to its successful implementation lies in correctly fixing integer ambiguities and extracting spatially correlated errors. This paper first introduces real-time data processing flow on the VRS server side. Subsequently, an improved ionosphere-weighted VRS approach is proposed based on single-differenced observations of GPS, GAL, and BDS. With the prerequisite of ensuring estimable integer properties of ambiguities, it directly estimates the single-differenced ionospheric delay and tropospheric delay between reference stations, reducing the double-differenced (DD) observation noise introduced by conventional models and accelerating the system initialization speed. Based on this, we provide an equation for generating virtual observations directly based on single-differenced atmospheric corrections without specifying the pivot satellite. This further simplifies the calculation process and enhances the efficiency of the solution. Using Australian CORS data for testing and analysis, and employing the approach proposed in this paper, the average initialization time on the server side was 40 epochs, and the average number of available satellites reached 23 (with an elevation greater than 20 ◦ ). Two positioning modes, ‘Continuous’ (CONT) and ‘Instantaneous’ (INST), were employed to evaluate VRS user positioning accuracy, and the distance covered between the user and the master station was between 20 and 50 km. In CONT mode, the average positioning errors in the E/N/U directions were 0.67/0.82/1.98 cm, respectively, with an average success fixed rate of 98.76% (errors in all three directions were within 10 cm). In INST mode, the average positioning errors in the E/N/U directions were 1.29/1.29/2.13 cm, respectively, with an average success fixed rate of 89.56%. The experiments in this study demonstrate that the proposed approach facilitates efficient ambiguity resolution (AR) and atmospheric parameter extraction on the server side, thus enabling users to achieve centimeter-level
Introduction
With the rapid advancement of communication technology, cloud servers, and multi-GNSS, a foundation has been established to offer users high-precision positioning services based on extensive GNSS data [1].The proliferation of applications and devices, such as autonomous driving, unmanned delivery, and consumer-grade drones, has led to the widespread popularity of real-time high-precision positioning services [2].Rapid, accurate, and stable positioning services have become crucial for realizing these applications.Traditional real-time kinematic (RTK) solutions require users to deploy reference stations, but under such a system, it is difficult to immediately obtain the precise coordinates of reference stations.Additionally, the estimation of spatial distance errors is complex, leading to a noticeable degradation in positioning accuracy as the distance increases [3,4].Precise point positioning (PPP) technology enables centimeter-level positioning with only a single station, and there is a plethora of research currently being conducted on real-time PPP.However, due to its relatively slow convergence time and the necessity to acquire multiple external services, the implementation of real-time dynamic applications remains challenging [5,6].PPP-RTK utilizes regional or wide-area reference stations to precisely estimate the necessary products for user positioning, ensuring the swift convergence of positioning results [7,8].Nevertheless, the user end adopts an algorithm that is self-consistent with the server side, and the protocol has not yet been fully unified, thus making it difficult to ensure compatibility with existing RTK technology users.Network RTK technology effectively overcomes the shortcomings of the aforementioned real-time positioning methods as it features rapid convergence and high precision, and does not require users to set up reference stations themselves, thereby improving operating efficiency and reducing associated costs.As a result, the widespread adoption of this technology is evident across various aspects of modern living [9][10][11].
To improve user positioning accuracy, which is affected by increasing spatial correlation errors due to the growing distances between users and reference stations, ref. [12] proposed utilizing modeled ionospheric delays within a multi-reference station network to rapidly achieve AR for user stations.Based on that research, virtual reference station (VRS) technology was introduced [13].VRS interpolates atmospheric correction between the master station and the user station according to the user's location on the server side, and it also generates virtual observations.For users, since it is compatible with conventional RTK solutions, this method is commercially well promoted and currently stands as the most popular network RTK technology [14].The Flachen Korrektur Parameter (FKP, in German) technology, introduced by Wübbena et al. in 1996 [15], models undifferenced distance-related errors within the network using interpolation algorithms and then transmits parameters to users through one-way communication.In contrast to the FKP, which establishes distance-related models on the server side, master-auxiliary concept (MAC) technology [16] conducts modeling on the user end.However, it involves the broadcasting of a substantial amount of information and is currently only applicable to Leica receivers.At present, due to limitations in communication protocol compatibility and the general applicability of user-receiver positioning algorithms, the popularity of MAC and FKP in practical applications is relatively low.Therefore, the network RTK algorithm proposed in this paper is a development of VRS.
In traditional VRS server-side baseline resolution, the typical procedure involves initially solving DD wide-lane (WL) ambiguities, which can be easily fixed with the wide-lane or Melbourne-Wübbena (MW) combination.Subsequently, the combination of ionospherefree observables is used to compute tropospheric delay and DD ionosphere-free ambiguities.Finally, the solutions for the raw integer ambiguities are determined [17][18][19][20].Due to the short wavelength of L1 in the narrow-line (NL) combination, which is unfavorable for fixing raw integer ambiguities, Tang et al. proposed an approach based on the classic three-step method, and this technique obtains the raw integer ambiguities using the linear relationship between WL and NL combinations [21][22][23].Notably, the method does not require solving equations and offers a fast computation speed.Ionospheric delay is a significant factor affecting rapid AR for medium to long baselines [24,25].However, the above approaches overlook the potential of ionospheric delay to serve as a constraint for AR.Consequently, investigations turned to using external ionospheric constraints to enhance model strength, thereby accelerating DD wide-lane AR.For NL ambiguities, a partial ambiguity resolution (PAR) method is employed, followed by the subsequent resolution of other parameters.
In [26,27], the authors demonstrate the effectiveness of this approach in resolving long baseline cases.
It is apparent that the aforementioned methods for AR between reference stations predominantly employ the classical three-step strategy of wide-lane, ionosphere-free, and narrow-lane combinations.Ionospheric delay, a crucial parameter in VRS, is eliminated during the AR process and re-obtained through geometry-free combination after ambiguities are fixed.Unfortunately, they neglected the influence of the ionospheric delay second-order term and introduced combined observation noise, thus to some extent disrupting the physicochemical characteristics of the ionospheric short-term smooth changes.Uncombined single-baseline solutions can, to some extent, address the above issues.In [28,29], the authors pointed out that the DD ionospheric delay within a regional range can be considered as zero.To further account for the uncertainty of ionospheric delay, different prior variances were set for baselines according to different lengths in the stochastic model, and thus, the ionosphere-weighted model was introduced.Experimental results demonstrated that the utilization of the ionosphere-weighted model can reduce convergence time and accelerate the initialization.
The DD observation model can eliminate errors associated with the receiver and satellites.However, the correlation between these observations is troublesome for quality control and identifying the source of outliers, and it may amplify observational noise [30].Compared to the DD model, the single-differenced (SD) model offers a simpler variancecovariance matrix.Furthermore, due to the retention of receiver errors, the model strength can be enhanced through the analysis of bias characteristics [31][32][33][34].Processing multisystem GNSS data has become the trend for future development as the combination of multi-GNSS observations allows for a more robust geometric observation structure, thereby significantly reducing the adverse effects of atmospheric errors.The expansion of satellite constellations and observation data is proving beneficial for rapid and accurate AR.Moreover, it facilitates precise modeling of ionospheric and tropospheric delays in local regions, thereby further improving positioning accuracy [35].Building upon this, a single-differenced ionosphere-weighted RTK method designed for multi-GNSS was proposed [36][37][38][39][40].By employing this algorithm, the initialization time and positioning accuracy are improved across single-frequency, dual-frequency, and multi-frequency scenarios.
In addressing the limitations of the previously mentioned approach, this paper proposes the SD ionosphere-weighted VRS server-side method based on GPS, GAL, and BDS observations.The approach utilizes SD uncombined observations and applies rank deficiency theory to guarantee the estimable integer properties of ambiguities, while directly estimating the SD ionospheric delay and the relative zenith tropospheric wet delay between receivers.By directly obtaining the SD atmospheric correction required for spatial error interpolation, it effectively reduces DD observation noise and renders it unnecessary to specify the pivot satellite, thus further simplifying the calculation process and improving the solution efficiency.Therefore, the method is more conducive to real-time processing.
This paper begins with a concise overview of the network RTK server-side algorithm workflow, detailing the construction of the ionosphere-weighted full-rank equation, the establishment of the stochastic model, and the validation of ambiguity resolution.Subsequently, we propose the single-differenced virtual observation generation equation, which eliminates the need for selecting a pivot satellite.Finally, we evaluate both the serverside service performance and the user-side positioning performance using data from the AUSCORS network.
Materials and Methods
This section will focus on the ionosphere-weighted network RTK (VRS) server-side method based on single-differenced observations of GPS, GAL, and BDS.We will present the mathematical model, stochastic model, and data processing strategy for estimating DD ambiguity, SD ionospheric delay, and undifferenced (UD) relative wet tropospheric delay between reference stations.
Brief Review of VRS Technology Principles and Server-Side Data Processing Flows
As illustrated in Figure 1, the fundamental principle of VRS can be succinctly summarized: the server side collects the original observation data from each reference station in the regional area and resolves the baselines.Upon receiving the user's positioning request and approximate coordinates, the server generates virtual observations and transmits them to the user.Finally, the user can obtain coordinates by processing a short baseline RTK, thereby achieving rapid and reliable high-precision positioning [13].
method based on single-differenced observations of GPS, GAL, and BDS.We will present the mathematical model, stochastic model, and data processing strategy for estimating DD ambiguity, SD ionospheric delay, and undifferenced (UD) relative wet tropospheric delay between reference stations.
Brief Review of VRS Technology Principles and Server-Side Data Processing Flows
As illustrated in Figure 1, the fundamental principle of VRS can be succinctly summarized: the server side collects the original observation data from each reference station in the regional area and resolves the baselines.Upon receiving the user's positioning request and approximate coordinates, the server generates virtual observations and transmits them to the user.Finally, the user can obtain coordinates by processing a short baseline RTK, thereby achieving rapid and reliable high-precision positioning [13].
GNSS Observation Equations
The reference station is a continuously operating station equipped with a stable antenna, offering favorable observation conditions and long-term high-quality observation data.Its precise coordinates can be obtained from PPP/PPP-AR.Consequently, coordinate estimation becomes unnecessary during the baseline solving process on the server side.
Assuming receiver
GNSS Observation Equations
The reference station is a continuously operating station equipped with a stable antenna, offering favorable observation conditions and long-term high-quality observation data.Its precise coordinates can be obtained from PPP/PPP-AR.Consequently, coordinate estimation becomes unnecessary during the baseline solving process on the server side.
with carrier phase and code observations at the same time, where n, m * , and f * represent the number of receivers, observed satellites, and the frequency, respectively, the undifferenced observed-minus-computed observation equations of GNSS can be expressed as [37,41]: In Table 1, we have provided a clearer and more intuitive explanation of the symbol system.
Symbol
Definition Description
E(•)
Expectation operator Observed-minus-computed code and phase observations (O-C) Utilizing the SD operation between receivers eliminates errors associated with satellites, such as residual orbit errors, satellite clock errors, and satellite phase and code biases.However, the equations become rank deficient after the SD operation (as shown in Equation ( 2)), and the rank deficiency is equal to the number of linear combinations of column vectors in the design matrix that produce a zero vector [42].
In Equation (2), subscripts 12 represent two reference stations, where 1 indicates the reference receiver in this paper.The term dt * 12 represent the receiver clock bias between stations for each system, τ 12 denotes the zenith relative wet tropospheric delay, l s * 12 represents the ionospheric slant delay between receivers on the first frequency of each system, and d 12,j * , δ 12,j * are the relative code/phase biases.N s * 12,j * represents the SD ambiguity.In Equation (2), there are three types of rank deficiency.By applying the S-basis theory [36,37] and introducing pseudo-observations, the rank-deficient parameters in the equation can be eliminated, resulting in a full-rank functional model.
The first type of rank deficiency arises from the relationships among receiver clock bias dt * 12 , code bias d 12,j * , and phase bias δ 12,j * , with a rank deficiency of 1.The code bias on the first frequency of each system is selected as the datum.
The second type of rank deficiency can be identified when the matrix columns for the between-receiver phase bias and ambiguity parameters are considered, with a rank deficiency of f G + f E + f C .The between-receiver ambiguity of the first (or pivot) satellite N 1 * 12,j * at each frequency is chosen as the datum.
The last type of rank deficiency arises from the relationships between-receiver clock bias, code/phase bias, and ionospheric delays.The rank deficiency can be eliminated by introducing additional ionospheric pseudo-observations.Through the resolution of rank deficiency using the three aforementioned steps, the full-rank single-differenced ionosphere-weighted model can be expressed as: In Equation (3), there have been changes in the estimable form of unknown parameters, and their detailed expression is provided in Table 2. Since the estimated ambiguity parameters are still in DD form, the integer properties of ambiguities have been preserved.
Stochastic Model
In addition to the functional model, the stochastic model plays a crucial role in the least square adjustment process of GNSS.This model describes the statistical characteristics of the variance-covariance form of observations, and a reasonable selection of the stochastic model is a prerequisite for high-precision parameter estimation.In this subsection, we introduce the stochastic model used in this paper.According to the law of error propagation, the variance-covariance matrix of single-system SD code/phase observations is given first, as shown in Equation (4).
Within Equation (4), Q * yy represents the variance-covariance (VCV) matrix of singlesystem SD observations, C * p and C * ϕ are the VCV matrix of the original code and undifferenced phase observations in the zenith direction, where σ 2 p , f * and σ 2 ϕ , f * are the a priori code and phase standard deviations (STD) of the undifferenced observations.The ratio of STD between the pseudo-range and carrier phase observations for the same GNSS system are considered to be 1:100.In this paper, we assume that GPS, Galileo, and BeiDou (MEO) observations have the same measurement accuracy, and the STDs are set to 0.3 m and 3 mm, respectively, with a scale factor f act = 1.For BeiDou's IGSO and GEO satellites, the a priori STD scale factors are set to 1.5 and 2 [43,44], respectively.D T n is the between-receiver difference matrix with a dimension of (n − 1) × n.W −1 m * represents the VCV matrix of the observations based on the weighted function of elevation and can be expressed in the form of Equation ( 5), where E s * m * is the elevation corresponding to satellite s in system m: The variance-covariance matrix of the single-system ionospheric pseudo-observations can be expressed as: where σ l * is the prior empirical standard deviation of the ionosphere, set to 0.96 mm/km in this paper, and W −1 l,m * represents the ionospheric variance-covariance matrix based on the weighted function of elevation and distance, as shown in Equation (7), where L represents the baseline length in kilometers.
Therefore, the statistical model of the single-system ionospheric weighted RTK method can be expressed as Q * yy , and the variance-covariance matrix of the ionospheric weighted model for combined GPS, GAL, and BDS is Q yy , as shown in Equation ( 8):
Ambiguity Closure Check
In this paper, a single-baseline solution mode is employed at the server-side.To ensure the correctness of parameter estimation, an ambiguity closure check is implemented.Following the completion of AR, in addition to passing the bootstrapped success rate and ratio test, each baseline necessitates that the DD ambiguity closure be zero for any closed reference station network composed of three or more connected reference stations.The expression is shown in Equation (9).
Virtual Observation Generation
Within our approach, the generated Delaunay triangles serve as the minimum solving units.After the closure check confirms the validity of DD ambiguities, the process of interpolation of spatial correlated errors begins.Considering that the distance between receivers in network RTK solutions typically does not exceed 200 km, and the maximum ranging error when using broadcast ephemeris for relative positioning does not surpass 5 cm [20], along with the availability of ultra-rapid ephemeris, interpolation is generally applied just for ionospheric delay and tropospheric delay in scenarios with small inter-station dis-tances.Commonly employed methods including the linear interpolation model (LIM) [13], the linear combination model (LCM) [45], the distance-based linear interpolation model (DIM) [17], and the modified combined bias interpolation (MCBI) [23,46].The performance distinctions among these methods are negligible.In the experiments conducted in this paper, the LIM method was selected for interpolation.
In contrast to the traditional approach of using corrections in DD form to generate VRS virtual observations, this study adopted a novel approach by directly utilizing corrections in SD form.It eliminates the necessity to select the pivot satellite, further simplifying the calculation process and improving the solution efficiency.The expression is given by Equation (10).
Raw phase observations f rom the master station.
In Equation ( 10), the master reference station is denoted as A, and the virtual reference station (VRS) is denoted as V. ∆d ion s * VA,j * and ∆d trop s * VA,j * represent the interpolated ionospheric delay and tropospheric delay, respectively.∆O s * VA,j * denotes orbit errors, and the meanings of other terms are specified in Equation (10).
Results
In this section, tests and analyses were conducted separately on the network RTK solution at the server side and user end.Firstly, the experiment setup was as described previously.Subsequently, we performed a statistical analysis on receiver-related biases, ADOP/PDOP/VDOP, the initialization time, and the available number of satellites for each subnet on the server side.Finally, an analysis of the user-end solution was carried out, including the ionospheric interpolation accuracy and the user positioning accuracy.
GNSS Data Collection and Processing Strategy
To validate the correctness and applicability of the algorithm proposed in this paper, CORS data from Australia on DOY 339, 2023 (5 December 2023), were chosen.A total of 14 continuously operating reference stations were selected, with seven stations serving as reference stations to estimate various parameters in the regional area and provide VRS services.In addition, seven other stations were used as user stations for positioning tests.The reference network comprised 12 baselines, with lengths ranging from 50 to 120 km and an average inter-station spacing of 82.32 km.The baseline information is detailed in Table 3, and the distribution of reference stations is depicted in Figure 2, where red triangles represent reference stations and blue dots represent user stations.
In Table 4, we present the processing strategies for both the server side and user end.Throughout the processing, a Kalman filter serves as the parameter estimator.A bootstrapped success rate threshold of 99.99% is employed to filter float solutions of ambiguities.Furthermore, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to achieve integer ambiguity resolution (IAR).It is crucial, during partial ambiguity resolution, to successfully fix a sufficient number of ambiguities (over 60% of float ambiguities in the current epoch) to ensure correct parameter estimation [47], thus guaranteeing the accuracy of user positioning solutions.Additionally, triangles are taken as the minimum computation unit during the solution processing.Interpolation and virtual observation generation for the respective satellites are performed only when passing the closure test, as shown in Equation (9).Ambiguity dilution of precision (ADOP) is an index that represents the strength of the ambiguity resolution model, proposed by Teunissen [48], and has been widely adopted.ADOP can describe the intrinsic precision characteristics of ambiguity parameters [49] and is also a measure of the volume of the ambiguity confidence ellipsoid [50].
Server-Side Test Results and Analysis
Ambiguity dilution of precision (ADOP) is an index that represents the strength of the ambiguity resolution model, proposed by Teunissen [48], and has been widely adopted.ADOP can describe the intrinsic precision characteristics of ambiguity parameters [49] and is also a measure of the volume of the ambiguity confidence ellipsoid [50].The formula is given by Equation (11): where n is the dimension of the ambiguity, Q â â is the variance-covariance matrix of the ambiguity in cycles, and |•| represents the determinant of the matrix.Since ADOP is a measure of the ambiguity search space, a smaller ADOP value indicates a higher success rate and reliability of ambiguities.Typically, it is considered that when ADOP is less than 0.12 cycles, the corresponding ambiguity success rate is greater than 99.9% [49].
An adequate quantity of satellites contributes to the estimation of various correction terms, and a favorable satellite geometry accelerates convergence time, reducing the impact of multipath effects to some extent.PDOP and VDOP are crucial values for measuring the precision of satellite positioning and the geometric strength of observations.From Figure 3a,b, it can be seen that, in comparison to occasional significant fluctuations in the PDOP and VDOP of a single system, the PDOP and VDOP of the combined G+E+C system are more stable, consistently stabilizing below the value of 1.This indicates that the three systems combined can achieve a better distribution of satellites, enhancing the accuracy and reliability of positioning.Figure 3c plots the time series of ADOP.It can be observed that after ADOP gradually converges and falls below the threshold of 0.12 cycles, the convergence and fluctuation behaviors of ADOP for a single system and the three systems combined are similar, with the latter converging the fastest, followed by BDS, GPS, and GAL.The initial convergence speed may be related to the number of available satellites and the accuracy of the remaining parameters estimated by each system.The available number of satellites and the number of fixed ambiguities for the combined G+E+C system are presented in Figure 3d, with an average number of satellites of 32 and an average number of fixed ambiguities of 49, which can provide sufficient correction terms for VRS observation generation.
Differently from the DD observation model, which can eliminate all errors related to the satellites and receivers, the SD model requires the estimation of the between-receiver relative clock bias and the receiver code and phase biases (RDCB and RDPB).Figure 4 illustrates the biases parameters related to the receiver for baseline BL06 in each system.From the figure, it can be observed that the receiver clock bias for the three systems combined exhibits similar variations but does not show a clear regular pattern.In the experiment, we treat the RDPB and RDCB parameters as white noise for estimation.Rows 2-4 in Figure 4 depict the time series of phase bias (GPS L1 and L2, BDS B1I and B3I, GAL E1 and E5b) and code biases (GPS L2, BDS B3I, GAL E5b), respectively, with the code bias on the first frequency serving as the datum and not plotted.It can be seen from the figure that the RDPB and RDCB parameters change during the day, confirming reports from other studies [34].Therefore, it is inappropriate to treat the RDCB and RDPB parameters as time-invariant, even though this could further enhance the model's strength.Conversely, treating the two types of bias parameters as white noise for estimation reflects, to some extent, their temporal changes but weakens the model's strength.This may lead to discontinuous and inconsistent ambiguity parameters, affecting the extraction of parameters such as ionospheric delay and tropospheric delay.Existing studies also indicate that receiver phase bias and code bias exhibit time-varying characteristics, and related experiments have demonstrated that the changes in the two types of biases may be closely related to environmental temperature [31,47,51].In recent years, some researchers have proposed modeling RDCB and RDPB through the establishment of a random-walk model or a temperature-related model [32,51], achieving a certain degree of progress.
and the accuracy of the remaining parameters estimated by each system.The a number of satellites and the number of fixed ambiguities for the combined G+E+C are presented in Figure 3d, with an average number of satellites of 32 and an number of fixed ambiguities of 49, which can provide sufficient correction terms observation generation.In contrast to the favorable observation conditions with open views at the reference station, network RTK technology users may be in "urban canyon" areas where observation conditions are less optimal.Therefore, the goal of the server side is to provide users with as many available satellite observations as possible.A sufficient number of available satellites is a crucial factor in achieving high-precision user positioning, especially in challenging urban environments.The initialization time of each subnet is another vital indicator for evaluating the server's solution performance.Figure 5 illustrates the initialization time and average number of available satellites for seven subnets, each restarting every four hours.To simulate real-world user scenarios and ensure the accuracy and availability of the provided service, the conditions for a successful subnet initialization are as follows:
•
Float ambiguities pass bootstrapped success rate test with threshold greater than 99.99%; • Ambiguities successfully fixed, and the integer DD ambiguity closure error is strictly zero for each subnet; • The number of available satellites is greater than 15, and the VRS observations of the three systems are all available.
eters such as ionospheric delay and tropospheric delay.Existing studies also indicate that receiver phase bias and code bias exhibit time-varying characteristics, and related experiments have demonstrated that the changes in the two types of biases may be closely related to environmental temperature [31,47,51].In recent years, some researchers have proposed modeling RDCB and RDPB through the establishment of a random-walk model or a temperature-related model [32,51], achieving a certain degree of progress.In contrast to the favorable observation conditions with open views at the reference station, network RTK technology users may be in "urban canyon" areas where observation conditions are less optimal.Therefore, the goal of the server side is to provide users with as many available satellite observations as possible.A sufficient number of availabl satellites is a crucial factor in achieving high-precision user positioning, especially in cha lenging urban environments.The initialization time of each subnet is another vital ind cator for evaluating the server's solution performance.Figure 5 illustrates the initializa tion time and average number of available satellites for seven subnets, each restartin every four hours.To simulate real-world user scenarios and ensure the accuracy an availability of the provided service, the conditions for a successful subnet initializatio are as follows: • Float ambiguities pass bootstrapped success rate test with threshold greater tha 99.99%; • Ambiguities successfully fixed, and the integer DD ambiguity closure error is strictl zero for each subnet; The number of available satellites is greater than 15, and the VRS observations of th three systems are all available.
The available satellites are counted under the above successful initialization cond tions, and just considering satellites with an elevation greater than 20°.In Figure 5, th orange boxplots illustrate the number of available satellites for each subnet, while the blu line represents the average initialization time.The graph reveals that the average numbe of available satellites reaches 23 (with an elevation greater than 20°) for each subnet.Thi ensures that the service fulfills the high-precision positioning requirements of users.Th average initialization time is approximately 40 epochs.Moreover, combining analysi with Figure 2 and Table 3 allows us to infer that the subnet initialization time correlate with the baseline length.Longer baselines tend to result in extended initialization time.
User-End Test Results and Analysis
The previous subsection analyzed the solution process and performance on th server side.This subsection will focus on testing and analyzing user ionospheric interpo lation accuracy and positioning performance in different positioning modes.
The primary focus of this paper is to present the network RTK solution method base on single-differenced observations.We chose the LIM interpolation method to comput ionospheric and tropospheric corrections for VRS.The available satellites are counted under the above successful initialization conditions, and just considering satellites with an elevation greater than 20 • .In Figure 5, the orange boxplots illustrate the number of available satellites for each subnet, while the blue line represents the average initialization time.The graph reveals that the average number of available satellites reaches 23 (with an elevation greater than 20 • ) for each subnet.This ensures that the service fulfills the high-precision positioning requirements of users.The average initialization time is approximately 40 epochs.Moreover, combining analysis with Figure 2 and Table 3 allows us to infer that the subnet initialization time correlates with the baseline length.Longer baselines tend to result in extended initialization time.
User-End Test Results and Analysis
The previous subsection analyzed the solution process and performance on the server side.This subsection will focus on testing and analyzing user ionospheric interpolation accuracy and positioning performance in different positioning modes.
The primary focus of this paper is to present the network RTK solution method based on single-differenced observations.We chose the LIM interpolation method to compute ionospheric and tropospheric corrections for VRS.
Table 5 provides statistics on ionospheric interpolation accuracy at different user stations, and Figure 6 illustrates the error bar of ionospheric interpolation for seven user stations.In the accuracy assessment process, utilizing the raw observations from the user station and its corresponding master reference station for RTK processing allows the calculation of ionospheric delay as a truth.From the figure and table, it can be observed that the mean values of ionospheric interpolation for GPS, Galileo, and BeiDou are close to 0. As the distance between the user station and the master reference station increases, the spatial correlation of ionospheric delay gradually decreases, and the corresponding STD increases.Relevant studies indicate that 5 cm is a critical threshold for ionospheric error.When it is less than 5 cm, the fixed rate of ambiguities can approach 100%, maintaining centimeter-level positioning accuracy [52].In this test, the distance between the user station and the master reference station covers 20-50 km, with STD ranging from 1.50 to 4.16 cm, and a mean STD near 2.7 cm.When the user is 50 km away from the master reference station (user station RAWS), the corresponding results for the three systems indicate that centimeter-level positioning can be achieved within this baseline length range.Short baseline RTK technology can achieve AR within seconds, providing highprecision positioning services by efficiently eliminating atmospheric errors.At this point, using the between-receiver SD model can eliminate the majority of atmospheric errors, especially ionospheric delays, making ambiguities less affected by system errors, thereby enhancing the geometric strength of ambiguity [53].Ionospheric errors play a crucial role in ambiguity resolution, directly impacting AR and positioning performance.Rapid AR can only be achieved with the accurate correction of ionospheric errors.ADOP was mentioned as a theoretical indicator reflecting AR performance.In this section, we evaluate the theoretical performance of AR using VRS observations corrected for atmospheric effects.Two different processing modes were employed in the experiment, 'Instantaneous' (INST) and 'Continuous' (CONT).INST mode refers to a single-epoch mode with no parameter transfer between epochs, while CONT mode only transfers float ambiguities and zenith tropospheric wet delays between epochs.Figure 7 depicts the ADOP of the user station WSEA.The left subplot is in CONT mode, while the right subplot is in INST mode.It is evident from the figure that in CONT mode, after ADOP convergence, it consistently maintains at a low level due to the transfer of float ambiguities between epochs, keeping the variance low.The mean of ADOP is 0.0047 cycles, with epochs below 0.12 cycles reaching 99.86%.Theoretically, this favors rapid AR.Under INST mode, where ambiguities are not transferred, the mean of ADOP is 0.0919 cycles, and epochs below 0.12 cycles still reach 97.32%.This indicates that VRS virtual observations generated by the server side showed high accuracy, providing favorable conditions for AR.
tions, and Figure 6 illustrates the error bar of ionospheric interpolation for seven user stations.In the accuracy assessment process, utilizing the raw observations from the user station and its corresponding master reference station for RTK processing allows the calculation of ionospheric delay as a truth.From the figure and table, it can be observed that the mean values of ionospheric interpolation for GPS, Galileo, and BeiDou are close to 0. As the distance between the user station and the master reference station increases, the spatial correlation of ionospheric delay gradually decreases, and the corresponding STD increases.Relevant studies indicate that 5 cm is a critical threshold for ionospheric error.When it is less than 5 cm, the fixed rate of ambiguities can approach 100%, maintaining centimeter-level positioning accuracy [52].In this test, the distance between the user station and the master reference station covers 20-50 km, with STD ranging from 1.50 to 4.16 cm, and a mean STD near 2.7 cm.When the user is 50 km away from the master reference station (user station RAWS), the corresponding results for the three systems indicate that centimeter-level positioning can be achieved within this baseline length range.Short baseline RTK technology can achieve AR within seconds, providing high-precision positioning services by efficiently eliminating atmospheric errors.At this point, using the between-receiver SD model can eliminate the majority of atmospheric errors, especially ionospheric delays, making ambiguities less affected by system errors, thereby enhancing the geometric strength of ambiguity [53].Ionospheric errors play a crucial role It is evident from the figure that in CONT mode, after ADOP convergence, it consistently maintains at a low level due to the transfer of float ambiguities between epochs, keeping the variance low.The mean of ADOP is 0.0047 cycles, with epochs below 0.12 cycles reaching 99.86%.Theoretically, this favors rapid AR.Under INST mode, where ambiguities are not transferred, the mean of ADOP is 0.0919 cycles, and epochs below 0.12 cycles still reach 97.32%.This indicates that VRS virtual observations generated by the server side showed high accuracy, providing favorable conditions for AR.Although ADOP and bootstrapped success rate (BSSR) are widely used as theoretical indicators of GNSS AR performance, they cannot fully represent the actual performance of AR.To more accurately assess the performance of AR, it is necessary to use positional accuracy assessments and improvements in the time taken to fix ambiguities to verify the final performance of AR.During user positioning, two modes were used, 'Instantaneous' Although ADOP and bootstrapped success rate (BSSR) are widely used as theoretical indicators of GNSS AR performance, they cannot fully represent the actual performance of AR.To more accurately assess the performance of AR, it is necessary to use positional accuracy assessments and improvements in the time taken to fix ambiguities to verify the final performance of AR.During user positioning, two modes were used, 'Instantaneous' and 'Continuous', and the positioning accuracy of both modes was analyzed.Unlike reference station estimating, ionospheric and tropospheric delays are no longer estimated.Figure 8 and Table 6, respectively, illustrate the positioning results for seven user stations.In CONT mode, the average positioning accuracy in the E/N/U directions is 0.67/0.82/1.98 cm, respectively, with an average success fixed rate of 98.76%.In INST mode (single-epoch solution), the average positioning error in the E/N/U directions is 1.29/1.29/2.13cm, respectively, with an average success fixed rate of 89.56%.From the Figure 9, it can be observed that using VRS observations generated by the server side enables centimeter-level high-precision positioning.When using CONT mode and the user is within 30 km of the master station, the horizontal accuracy is better than 1 cm and the vertical accuracy is better than 2 cm.When the user station is 30-50 km away from the master station, the horizontal accuracy is greater than 1.5 cm and the vertical accuracy is still greater than 2.5 cm.To more accurately evaluate the AR performance, this paper defines the AR success fixed rate as follows: passing ratio and BSSR tests, and errors in the E/N/U directions smaller than 10 cm.According to the results, the AR success fixed rate in CONT mode is higher than that in INST mode.The success fixed rate in INST mode reflects the single-epoch AR ability, directly indicating the accuracy of ionospheric and tropospheric interpolation and virtual observations.From the statistical results, the overall success fixed rate decreases as the distance from the master reference station increases.The success fixed rate for user station WORI is smaller than that for user station BMSH.The main reason is that its ionospheric interpolation accuracy is slightly lower than that of BMSH, indicating that ionospheric interpolation accuracy significantly affects positioning accuracy and AR success fixed rate.
Remote Sens. 2024, 16, x FOR PEER REVIEW 16 of 20 cm.To more accurately evaluate the AR performance, this paper defines the AR success fixed rate as follows: passing ratio and BSSR tests, and errors in the E/N/U directions smaller than 10 cm.According to the results, the AR success fixed rate in CONT mode is higher than that in INST mode.The success fixed rate in INST mode reflects the singleepoch AR ability, directly indicating the accuracy of ionospheric and tropospheric interpolation and virtual observations.From the statistical results, the overall success fixed rate decreases as the distance from the master reference station increases.The success fixed rate for user station WORI is smaller than that for user station BMSH.The main reason is that its ionospheric interpolation accuracy is slightly lower than that of BMSH, indicating that ionospheric interpolation accuracy significantly affects positioning accuracy and AR success fixed rate.
The error distribution characteristics under the two user positioning modes will now be further analyzed by taking WSEA as an example.In the error distribution depicted in Figure 9, it is evident that the most notable distinction between the two positioning modes lies in the error distribution of the float solution.Owing to the transmission of float ambiguities between epochs in CONT mode, its float positioning results are considerably better than the float positioning accuracy of INST mode, accompanied by an apparent process of position convergence.Additionally, when considering the proportion of horizontal positioning error within 2 cm, the percentages for the two modes are 93.64% and 86.31%, respectively, with CONT mode maintaining superiority over INST mode.
Conclusions
In summary, the utilization of the single-differenced ionosphere-weighted network RTK algorithm based on GPS, GAL, and BDS proposed in this paper enables rapid initialization on the server side and achieves fast centimeter-level positioning accuracy at the user end.
This paper has proposed a SD ionosphere-weighted network RTK function model based on GPS, GAL, and BDS.While ensuring the estimability of integer ambiguity, the model directly estimates the single-differenced ionospheric delay and tropospheric delay between stations, reducing the noise in DD observations.Benefiting from the direct estimation of atmospheric delay in SD form between receivers, there is no need to further determine the pivot satellite apart from selecting the initial datum satellite for ambiguities.This is beneficial for real-time filtering and virtual observation generating.
Firstly, the PDOP/VDOP/ADOP and the number of available satellites were statisti- The error distribution characteristics under the two user positioning modes will now be further analyzed by taking WSEA as an example.In the error distribution depicted in Figure 9, it is evident that the most notable distinction between the two positioning modes lies in the error distribution of the float solution.Owing to the transmission of float ambiguities between epochs in CONT mode, its float positioning results are considerably better than the float positioning accuracy of INST mode, accompanied by an apparent process of position convergence.Additionally, when considering the proportion of horizontal positioning error within 2 cm, the percentages for the two modes are 93.64% and 86.31%, respectively, with CONT mode maintaining superiority over INST mode.
Conclusions
In summary, the utilization of the single-differenced ionosphere-weighted network RTK algorithm based on GPS, GAL, and BDS proposed in this paper enables rapid initialization on the server side and achieves fast centimeter-level positioning accuracy at the user end.
This paper has proposed a SD ionosphere-weighted network RTK function model based on GPS, GAL, and BDS.While ensuring the estimability of integer ambiguity, the model directly estimates the single-differenced ionospheric delay and tropospheric delay between stations, reducing the noise in DD observations.Benefiting from the direct estimation of atmospheric delay in SD form between receivers, there is no need to further determine the pivot satellite apart from selecting the initial datum satellite for ambiguities.This is beneficial for real-time filtering and virtual observation generating.
Firstly, the PDOP/VDOP/ADOP and the number of available satellites were statistically analyzed.The results suggest that utilizing multi-system observations ensures a uniform distribution of satellite geometry, enhancing the success fixed rate of AR.Subsequently, an analysis of the receiver biases for one of the baselines was conducted.Finally, we tested the initialization and solution status of each subnet.The statistical results indicate that each subnet has an average initialization time of 40 epochs and an average number of available satellites of 23 (with an elevation greater than 20 degrees), meeting users' positioning requirements.
Two positioning modes, CONT and INST, were employed to assess the positioning accuracy of VRS users.The distance between the user station and the master station ranged from 20 to 50 km, aligning with practical application scenarios.In CONT mode, the average positioning accuracy in the E/N/U directions was 0.67/0.82/1.98 cm, respectively, with an average success fixed rate of 98.76%.In INST mode (single-epoch solution), the average positioning accuracy in the E/N/U directions was 1.29/1.29/2.13cm, respectively, with an average success fixed rate of 89.56%.Moreover, the analysis of ionospheric interpolation accuracy indicates that ionospheric interpolation values are near to zero.The STD increases with the distance between the user and the master station, and ionospheric delay interpolation accuracy directly impacts the positioning accuracy and success fixed rate of users.
Figure 1 .
Figure 1.Principle of network RTK algorithm based on real-time data stream.
Figure 1 .
Figure 1.Principle of network RTK algorithm based on real-time data stream.
Figure 2 .
Figure 2. The distribution map of stations.Red triangles indicate reference stations; blue dots represent user stations.
Figure 2 .
Figure 2. The distribution map of stations.Red triangles indicate reference stations; blue dots represent user stations.
Figure 3 .
Figure 3. DOP and # of satellites for BL06 on DOY 339, 2023.(a) PDOP, (b) VDOP, (c) AD threshold of 0.12 cycles is delineated by the presence of the orange dashed line.(d) The represents the total # of G+E+C satellites, while the red line denotes the # of fixed ambiguit
Figure 3 .
Figure 3. DOP and # of satellites for BL06 on DOY 339, 2023.(a) PDOP, (b) VDOP, (c) ADOP; the threshold of 0.12 cycles is delineated by the presence of the orange dashed line.(d) The blue line represents the total # of G+E+C satellites, while the red line denotes the # of fixed ambiguities.
Figure 4 .
Figure 4. Time series of differential clock bias, differential phase bias, and differential code bias between receivers for baseline BL06 on DOY 339, 2023.Columns represent GPS, Galileo, and BeiDou receiver bias terms, respectively, with mean and standard deviation values annotated in nanoseconds (ns).
Figure 4 .
Figure 4. Time series of differential clock bias, differential phase bias, and differential code bias between receivers for baseline BL06 on DOY 339, 2023.Columns represent GPS, Galileo, and BeiDou receiver bias terms, respectively, with mean and standard deviation values annotated in nanoseconds (ns).
Figure 5 .
Figure 5. Availability of satellites and initialization time on DOY 339, 2023.The orange boxplot de picts the quantity of satellites satisfying initialization conditions and with elevation above 20 de grees.The blue line denotes the average initialization time, conducted at four-hour intervals.The x axis is annotated with the user station names representing their respective subnetworks.
Figure 5 .
Figure 5. Availability of satellites and initialization time on DOY 339, 2023.The orange boxplot depicts the quantity of satellites satisfying initialization conditions and with elevation above 20 degrees.The blue line denotes the average initialization time, conducted at four-hour intervals.The x-axis is annotated with the user station names representing their respective subnetworks.
Figure 6 .
Figure 6.Error bar of ionospheric interpolation errors at user stations on DOY 339, 2023: GPS (top row), GAL (middle row), and BDS (bottom row); the x-axis represents the names of user stations and their distances to the nearest master reference station.
Figure 6 .
Figure 6.Error bar of ionospheric interpolation errors at user stations on DOY 339, 2023: GPS (top row), GAL (middle row), and BDS (bottom row); the x-axis represents the names of user stations and their distances to the nearest master reference station.
Figure 7 .
Figure 7.The time series of ADOP at user station WSEA on DOY 339, 2023.The left panel depicts the "Continuous" mode, while the right panel illustrates the "Instantaneous" mode.
Figure 7 .
Figure 7.The time series of ADOP at user station WSEA on DOY 339, 2023.The left panel depicts the "Continuous" mode, while the right panel illustrates the "Instantaneous" mode.
Figure 8 .
Figure 8. Statistical analysis of user station positioning results on DOY 339, 2023.The red bar chart illustrates the positioning accuracy in "CONT" mode, while the blue bar chart represents the positioning accuracy in "INST" mode.The red line depicts the success fixed rate in "CONT" mode, whereas the blue line illustrates the success fixed rate in "INST" mode.
Figure 8 .
Figure 8. Statistical analysis of user station positioning results on DOY 339, 2023.The red bar chart illustrates the positioning accuracy in "CONT" mode, while the blue bar chart represents the positioning accuracy in "INST" mode.The red line depicts the success fixed rate in "CONT" mode, whereas the blue line illustrates the success fixed rate in "INST" mode.
Figure 9 .
Figure 9. Error distribution in user station WSEA (east/north/up directions) on DOY 339, 2023.The left subfigure (a) illustrates the error distribution in "CONT" mode, while the right subfigure (b) depicts the error distribution in "INST" mode.
Figure 9 .
Figure 9. Error distribution in user station WSEA (east/north/up directions) on DOY 339, 2023.The left subfigure (a) illustrates the error distribution in "CONT" mode, while the right subfigure (b) depicts the error distribution in "INST" mode.
Table 1 .
Symbol systems and definitions.
Table 4 .
Data processing strategy used in the study.
3.2.Server-Side Test Results and Analysis
Table 4 .
Data processing strategy used in the study.
Table 5 .
Ionospheric interpolation result of subnets.
Table 5 .
Ionospheric interpolation result of subnets.
Table 6 .
User station results overview.
Table 6 .
User station results overview.: master station for VRS; SFR: success fixed rate.CONT: continuous mode; INST: instantaneous mode. | 10,854.2 | 2024-06-21T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
ASAP : A MAC Protocol for Dense and Time Constrained RFID Systems
In this paper, we introduce a novel medium access control (MAC) protocol for Radio Frequency Identification (RFID) systems which exploits the statistical information collected at the reader. The protocol, termed Adaptive Slotted ALOHA Protocol (ASAP), is motivated by the need to significantly improve the total read time performance of the currently suggested MAC protocols for RFID systems. In order to accomplish this task, ASAP estimates the dynamic tag population and adapts the frame size in the subsequent round. We demonstrate that ASAP provides significant improvement in total read time performance over the current RFID MAC protocols. We extend the design to mobile RFID systems where tags move at constant velocity in the reader's field, and show that ASAP performs well in mobile scenarios as well.
I. INTRODUCTION
Radio Frequency Identification (RFID) systems provide an efficient and inexpensive mechanism for automatically collecting the identity information of an object [1], [2]. In these systems, tags with unique identity communicate with an RFID reader over a wireless multi-access channel [3], [4]. Recently, There has been an intense effort towards the development of RFID systems for their many promising applications from providing security to factory automation to supermarket checkouts [5], [6]. All of these envisioned applications call for a need to deploy a large number of tags in small geographical areas and have the tags autonomously communicate with the reader(s). As such, RFID systems of the near future will be dense wireless ad hoc networks with limited radio resources that will have to be shared by the tags via contention based methods. Further, these systems will be considered operational when most or all of the tags in a reader field are successfully identified in a short amount of time.
In such a network setting, the design of an efficient MAC protocol is of paramount importance. The performance degrading impact of excessive collisions in random multicaccess communications is well known [7]. Indeed, tag collisions, which occur when multiple tags simultaneously transmit information in the same channel severely limit the performance * This research is supported in part by Techcollaborative Round 11 project "Design of Efficient RFID Systems" of RFID systems. In this paper, we will focus on alleviating this limitation via intelligent MAC design.
In recent years, many attempts have been made to confront the tag-collision problem. The methods suggested for RFID systems up to date can be classified into two categories: variants of ALOHA that rely on randomizing the access times of tags to reduce collisions; and tree search methods that aim to avoid collisions and identify one tag at a time. STAC, based on slotted ALOHA, has been proposed in [3] for Class 1 RFID systems. Binary tree search has been proposed for Class 0 RFID systems [4]. As neither of the methods provide acceptable performance for dense networks, several modifications have been suggested up to date that provide limited performance improvement over their originally proposed counterparts [3], [4], [8], [9].
In this paper, we propose a novel MAC protocol for RFID systems employing a large number of passive tags. The underlying motivation is to design a MAC protocol that is compatible with the suggested standard in [3], and obtain substantial improvement in read-time performance. Thus, the Adaptive Slotted ALOHA Protocol (ASAP) is based on framed Slotted-ALOHA [10], and it utilizes the statistical information related to the tag population inherently collected at the reader in each round (frame) in order to adaptively adjust the frame size in the subsequent round. This strategy aims at reducing the probability of tag collisions while simultaneously expediting the identification of RFID tags.
The design of the proposed protocol is motivated by the fact that variants of slotted ALOHA with a fixed frame size, such as STAC [3], typically do not perform well in a dense and/or dynamic scenario. Specifically, the presence of a large number of tags results in excessive collisions, while very few tags may lead to under-utilization of the channel, both resulting in extended average tag identification time and low throughput for the RFID system. The problem is even more pronounced in mobile set-ups, where the number of tags may vary rapidly with time. On the other hand, if the reader can adapt the frame size based on the tag population, this performance limitation can be alleviated to a large extent.
The design of ASAP entails an ML-based estimation algo- rithm for the number of tags to be identified with the frame size decision algorithm designed to optimize an efficiency function defined in the sequel. We also extend the design of ASAP to handle mobile RFID systems (m-ASAP) where tags move in the reader's field. We demonstrate that both ASAP and m-ASAP have impressive performance in terms of total read time in dense RFID systems.
II. SYSTEM MODEL AND MECHANICS OF ASAP
We consider the collision limited 1 900MHz UHF RFID system where large number of passive tags try to communicate with one reader over a shared channel. Each passive tag transmits a data packet consisting of 64 bit EPC and 16 bit CRC with a symbol duration of 4µs [4], [12]. Tags transmit the data bits by employing FSK using backscatter modulation [4]. The reader transmits a 900 MHz continuous wave to provide the power required to activate the passive tags.
Reader to tag communication is accomplished using '0', '1' and 'Null' data symbols as defined in [4]. The reader uses '0' and '1' to form commands, and 'Nulls' to signify the beginning of a command, the end of a command, and to close the slots within a frame. The reader transmits data in the former portion of the 12.5µs symbol duration [4]. Communications between the reader and the tags takes place in rounds whose structure is shown in Figure 1. This structure is compatible with STAC [3].
To explain the communication between the reader and the tags, consider tag state machine described in Figure 2. Initially, the tags are in an inactive 'unpowered' state and they transition to the 'activated' state, when they "listen" to the 'reset', the 'oscillator calibration signals' and the 'data symbol calibration signals' as defined in [4]. The 'reader command' provides the frame size for the ongoing round. The tags in the 'activated' state collect the frame size information and transition to the 'select and transmit' state. In this state, each tag randomly selects a slot for transmission and transmits its packets.
'Null' signals the completion of a command and the end of every slot in a frame. This facilitates re-synchronization of the tags with the slot boundaries and allows the tags to keep track of the slot number in the current frame. The duration for the detection of an idle slot is 10 data symbols.
Tags go to 'ack wait' state after sending their identification strings. The reader transmits an 'ACK command' at the end of the round. The length of the command varies in proportion to the frame size of the round. The reader transmits '1', if the transmission in the corresponding slot was successful. It 1 The received SNR is shown to be high enough to justify this assumption with passive tags communicating in a short range in [11]. III. ASAP ASAP proposes the optimum frame size for each round after estimating the number of tags present in the reader's field. In this section, we discuss the design of an optimum frame size followed by a tag count estimation algorithm.
A. Design of an optimum frame size
Consider first that the reader has already acquired the knowledge of the tag count. We will explain how the reader obtains the ML estimate of the tag count later in the paper.
Define the duration of an idle slot, T I , and an occupied (successful or unsuccessful) slot, T B . Note that in ASAP, T I = T B since idle slots are closed prematurely. Given these definitions, we consider an efficiency function, p ef f , defined as the ratio of expected time taken by the successful slots to the expected time taken by the idle and the unsuccessful slots, as our performance metric. The motivation behind defining such a metric is that maximizing this function simultaneously increases the time due to successful transmissions, and decreases the time due to idle and unsuccessful transmissions, thus minimizing the waste of resources. We have are the expected number of successful slots, idle slots, and unsuccessful slots, respectively. Given the (estimated) tag count in the reader's field, K, the problem is to devise a frame size, N, that maximizes the efficiency of the round, p ef f . Since each tag independently selects any particular slot with equal probability, the expected number of successful, idle, and unsuccessful slots in a frame Substituting (2)- (3), (1) becomes Generally speaking, N should be a function of K, i.e., N = f (K). In this paper, we consider a class of simple policies and assume that N is linearly related to K, i.e., N = β K and focus on finding the optimum multiplier. In this case, a closed form for the maximizer of p ef f can easily be found for large K. Using the approximation: (4) simplifies to which is strictly pseudo concave. As a result, the local maximum found at β * = 1.943 is also the global maximum for β > 0 [13]. Therefore, we propose that the frame size in each round should be N = β * K = 1.943K.
B. Tag Count Estimation Algorithm
β * was found under the assumption that the reader knows the tag count. In practice, the reader may not have the tag count. Hence, the reader has to estimate this parameter.
In ASAP, the tags respond with their identification strings in their chosen slots once in a round. Functionally, the reader collects tags' transmissions, performs cyclic redundancy checks, acknowledges successful identifications, and in the process, it inherently collects statistics on the total idle slot count (Z I ), the successful slot count (Z S ) and the unsuccessful slot count (Z U ). We propose to utilize this information to estimate the active tag count. In particular, we can use Z I which has the probability mass function (PMF) for Z I [14] is given by The ML estimation problem becomeŝ The likelihood function in (8) can be enumerated for different K values to find its maximum. Note that we rely on Z I and not Z S for the ML estimation simply because the PMF of Z S [9] has local maxima.
In tag count estimation, one obvious concern is the range of K over which the likelihood function needs to be enumerated. We can use K = Z S + 2Z U as the lower bound since we have ruled out the possibility of erroneous receptions in a slot occupied by a single tag as well as the capture effect. In this case, there are at least the number of successful tags plus twice the number of unsuccessful tags, because when there is an unsuccessful slot, at least two tags contend for the slot. We can also use the fact that for a given N and Z I , the likelihood function has a unique maximum and it is a monotonically decreasing function for K >K ML . Thus, the search forK ML is stopped when the likelihood function value begins to decrease, for increasing K.
Even with this reduction in complexity, the two factorials in (7) may render the enumeration of the likelihood function computationally complex for large N and K. An alternative simpler estimator can be obtained by rearranging the expression in equation (2) Our numerical results, a sample set of which is given in Table I, consistently suggest that the average of the tag count estimate for alternative method compares very closely with the average of ML estimator, even for smaller values of N and K. Note that the alternative tag count estimation method does not consider the observations, Z S and Z U . The ML tag estimation algorithm cannot be invoked when Z I = 0. Similarly, the alternative estimation method cannot be used, when Z I = 0 or 1. In such cases, the tag count is adjusted as the lower bound (Z S + 2Z U ). This is the reason behind the relatively large error in the tag count estimate for N = 25 and K = 80. In all other scenarios, the average of the tag count estimate for both methods is very close to the actual tag count.
IV. EXPECTED TOTAL READ TIME In this section, we derive the expressions for the expected total identification time for reading K tags. The reader recursively offers rounds with adaptive frame sizes N j = βK j , where N j is the frame size in the j th round and K j is the unidentified tag count at the beginning of the j th round. Define T j as the expected time duration of the j th round. Then where S j , I j , and U j denote the successful, idle, and unsuccessful slots respectively in the j th round. For large K, equation (10) simplifies to This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2006 proceedings.
We define total expected identification time, T as where K j is given by Using (12) and (5), we get which is the total identification time of K 1 = K tags when the reader employs the policy of offering an adaptive frame size of β times the unidentified tags participating in the round. We note that using (5) for derivation of T results in an underestimate of the actual duration of a round for small K because (1 − 1 βK ) K is smaller than e −1/β for small K, thus, this analysis can be considered a pessimistic view of the performance of the proposed policy.
V. m-ASAP
The biggest challenge that the mobile tags introduce is the time-constrained presence in the RFID field. The time the tag will spend in the reader's field clearly depends on the speed and the coverage of the reader. Tag density in the reader's field also affects the performance. In mobile RFID systems, the tag's basic communication mechanism is still the same: a tag enters the field, collects frame size information and repeatedly attempts the transmission of identification string. The difference is that the tag mutes not only when its transmission succeeds but also when it departs from the RFID field, whichever occurs first. In this setup, new tags continuously arrive into the RFID field. Consequently, a substantial tag population is there to schedule the transmissions in every round. We propose mobile (m)-ASAP for such RFID system setups and we focus on designs that improves the percentage of identified tag in the backdrop of the restricted time-presence of RFID tags. We design the initial tag count, the tag arrival rate and the tag departure rate in a mobile RFID system, such that P % tags are identified.
We assume that passive tags arrive into an RFID reader's field on a conveyor belt moving at a constant velocity, V. In stationary RFID system, the reader schedules the transmission of the 'reset' and 'oscillator calibration signal' cycle in the beginning of an identification process to energize and synchronize the tag's IC chip. In the mobile setting however, new tags arrive in the middle of an identification process and hence we need additional intermediate 'oscillator calibration signal' cycle to provide the synchronization information. Therefore, we propose that in m-ASAP, the reader schedules 'oscillator calibration signal' cycle of duration T cal before the beginning of every new round as shown in Figure 3. The combination of the 'oscillator calibration signal' cycle, followed by a 'Null' and a 'round' is defined as the extended round of duration T.
The system model for m-ASAP is shown in Figure 4. We denote the maximum operating range of the reader as d max and the vertical distance between the reader and the conveyor belt as h. We denote the total time spent by each tag in the RFID field as t = t e + t f . Here, t e is the time during which new arriving tags energize and collect synchronization information and t f is the time during which the tags schedule the transmission of their packets i.e., EPC and CRC. We choose t e = T + T cal as it ensures that new tags receive at least one 'calibration cycle' after collecting sufficient power while they transit the distance d e . Accordingly, we compute t f as The new tags enter the zone d f when the reader broadcasts an intermediate 'reader command' and this instance also marks the beginning of each tag's infield timer. We denote the tags that enter the reader field at the stroke of the i th 'reader command', or equivalently at the beginning of the round i as group, G i tags. Therefore, the timer t f for a group of tags arriving together in the reader field will expire at the same time.
We define the tag arrival rate as ψ. Since the tags are moving within the reader's field at a constant velocity, the tag arrival rate is equal to the tag departure rate. Other assumptions in the system model remain the same as before. In the mobile scenario, we design the MAC such that P % percentage of tags are identified. This will be accomplished by offering a sufficient number of rounds within time t f for tags arriving in each group such that the desired percentage of the tags from each group are identified.
Assume that G 1 tags arrive into the reader's field at the beginning of the first round. By design, ASAP will dictate that the reader offers a frame size of N = βG 1 to optimize the efficiency of the first round. Recall that in this case, the expected time of a round is given by (11). Thus, in m-ASAP we have where T overhead = T Cal + T Null + T RC + T Ack = 403.5µs.
The key in m-ASAP is to keep an approximately constant number of tags in each round (G 1 ) leading to a duration of T per round. This in turn dictates an arrival rate ψ that can guarantee P % tag identification. The desired arrival rate can be found as follows. For large values of G 1 and N , the expected number of successful tags is given by We thus require the number of new tags that arrive in the second round as G 2 = G 1 e −1/β . When ψ is the tag arrival rate, then the expected value of new tags in the round will be given by ψT . Therefore, ψ must satisfy ψT = G 1 e −1/β : In order to find G 1 , we take advantage of equation (13), which gives us the percentage of unidentified tags left when the reader recursively offers n rounds of appropriate frame sizes in ASAP. Recall that Equivalently, the percentage of tags that remain at the beginning of the n th round is Kn K1 100 (%). Basically, if the reader offers an appropriate frame size in every round in view of the instantaneous tag population, then for large number of experiments, the total number of offered slots in each round will divide proportionally to the remaining tags of each group. In view of this, we can separate the tags from each group and can perform an independent analysis on each group of tags. Hence, we use equation (18) to find the number of rounds, n r that every group of tags must participate in, such that the individual percentage of tags identified from every group is P % . We obtain n r = (n − 1) from Subsequently, we use n r to compute the acceptable expected round duration as T = t−te nr = t−T cal nr+1 . We substitute T in equation (15) to compute G 1 as: We further substitute the value of G 1 in equation (17) to compute the arrival rate that should be met for the target P % . Note that in this design, the reader attempts to offer an approximately fixed duration frame in every round. However, each tag chooses a slot randomly and independently and we also know that the duration of an idle slot is different from the duration of a busy slot within a frame. Consequently, the deviation in the statistics (Z I , Z S , Z U ) in a given frame has the effect of producing a variable duration round. In view of this discussion, it is possible that the timer of a particular group of tags may expire before they participate in all n r rounds. Hence, we propose that the reader should design for either (n − 1) + 1 rounds, or use a threshold time, t th < t f to compute T and G 1 .
VI. NUMERICAL RESULTS
In this section, we provide the simulation result. The simulation was done by using Matlab. We begin by comparing the performance of the ASAP and the fixed frame size policies where the reader offers the same frame size for every round and without any attempt to estimate the tag density. We also compare the performance of the case where the reader has the exact tag count (termed Ideal ASAP) with the case where the reader has the estimated count.
In Figure 5, the average tag identification time (T Av ) for Ideal ASAP is significantly better than the fixed frame policies for any K and is approximately constant (0.578 ms ≈ identification of approximately 1730 tags/second). In contrast, the fixed frame size policies show the best results when N ≈ 2K 1 . When the frame size offsets by a large value from N ≈ 2K 1 , the T Av increases exponentially. For example, a very high values of T Av was observed when (i) K 1 ≥ 200 with N = 50, and (ii) K 1 ≥ 500 with N = 100. Note that we do not observe the instability problem of ALOHA [15], [7], since the tag count is fixed and it decreases as the successful tags do not transmit in subsequent rounds. Next, we look into the performance of ASAP when the reader proposes an arbitrary frame size in the first round and subsequently, it estimates the tag count to propose the optimal frame size. In these simulations, we used the ML estimator, when both N and Z I < 80, and the alternative estimator, otherwise. In Figure 6, We observe that T Av remains below 0.7 ms for any large K (≈ 1400-1450 tags/second for K> 50), even when the frame size is small in the first round. This choice of frame size, however, impacts the T Av for small tag count significantly, e.g., T Av of 1.3 ms, when K is 10 and N 1 = 150. Figure 7 compares the performance of ASAP with different multipliers. As expected β * = 1.943 performs the best. We observe that the multiplier values close to the optimum value, e.g., 2, perform almost as For m-ASAP, we performed simulations for P % = 99%. We set V = 5 m/s, h = 1 m and d max = 2m to get t = 692.82 ms. The exit criterion of each iteration is the arrival of a total of 50000 tags in the reader's field. The tags arrive a Poisson distributed with the arrival rate ψ that is determined for one target P % . The simulation results are shown in Table II. We observe that m-ASAP as impressive performance in terms of the achieved percentage. We also notice the improvements, when we offer an additional round to each group of tags to ensure that each group of tag must participate in at least n r rounds. We observe that T Av remains close to 0.58ms. This is since the design of m-ASAP ensures that an appropriate frame size is offered in each round.
VII. CONCLUSIONS
In this paper, we proposed ASAP, a MAC protocol tailored for RFID systems with passive tags. Specifically, ASAP takes advantage of the fact that the envisioned RFID systems with passive tags will be collision limited, and utilizes tag count related information inherently collected at the RFID reader to adjust the frame size in a framed slotted ALOHA setting. The MAC protocol relies on obtaining an estimate of the number of tags in the reader's field based on the observation of the number of idle, successful, and unsuccessful slots in the current frame, to determine the size of the next frame. It is shown that the adaptive frame size improves the currently suggested slotted ALOHA based STAC significantly in terms of the read time of the tags. We also extended the design of ASAP to the scenario with mobile to guarantee that a large percentage of the tags will be identified within the duration they spend in the reader's field. The protocol proposed in this paper aims to gain significant performance improvement with virtually no additional complexity over existing standards. To that end, we note that the frame size can be further fine tuned by assuming estimators with longer memory at the expense of additional complexity. | 5,982.2 | 2006-12-11T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Institutional Distance , Investment Motivation and OFDI Location — Taking the Countries along the “ Belt and Road ” as an Example
This paper selects 2008-2017 years of relevant investment data and uses the expanded gravity model to conduct an empirical analysis to explore the moderating effect of China’s investment motivation and institutional distance on the countries with different levels of development along the “Belt and Road”. The main innovation of this paper is to classify the countries in different economic development stages along the “Belt and Road” countries. On the basis of investment motives, this paper discusses how institutional distance is used as a regulatory variable to affect the investment of different motives. The results show that small distance between the host country and China’s normative system promotes the expansion of China’s investment scale. The distance between regulatory regimes has a reverse regulatory effect on investment driven by market size. For the middle and high income countries, the negative impact of regulatory distance on labor force and technology factor-seeking investment is particularly significant, while for low-income countries, regulatory distance has a very significant positive regulatory effect on natural resource-seeking investment. Finally, this paper provides targeted recommendations based on the conclusions to help investors reduce risk. Investors should make good use of the effect of institutional distance according to their own motives in order to reduce investment costs and risks. Relevant departments need to further improve the domestic regulatory environment and promote the development of OFDI in the future.
Introduction
With the continuous advancement of the globalization process, economic and trade cooperation between countries has become increasingly close.Both the "going out" strategy and the "One Belt, One Road" initiative have shown that China actively participates in cooperation among countries in the world.As an important part of the globalization process, OFDI plays a vital role in international economic and trade cooperation.Since 2002, China's foreign direct investment has maintained a momentum of continuous growth for 14 consecutive years.After the "One Belt, One Road" initiative was launched in 2013, China's outward foreign direct investment grew rapidly.However, while the scale of investment continues expands, problems such as unregulated investment and even false investment also follow.At the end of 2016, the government increased the review of the authenticity and compliance of outward foreign direct investment.
Investment entities have gradually become rational.According to "the 2017 China Foreign Investment Bulletin", China's OFDI flow in 2017 reached $158.29 billion, ranking third in the world.The global share has exceeded 10% for two consecutive years and the investment structure has been further optimized.The investment industry is widely distributed, mainly in manufacturing, wholesale, retail, and financial industries.The investment flow to countries along the "Belt and Road" is $20.17 billion.On the one hand, with the promotion of the "Belt and Road Initiative" and the improvement of related systems, it is foreseeable that the future cooperation between China and the countries along the "Belt and Road" will be broad, but on the other hand, we must pay attention to some shortcomings while seeing the gratifying results of China's investment.From the comparison of the stock of outward foreign direct investment, we can see that China accounts for only about one-fifth of the United States.There is still a considerable gap.Along with the expansion of China's investment scale, the distribution of investment locations appears to be concentrated in a few regions, such as Vietnam and Russia.The excessive concentration of investment limits the potential of China's OFDI and is detrimental to the risk of diversification.Deng Ning decomposed the location advantage into the factor advantage and the investment environment advantage.The former is the internal motivation of investment, which mainly includes three aspects: natural resource, technical element and labor factor.The latter is reflected in the host country's external investment environment, which mainly includes the host country's politics, culture, rule of law, institutional environment and government policies.The improvement of the host country's environment will greatly reduce China's investment risk.Better institutional environment will significantly enhance its attractiveness to investors.
The research on location selection can be traced back to the cost theory.In addition to the traditional location factors, foreign investors have a disadvantage of foreign identity compared with host enterprises.They face greater uncertainty in purchasing materials, acquiring skilled labor and managing the business.So they need to pay higher information costs than local companies.In this paper, Habib and Zubawicki (2002) [1] proposed the theory of "institutional close preference", which indicated that investors often prefer countries or regions similar to their own systems when selecting investment objects.Large institutional differences between the investment home country and the host country will inhibit investment to a certain extent.Kolstad and Wiig (2010) [2] indirectly supported this conclusion by analyzing China as a research object.They found that institutional differences may hinder companies from conducting cross-border investment.Cui and Jiang (2009) [3] explored the differences in the determinants of investment between China and developed countries.They proposed that Chinese companies are deeply influenced by the host country system and pay more attention to government support [4].
Domestic research on location selection started late, but related research has increased in recent years.Liu Haiping, Song Yihong, and Wei Wei (2014) [5] found that the host country's resource elements, historical factors, institutional conditions and joining relevant organizations have an important impact on foreign capital inflows.Fu Shaojun (2018) [6] empirically analyzed the influence of the host government's governance level on China's OFDI location selection.Ji Shengbao, Li Shuhui, and Ma Shujuan (2018) [7] empirically studied the effect of multi-dimensional distances on the distribution of investment.Tian Yuan and Li Jianjun (2018) [8] analyzed the location preference of China's investment in the countries along the "Belt and Road" from the perspective of resources and systems.He Yaping and Xu Kangning (2018) [9] focused on the influence of the economic system by studying the location distribution of China's OFDI in countries along the "Belt and Road".Di Yuna, You Linqing (2018) [10] used Heckman two-stage estimation method to empirically study the economic motive and multi-dimensional distance factors in China's investment location selection.Liu Shuangqin and Li Minyan's (2018) [11] research results show that: the normative institutional distance will inhibit China's OFDI, while the regulatory system distance will positively affect the scale of investment.Liu Juan (2018) [12] systematically examined the relationship between the institutional environment of the host country, the orientation of market, resource investment and OFDI.Zhang Yabin (2016) [13] proposed that the improvement of the host country's economic environment has the greatest impact on OFDI.Peng Dongdong and Lin Hong (2018) [14] empirically tested the influence of the institutional system of the host country on the choice of China's OFDI location driven by different motives.Lin Liangpei, Jie Xiaowen (2017) [15] Since the empirical part of this article involves a large number of variables, the nomenclature is introduced as follows for the convenience of reading: the dependent variable, the foreign direct investment is named OFDI; six independent variables include the natural resource variable named na, the labor resource variable named la, the technical element variable named tec, the market size variable named gdp, the normative system distance variable named gd, the regulatory system distance variable named gud; the three control variables include the bilateral economic and trade tightness variable named tight, the inflation rate variable named ci, the trade distance variable named trdis.
Indicator Selection Description
The selection of variables and related descriptions are now shown in Table 1.
Model Design
By expanding the traditional trade gravity model of Anderson (1979) [19] to construct the investment gravity model, the investment motives such as nature resource, labor cost, market size and technical factor are taken into consideration.For the consideration of the distance factor, the institutional distance is added on the basis of the spatial geographical distance.The empirical model of this paper is as follows: The subscript i stands for the country, t stands for the year, 0 β is the inter- cept term, m X is the investment motivation variable, including the market size, the natural resource variable, the labor resource variable, the technical factor variable; n X is the institutional distance variable, including the normative and regulatory institutional distance; it ε is error term.
Independent Variables
This article draws on the practice of Liu Jing (2012) [20] and other scholars to subdivide the institutional distance into the distance between the regulatory system and the normative system, which is used to measure the institutional environmental gap between China and the countries along the "Belt and Road".The specific calculation method is to measure the regulatory and normative institutional distance by the absolute value of the difference between the average values of the three indicators between China and the countries along the "Belt and Road" in each year.
Discourse rights and accountability distance, political stability and non-riot distance and corruption distance are used to measure the normative institutional distance.The normative system is mainly informal.It is the system that people form in their lives to guide their behavior and decision-making.The normative system distance is mainly reflected in the gap between the investment country and the host country in terms of customs and personal behaviors.Generally speaking, the smaller the distance of the normative system is, the closer the normative system of the two countries is.The transaction cost of the investment is smaller.
Hypothesis 1: Normative institutional distance has a negative impact on the expansion of investment scale.
The regulatory system distance is usually measured by the government efficiency distance and the distance between supervision and the rule of law.On the one hand, the regulatory system of developed countries is perfect, and the relevant requirements for investment will be more stringent.If the regulatory system distance is small, it means high consistency with China.It will help reduce the "Liability of Foreignness" costs brought about by differences in regulatory systems and promote investment; On the other hand, most of the countries along the "Belt and Road" are developing countries.Problems such as inadequate supervision by government, the inefficiency of the relevant departments and imperfect rule of law systems are still serious, so investment risks are high.However, China's investment entities have not reduced or stopped investing in these countries.We can understand from the following two aspects: First, under the framework of "One Belt, One Road", most of China's investment projects in these countries are aimed at helping them to improve domestic infrastructure construction, so they are welcomed by the government and the majority.
Second, countries such as Pakistan, whose abundant natural resource elements can offset the negative impacts caused by the regulatory system environment.The main goal of market-oriented investment is to occupy overseas markets and cross trade protection barriers.On the one hand, in order to alleviate the anti-dumping pressure, more and more enterprises choose OFDI as another way to participate in international economic and trade cooperation.On the other hand, as a big manufacturing country in the world, China's domestic market is still immature and the competition is fierce.It is far from meeting the needs of many enterprises' products.In addition to the national "going out" strategy, some enterprises respond to the government's call for transnational operations.
Hypothesis 7 is proposed: the market size of the host country is positively correlated with the scale of OFDI.
Control Variables
Based on the existing research, this paper draws on Wu Xianming and Hu Cuiping [21]'s approach to select the three factors of economical trade closeness, inflation rate and geographical distance as the control variables of this paper.
Bilateral economic and trade tightness (tight): The close economic and trade cooperation between the two countries helps the investment entities to obtain various types of information.Therefore, it is expected that the bilateral trade and economic tightness will be positively correlated with the scale of OFDI.
Inflation rate (ci): A country's high inflation rate means that its macro economy is relatively unstable, which in turn increases the risk of investment.Therefore, it is expected that the inflation rate will be negatively correlated with the scale of OFDI.graphical distance and oil price in transportation costs.In general, the farther the trade distance is, the higher the transportation cost is.Therefore, it is expected that the trade distance will be negatively correlated with the scale of OFDI.
Model Test and Regression Method Selection
This paper selects the 2008-2016 China's OFDI panel data for regression analysis.Firstly, in order to reduce the influence of heteroscedasticity, the data other than the percentage is logarithmically processed.Secondly, the Hausman test results show that the corresponding chi-square value is greater than 100 and the p-value is 0.000, so the null hypothesis is rejected and the fixed-effect panel regression method is finally selected.In order to ensure the robustness of the results, the linear correlation analysis of the main variables is first carried out.The maximum coefficient of the correlation coefficient matrix of the main variables is 0.584, and there is no variable group exceeding 0.6.Further multicollinearity tests are performed on each model.The relevant test parameters indicate that there were no serious multicollinearity problems among the variables in all models.
In order to further compare the differences in investment motives among different income countries and the effect of institutional distances in different types of host countries, the sub-sample analysis is carried out separately based on the analysis of the whole sample countries.
Since the direction of the influence of the regulatory system distance is uncertain, the interaction term between the investment motivation and the regulatory system is added to the model to examine the effect of the regulatory system distance on the OFDI driven by different motives.
Analysis of Empirical Results
According to Table 2, it can be seen that motivation for seeking the technical elements of the host country in the whole sample is not significant (p > 0.1), while the other three factors: the influence of the host country's labor force, natural resources, and market size on the scale of investment are consistent with the previous assumptions.After being divided into three groups, it can be found that the coefficient of natural resource is positive in each sample, but in the middle and the high-income country sample is not significant (p > 0. very strong.The market size of the host country is significantly positively correlated with the location choice of China's investment (β = 7.865, 1.4, 2.954; p < 0.01, p < 0.01, p < 0.05), indicates that when choosing the investment location in China, it is more inclined to choose a host country with a larger market size.The natural resource factor coefficient is positive in each sample, and is more significant in low-income countries (β = 0.122, p < 0.05), indicating that the abundant natural resources of low-income countries have a great positive appeal to investment.This shows that the motivation for seeking natural resources in the more developed countries is not significant (p > 0.1).In addition, the labor resources factors of high-income countries and the technical elements of countries of low-income countries are not the main considerations for investment.It is worth noting that the correlation coefficient of the market size in the whole sample and the three sub-samples is significantly positive (β = 7.865, 1.4, 2.954; p < 0.01, p < 0.01, p < 0.05), indicating that the market size of the countries along the "Belt and Road" is an important decision-making factor.The normative institutional distance between low-income countries and high-income countries is significantly negative for China's investment location choice (β = −0.67,−1.103; p < 0.1, p < 0.1), indicating that investors are more willing to choose a host country with similar cultural practices to invest to reduce investment costs.The regulatory institutional distance from low-income countries (β = 0.06, p < 0.1) is significantly positively correlated with investment, while the regulatory institutional distance from middle and high-income countries is significantly negatively correlated with investment (β = −0.051,−1.177; p < 0.05, p < 0.1).The normative system distance correlation coefficient is significantly negative at the level of 1% (β = −0.67,−1.103; p < 0.1, p < 0.1), and the conclusions of the whole sample and the subsample are consistent.That is, the investment entity is more willing to choose the host country that is closer to China's normative system to invest.In the full-sample and low-income host countries, the regulatory institutional distance is significantly positively correlated with the size of the investment (β = 1.346, 0.06; p < 0.01, p < 0.1).However, in the sample of medium and high-income countries, the result is opposite (β = −0.051,−1.177; p < 0.05, p < 0.1).The smaller the regulatory system distance is, the larger the investment scale is.The hypothesis 2 is verified.
The results for the control variables are roughly consistent with the expected assumptions.The correlation coefficient of trade distance is negative as expected, indicating that investors tend to choose neighboring countries as investment targets.The inflation rate is a substitute for the macroeconomic stability of the host country.Its correlation coefficient is also negative, indicating that investment tends to flow into a host country with relatively stable macroeconomics.The economic and trade tightness is significantly positively related to China's investment.Therefore, the host country with closer economic and trade ties with China is more attractive to investment entities.
Empirical Analysis of the Effect of Regulatory System Distance
In order to further analyze the effect of regulatory system distance on different internal investment motives, the interaction between institutional distance and investment motivation is introduced into the model to conduct empirical research.The interaction variables are averaged and centralized in advance to avoid multicollinearity with the main variables.The results are shown in Table 3.
Firstly, for the three groups of host countries at different stages of economic development, the coefficient of the interaction between the regulatory system distance and the market size is significantly negative, (β = −1.343,−3.804, −1.106; p < 0.01, p < 0.05, p < 0.01) which means that the regulatory system distance has a reverse effect on the market-seeking OFDI.Investors are more inclined to invest in host countries similar to China's regulatory system to obtain their market share.Under similar regulatory circumstances, investment entities are relatively more familiar with the government and legal system.Investors can use low transaction costs to increase their market share in the host country and increase their international influence.
Secondly, for high-income host countries, the coefficients of interaction between the regulatory system distance and the investment motive are mostly negative, the coefficient of interaction with technical factors is significantly negative at 1% (β = −0.066,p < 0.01), which means that for high-income countries, the regulatory system distance has an adverse impact on the investment driven by different motivations, especially for technology-seeking investment.
For middle-income countries, the coefficient of interaction between labor cost and regulatory system distance is significantly positive at 5% (β = 0.898, p < 0.05), which means that the distance between the host country and China's regulatory system has a significant reverse regulation effect on labor-seeking investment.It shows that investors will also consider the impact of differences in regulatory systems while considering cheap labor resources.When the regulatory system is relatively close, multinational corporations can relatively easily adapt to the local regulatory environment, so they will choose to expand their investment scale.
Finally, for low-income countries, the cross-term correlation coefficient between regulatory system distance and natural resources is significantly positive at the level of 1% (β = 0.0009, p < 0.01), which means that the regulatory system distance has a very significant positive adjustment effect on natural resource-seeking investment.Even if the host country's regulatory system is not perfect, abundant natural energy such as ore metal will be very attractive to Chinese investors, which can offset the negative impact of the regulatory system to some extent.
Conclusions and Recommendations
Firstly, this paper analyzes the impact of investment motivations on the scale of OFDI.The motivation for seeking the technical elements of the host country is not significant in the whole sample, and the other three motivation factors are consistent with the previous assumptions.After being divided into three groups, we can find that China's investment motivations for middle and high-income countries are mainly technical elements.The natural and labor resources of low-income countries are the main considerations for investment.As an important decision-making factor that positively influences the choice of investment location, market size has great appeal to investment entities.
Secondly, it analyzes the influence of institutional distance on the overall investment scale.The normative system distance correlation coefficient is significantly negatively correlated with the investment.The conclusions of the whole sample and the group sample are the same.That is, investors are more willing to choose a host country with similar cultural practices to invest to reduce investment costs.In the whole sample and the sample of low-income host countries, the regulatory institutional distance is significantly positively correlated with the investment scale, but in the sample of medium and high-income countries, the result is opposite.The regulatory system distance has a negative effect on the investment scale.
Finally, it discusses the adjustment effect of the regulatory system distance on the investment.In all the samples, the regulatory system has a reverse adjustment effect on the market-oriented investment.For high-income countries, the regulatory system distance has a negative impact on the investment driven by different motivations, especially for technology-seeking investment.For middle-income countries, the regulatory system distance has a significant reverse adjustment effect on labor-seeking investment.For low-income countries, the regulatory system distance has a very significant positive effect on natural resource-seeking investment.
Based on the above conclusions, the following suggestions are proposed for the location selection of Chinese investment entities: First, China's investment entities should consider the institutional distance between China and the host country when making investment location choices.
In views of the fact that the normative system distance is not conducive to in- fact that the regulatory system distance has a negative effect on market-seeking investment, it also has a significant hindrance to the labor-seeking and technology-seeking investment in middle and high-income countries.It is necessary to reduce the regulatory system distance between China and the host countries in order to expand the scale of OFDI.On the one hand, it requires investment entities to passively choose investment objects with similar regulatory environment.
On the other hand, it is also necessary for the government to draw attention.
Relevant departments should improve the environment of their own regulatory systems to reduce the gap with the host countries.
Third, it is necessary to establish a relevant risk prediction and prevention system from the beginning of the selection of investment objects to the overseas operations after investment.Most of the countries along the "Belt and Road" are still developing countries.Some countries are facing the threat of violence and terrorist attacks, which greatly increases the possibility of uncertainty in the investment process.Therefore, it is necessary to establish a relatively complete risk assessment and control system, and to do a good job of pre-forecasting, in-process control and post-processing.
Hypothesis 2 :
The regulatory system distance between China and the developed host countries has a negative effect on the expansion of China's OFDI H. R. Zhang DOI: 10.4236/jss.2019.72009124 Open Journal of Social Sciences scale.Hypothesis 3: The regulatory system distance between China and the underdeveloped host countries has a positive effect on the expansion of China's OFDI scale.While China's economy is developing at a rapid pace, the scarcity of natural resources is becoming more and more serious.The goal of nature resource-seeking investment is to obtain the natural resources at a low cost.Hypothesis 4 is proposed: Host country's natural resource abundance is positively correlated with the scale of OFDI.With the gradual disappearance of the demographic dividend, the low-cost advantage of the manufacturing industry has not existed.So manufacturing industry begins to seek a lower-cost transformation, which is the purpose of labor resources-seeking OFDI.Hypothesis 5 is proposed: the labor cost of the host country is negatively correlated with the scale of OFDI.In recent years, more and more multinational companies in China have chosen developed countries as the target of investment.The main purpose is to learn the advanced technology and management experience of the host country.Hypothesis 6 is proposed: the development of the technical level of the host country is positively correlated with the scale of OFDI.
creasing investment, the investment entity should strengthen communication and cooperation with local enterprises and the public and make good use of the advantages of the Chinese population in the host country.They can learn about local customs and habits through intermediaries or organize relevant personnel to conduct overseas exchanges and other means to promote China's excellent culture in order to obtain the cultural identity of local people and reduce transaction costs caused by differences in normative systems.Second, investment entities need to maximize the use of institutional distance adjustments in response to their different investment motivations.In view of the H. R. Zhang DOI: 10.4236/jss.2019.72009130 Open Journal of Social Sciences
Table 1 .
Indicator selection instructions and data sources.
H. R. Zhang DOI: 10.4236/jss.2019.72009122 Open Journal of Social Sciences as an indicator to measure the level of China's investment.Since the annual investment flow data varies greatly, some are negative or vacant, and the stock data is ultimately selected.
3.1.DependentVariableChina's Outward Foreign Direct Investment (OFDI): This paper selects the investment stock data of 57 countries along the Belt and Road in China from 2008 H. R. Zhang DOI: 10.4236/jss.2019.72009123 Open Journal of Social Sciences to 2017
Table 2 .
Empirical results of institutional distance and investment motivation.
Table 3 .
Regulatory system distance adjustment effect.: The numbers in parentheses are t values; "*", "**" and "***" indicate that the regression coefficients pass the 1%, 5%, and 10% significance test.The variables gn, gg, gl, and gt represent the interactions between the regulatory system distance and natural resources, market size, labor costs, and technical elements. Note | 5,910.8 | 2019-02-15T00:00:00.000 | [
"Economics"
] |
Antibacterial Effect of Eicosapentaenoic Acid against Bacillus cereus and Staphylococcus aureus: Killing Kinetics, Selection for Resistance, and Potential Cellular Target
Polyunsaturated fatty acids, such as eicosapentaenoic acid (EPA; C20:5n-3), are attracting interest as possible new topical antibacterial agents, particularly due to their potency and perceived safety. However, relatively little is known of the underlying mechanism of antibacterial action of EPA or whether bacteria can develop resistance quickly against this or similar compounds. Therefore, the aim of this present study was to determine the mechanism of antibacterial action of EPA and investigate whether bacteria could develop reduced susceptibility to this fatty acid upon repeated exposure. Against two common Gram-positive human pathogens, Bacillus cereus and Staphylococcus aureus, EPA inhibited bacterial growth with a minimum inhibitory concentration of 64 mg/L, while minimum bactericidal concentrations were 64 mg/L and 128 mg/L for B. cereus and S. aureus, respectively. Both species were killed completely in EPA at 128 mg/L within 15 min at 37 °C, while reduced bacterial viability was associated with increased release of 260-nm-absorbing material from the bacterial cells. Taken together, these observations suggest that EPA likely kills B. cereus and S. aureus by disrupting the cell membrane, ultimately leading to cell lysis. Serial passage of the strains in the presence of sub-inhibitory concentrations of EPA did not lead to the emergence or selection of strains with reduced susceptibility to EPA during 13 passages. This present study provides data that may support the development of EPA and other fatty acids as antibacterial agents for cosmetic and pharmaceutical applications.
Introduction
The marine-derived polyunsaturated fatty acid (PUFA) eicosapentaenoic acid (EPA; C20:5 n-3) has antimicrobial properties and there is increasing interest in developing fatty acids as new antibacterial agents, especially given the rise of bacterial pathogens with resistance against existing antibiotics [1][2][3][4]. Similar to many other PUFAs, EPA exerts potent effects against Gram-positive species, including human pathogens Bacillus cereus and Staphylococcus aureus [3]. S. aureus causes a multitude of clinical problems from mild skin complaints, such as impetigo, to more serious soft tissue infections, osteomyelitis, and systemic bacteraemia [5]. Meanwhile, B. cereus is a well-known foodborne pathogen that causes infections of the gastrointestinal tract, but this bacterium is also responsible for severe infections of the eyes, lungs, cutaneous tissues, and central nervous system [6]. Importantly, both pathogens can cause serious infections of wounds and surgical sites [5,6] and new effective treatment options are highly desirable.
In clinical and cosmetic applications, free fatty acids such as EPA could be applied topically to bolster the free fatty acids present naturally on the skin and mucosal surfaces as part of innate immunity to protect against microbial infection [3,4,[7][8][9][10]. In addition to antimicrobial activities, EPA exerts beneficial anti-inflammatory actions [11] and has other positive attributes that would support its development as a new topical antibacterial agent, including wound healing properties [12], potency and perceived safety [1,4,13], and a suspected lack of acquired bacterial resistance mechanisms against this and other fatty acids [14]. However, little is known of whether or not bacteria can develop resistance quickly against this compound, or the underlying mechanisms of antibacterial action of EPA [3]. Addressing these knowledge gaps may hasten the development of EPA and other fatty acids as new topical antibacterial agents [1].
The aim of the present study was to characterize the antibacterial activity of EPA against two Gram-positive pathogens, B. cereus and S. aureus, and investigate whether the bacteria could develop reduced susceptibility to this fatty acid upon repeated exposure and determine the possible mechanism of action.
Results
The susceptibility of B. cereus NCIMB 9373 and S. aureus Newman to EPA was assessed by broth micro-dilution according to Clinical and Laboratory Standards Institute protocols [15,16]. EPA demonstrated both growth inhibitory and bactericidal activities against B. cereus and S. aureus. The minimum inhibitory concentration (MIC) was 64 mg/L for EPA against both B. cereus and S. aureus, while the minimum bactericidal concentration (MBC) for B. cereus and S. aureus was 64 and 128 mg/L, respectively. In trials to determine kill kinetics at 128 mg/L EPA, no colonies formed by surviving cells were detected after plating 5 × 10 5 colony forming units (CFU)/mL suspensions of B. cereus and S. aureus in Mueller-Hinton (MH) broth at 15 min or at subsequent sample times ( Figure 1). As expected, some cell division occurred in the control suspensions in MH broth during the 4-h incubation ( Figure 1). This experiment was repeated for cell suspensions prepared in phosphate-buffered saline (PBS) to determine whether active bacterial growth was necessary for the killing activity of EPA, but again no colonies formed by surviving cells were detected within 15 min and there was little change in CFU/mL during the 4-h incubation in the control suspensions ( Figure 1). In clinical and cosmetic applications, free fatty acids such as EPA could be applied topically to bolster the free fatty acids present naturally on the skin and mucosal surfaces as part of innate immunity to protect against microbial infection [3,4,[7][8][9][10]. In addition to antimicrobial activities, EPA exerts beneficial anti-inflammatory actions [11] and has other positive attributes that would support its development as a new topical antibacterial agent, including wound healing properties [12], potency and perceived safety [1,4,13], and a suspected lack of acquired bacterial resistance mechanisms against this and other fatty acids [14]. However, little is known of whether or not bacteria can develop resistance quickly against this compound, or the underlying mechanisms of antibacterial action of EPA [3]. Addressing these knowledge gaps may hasten the development of EPA and other fatty acids as new topical antibacterial agents [1].
The aim of the present study was to characterize the antibacterial activity of EPA against two Gram-positive pathogens, B. cereus and S. aureus, and investigate whether the bacteria could develop reduced susceptibility to this fatty acid upon repeated exposure and determine the possible mechanism of action.
Results
The susceptibility of B. cereus NCIMB 9373 and S. aureus Newman to EPA was assessed by broth micro-dilution according to Clinical and Laboratory Standards Institute protocols [15,16]. EPA demonstrated both growth inhibitory and bactericidal activities against B. cereus and S. aureus. The minimum inhibitory concentration (MIC) was 64 mg/L for EPA against both B. cereus and S. aureus, while the minimum bactericidal concentration (MBC) for B. cereus and S. aureus was 64 and 128 mg/L, respectively. In trials to determine kill kinetics at 128 mg/L EPA, no colonies formed by surviving cells were detected after plating 5 × 10 5 colony forming units (CFU)/mL suspensions of B. cereus and S. aureus in Mueller-Hinton (MH) broth at 15 min or at subsequent sample times ( Figure 1). As expected, some cell division occurred in the control suspensions in MH broth during the 4-hour incubation ( Figure 1). This experiment was repeated for cell suspensions prepared in phosphatebuffered saline (PBS) to determine whether active bacterial growth was necessary for the killing activity of EPA, but again no colonies formed by surviving cells were detected within 15 min and there was little change in CFU/mL during the 4-h incubation in the control suspensions ( Figure 1). Next, to investigate the possibility to select experimentally for strains with reduced susceptibility to EPA quickly, B. cereus and S. aureus were serially passaged 13 times in the presence of sub-inhibitory concentrations of this fatty acid in the wells of a 96-well microtitre plate. At each sub-passage, the contents of the wells used to inoculate the subsequent cultures were stored at −70 • C in a cryogenic tube with 15% glycerol (v/v), so that the susceptibility of each passage isolate to EPA could be determined by MIC and compared to the parent strains. After passage of the B. cereus strain in sub-inhibitory concentrations of EPA, the isolates from each of 13 passages and the parent strain showed no change in susceptibility to EPA as all isolates had identical MIC and MBC values, indicating the lack of selection of B. cereus cells with reduced susceptibility to EPA (Figure 2). Similarly, the MIC values of the corresponding S. aureus passage isolates were the same as the parent strain, though the MBC value of each passaged isolate (except for the final passage isolate) was lower than the MBC of the parent strain ( Figure 2). Still, there was no evidence for the selection of S. aureus cells with reduced susceptibility during repeated exposure to sub-inhibitory concentrations of EPA. Next, to investigate the possibility to select experimentally for strains with reduced susceptibility to EPA quickly, B. cereus and S. aureus were serially passaged 13 times in the presence of subinhibitory concentrations of this fatty acid in the wells of a 96-well microtitre plate. At each subpassage, the contents of the wells used to inoculate the subsequent cultures were stored at −70 °C in a cryogenic tube with 15% glycerol (v/v), so that the susceptibility of each passage isolate to EPA could be determined by MIC and compared to the parent strains. After passage of the B. cereus strain in sub-inhibitory concentrations of EPA, the isolates from each of 13 passages and the parent strain showed no change in susceptibility to EPA as all isolates had identical MIC and MBC values, indicating the lack of selection of B. cereus cells with reduced susceptibility to EPA ( Figure 2). Similarly, the MIC values of the corresponding S. aureus passage isolates were the same as the parent strain, though the MBC value of each passaged isolate (except for the final passage isolate) was lower than the MBC of the parent strain ( Figure 2). Still, there was no evidence for the selection of S. aureus cells with reduced susceptibility during repeated exposure to sub-inhibitory concentrations of EPA. Finally, to determine the mechanism of antibacterial action of EPA, leakage of 260-nm (A260)absorbing material from the bacterial cells in suspension was quantified after exposure to increasing concentrations of EPA for 30 min, according to a protocol modified from Carson et al. [17]. The detection of A260-absorbing material can indicate membrane perturbation and an increase in membrane permeability, and these measurements were taken concomitant with bacterial viability assessments by plating of the cell suspensions on agar. The bacterial inoculums at the start of incubation were 1.51 × 10 9 ± 0.41 × 10 9 CFU/mL (mean ± standard error) and 1.57 × 10 9 ± 0.15 × 10 9 CFU/mL for B. cereus and S. aureus, respectively, and thus were considerably greater than used in the killing kinetics experiment above. The carrier solvent (ethanol) had little effect on bacterial viability and at the greatest concentration of ethanol (2.56%, v/v) the bacteria recovered at 30 min was 1.31 × 10 9 ± 0.10 × 10 9 CFU/mL and 2.79 × 10 9 ± 0.05 × 10 9 for B. cereus and S. aureus, respectively (data not shown). Control incubations in the presence of carrier solvent (ethanol) showed that negligible quantities of A260-absorbing material were detected in cell-free filtrates (data not shown). However, leakage of A260-absorbing material was detected from B. cereus and S. aureus cell suspensions that had been incubated in the presence of ≥64 mg/L EPA for 30 min, and greater concentrations of EPA led to the detection of greater quantities of A260-absorbing material released from both species of bacteria ( Figure 3). Importantly, the increasing quantities of A260-absorbing material coincided with Finally, to determine the mechanism of antibacterial action of EPA, leakage of 260-nm (A260)-absorbing material from the bacterial cells in suspension was quantified after exposure to increasing concentrations of EPA for 30 min, according to a protocol modified from Carson et al. [17]. The detection of A260-absorbing material can indicate membrane perturbation and an increase in membrane permeability, and these measurements were taken concomitant with bacterial viability assessments by plating of the cell suspensions on agar. The bacterial inoculums at the start of incubation were 1.51 × 10 9 ± 0.41 × 10 9 CFU/mL (mean ± standard error) and 1.57 × 10 9 ± 0.15 × 10 9 CFU/mL for B. cereus and S. aureus, respectively, and thus were considerably greater than used in the killing kinetics experiment above. The carrier solvent (ethanol) had little effect on bacterial viability and at the greatest concentration of ethanol (2.56%, v/v) the bacteria recovered at 30 min was 1.31 × 10 9 ± 0.10 × 10 9 CFU/mL and 2.79 × 10 9 ± 0.05 × 10 9 for B. cereus and S. aureus, respectively (data not shown). Control incubations in the presence of carrier solvent (ethanol) showed that negligible quantities of A260-absorbing material were detected in cell-free filtrates (data not shown). However, leakage of A260-absorbing material was detected from B. cereus and S. aureus cell suspensions that had been incubated in the presence of ≥64 mg/L EPA for 30 min, and greater concentrations of EPA led to the detection of greater quantities of A260-absorbing material released from both species of bacteria ( Figure 3). Importantly, the increasing quantities of A260-absorbing material coincided with reductions in viable CFU/mL in the suspensions (Figure 3). Taken together, these observations suggest membrane disruption and probable cell lysis of the bacterial cells by EPA. The bacterial inoculums at the start of incubation were 1.51 × 10 9 ± 0.41 × 10 9 CFU/mL (mean ± standard error) and 1.57 × 10 9 ± 0.15 × 10 9 CFU/mL for B. cereus and S. aureus, respectively. The carrier solvent (ethanol) had little effect on bacterial viability and at the greatest concentration of ethanol (2.56%, v/v) the bacteria recovered at 30 min was 1.31 × 10 9 ± 0.10 × 10 9 CFU/mL and 2.79 × 10 9 ± 0.05 × 10 9 for B. cereus and S. aureus, respectively (data not shown). Meanwhile, control incubations in the presence of carrier solvent (ethanol) showed that negligible quantities of A260-absorbing material were detected in cell-free filtrates (data not shown). Data are mean (geometric mean for CFU values) ± standard error (not all error bars are visible); n = 3 for A260 values, n = 2 for CFU/mL determinations (detection limit was 2 log10 CFU/mL); note that the secondary y-axis (A260) scales differ for (a) and (b).
Discussion
EPA is antimicrobial and this property is being exploited in the development of new topical cosmetics and pharmaceuticals [1][2][3]; however, relatively little is known for its antibacterial mechanisms or the ease with which it is possible to select for strains with reduced susceptibility. In this present study, EPA was observed to kill rapidly two species of Gram-positive pathogen, probably by causing cell lysis, and there was little evidence for the selection of strains with reduced susceptibility after 13 passages.
In this present study, EPA inhibited the growth and killed both B. cereus and S. aureus at concentrations similar to previous reports for these and other Gram-positive species [2,3,18,19]. For B. cereus, MIC and MBC values were the same (64 mg/L) and killing was observed in PBS and culture medium within 15 min, indicating that actively dividing cells were not essential for bactericidal action. In conjunction with evidence of leakage of A260-absorbing material from cells at growth inhibitory and bactericidal concentrations, these data support the likely catastrophic loss of bacterial cell membrane integrity once a concentration threshold of EPA is reached. Meanwhile, for S. aureus, there was a two-fold difference between MIC and MBC values of EPA (64 and 128 mg/L, respectively) and EPA killed cells within 15 min, which is consistent with previous reports [2,18]. Similar to B. cereus, there was no evidence of the need for actively dividing cells to exert antibacterial action, as EPA killed S. aureus equally as effectively in PBS and MH broth. Notably, the leakage experiment showed that 2.10 × 10 4 CFU/mL of S. aureus survived even at the greatest concentration of EPA (i.e., The bacterial inoculums at the start of incubation were 1.51 × 10 9 ± 0.41 × 10 9 CFU/mL (mean ± standard error) and 1.57 × 10 9 ± 0.15 × 10 9 CFU/mL for B. cereus and S. aureus, respectively. The carrier solvent (ethanol) had little effect on bacterial viability and at the greatest concentration of ethanol (2.56%, v/v) the bacteria recovered at 30 min was 1.31 × 10 9 ± 0.10 × 10 9 CFU/mL and 2.79 × 10 9 ± 0.05 × 10 9 for B. cereus and S. aureus, respectively (data not shown). Meanwhile, control incubations in the presence of carrier solvent (ethanol) showed that negligible quantities of A260-absorbing material were detected in cell-free filtrates (data not shown). Data are mean (geometric mean for CFU values) ± standard error (not all error bars are visible); n = 3 for A260 values, n = 2 for CFU/mL determinations (detection limit was 2 log 10 CFU/mL); note that the secondary y-axis (A260) scales differ for (a,b).
Discussion
EPA is antimicrobial and this property is being exploited in the development of new topical cosmetics and pharmaceuticals [1][2][3]; however, relatively little is known for its antibacterial mechanisms or the ease with which it is possible to select for strains with reduced susceptibility. In this present study, EPA was observed to kill rapidly two species of Gram-positive pathogen, probably by causing cell lysis, and there was little evidence for the selection of strains with reduced susceptibility after 13 passages.
In this present study, EPA inhibited the growth and killed both B. cereus and S. aureus at concentrations similar to previous reports for these and other Gram-positive species [2,3,18,19]. For B. cereus, MIC and MBC values were the same (64 mg/L) and killing was observed in PBS and culture medium within 15 min, indicating that actively dividing cells were not essential for bactericidal action. In conjunction with evidence of leakage of A260-absorbing material from cells at growth inhibitory and bactericidal concentrations, these data support the likely catastrophic loss of bacterial cell membrane integrity once a concentration threshold of EPA is reached. Meanwhile, for S. aureus, there was a two-fold difference between MIC and MBC values of EPA (64 and 128 mg/L, respectively) and EPA killed cells within 15 min, which is consistent with previous reports [2,18]. Similar to B. cereus, there was no evidence of the need for actively dividing cells to exert antibacterial action, as EPA killed S. aureus equally as effectively in PBS and MH broth. Notably, the leakage experiment showed that 2.10 × 10 4 CFU/mL of S. aureus survived even at the greatest concentration of EPA (i.e., 512 mg/L) despite the release of A260-absorbing material being four times greater at this concentration than observed for B. cereus when no surviving cells were detected. This observation may derive from differences in the physiology of the cell membranes of these species, and it could be that EPA causes differential effects on membrane permeability of the two bacteria. Moreover, S. aureus may tolerate greater membrane perturbation but remain viable (for longer at least), whereas similar disruption of the B. cereus membrane may be lethal. Indeed, the species-specific variations in the action of EPA observed in this present study are worthy of further investigation. In addition, the composition and quantity of A260-absorbing material (typically nucleic acids [17]) in the cytoplasmic components could differ between the species and this also would need to be determined. Taken together, these observations suggest possible concentration-dependent inhibitory and bactericidal mechanisms of action [4], and EPA probably affects cell membrane-associated metabolic systems or increases permeability, ultimately leading to cell lysis. This suggestion is consistent with other studies that have proposed the cell membrane to be the main site of action for antibacterial free fatty acids, with detrimental effects caused through disruption of vital metabolic processes including cellular respiration [8,[20][21][22][23] and nutrient uptake [24], or physical disturbance leading to increased permeability, leakage of cellular components [8,23,[25][26][27][28], and cell lysis (reviewed by Desbois and Smith [14]).
Certain bacteria intrinsically resist the actions of fatty acids and the cell wall of Gram-positive species can confer protection against free fatty acids [25]. Some bacteria increase cell wall synthesis or decrease cell surface hydrophobicity on exposure to free fatty acids [29][30][31]. The presence of cell-membrane-stabilizing carotenoids that decrease fluidity may also reduce susceptibility to free unsaturated fatty acids [32,33]. Still, there have been few studies on the selection of bacterial strains with reduced susceptibility to antibacterial free fatty acids, particularly for Gram-positive species, and, to our knowledge, this present study is the first to perform serial passage to select for any strains with reduced susceptibility to EPA. Previously, strains of Escherichia coli with reduced susceptibility to caprylic acid (C8:0) or capric acid (C10:0) were selected successfully after 10 serial transfers on agar containing the fatty acids at sub-inhibitory concentrations [34], though the mechanisms underlying this phenomenon were not investigated further. Moreover, Petschow et al. [35] reported the isolation of Helicobacter pylori mutants on agar containing 10× MIC of the medium-chain length saturated fatty acid lauric acid (C12:0) at a rate of 10 −8 , but the susceptibility of individual colonies was not subsequently confirmed. Additionally, Obonyo et al. [36] isolated H. pylori cells that resisted a previously bactericidal concentration of linolenic acid (C18:3 n-3) after just three sub-cultures in a sub-bactericidal concentration of this fatty acid. In contrast, Sun et al. [37] reported no change in susceptibility to lauric acid of H. pylori in response to serial passage six times in sub-inhibitory concentrations. Meanwhile, Lacey and Lord [38] were unable to select stable S. aureus strains with reduced susceptibility to linolenic acid including mutants generated by chemical mutagenesis, and, elsewhere, no S. aureus strains resistant to linoleic acid (C18:2 n-6) were detected in a 5000 clone transposon insertion library [30]. The opportunity for B. cereus to develop resistance to EPA may be reduced by MIC and MBC values being the same as the concentration inhibiting growth is close to the concentration having a lethal effect. However, for S. aureus, culturable cells were detected after 30 min exposure to EPA at 512 mg/L and there exists a difference between MIC and MBC values, meaning cells are inhibited but not killed at concentrations in this window, thus potentially permitting the opportunity to select for spontaneous resistant mutants in the surviving population; nevertheless, this was not borne out in practice and serial passage of both bacteria in the presence of sub-inhibitory concentrations of EPA did not lead to the emergence or selection of strains with reduced susceptibility. These observations are consistent with the suggestion that it is more difficult to select for resistance against compounds that exert their antibacterial action by acting on multiple cellular targets and the cell membrane. This present study provides some indication of the difficulty in rapidly selecting for resistance against EPA, but future investigations will use further bacterial species and strains, undertake more passages, and employ more incremental sub-inhibitory PUFA concentrations.
To conclude, the data in this present study provide support for the development of EPA as a possible new antibacterial agent due to its favorable potency against Gram-positive pathogens, lack of rapid selection of bacterial strains with reduced susceptibility or resistance, and bactericidal mechanism of action.
Reagents and Bacteria
EPA (>99% purity) and culture media were purchased from Sigma-Aldrich Ltd. (Poole, Dorset, UK). An EPA stock was made in ethanol (≥99.5%) to 20 mg/mL and stored at −20 • C. All other solutions and media were made with ultrapure deionized water (Option 3; Elga, High Wycombe, Bucks, UK) and were sterilized by autoclaving at 121 • C for 15 min or by filtration (polyethersulphone, 0.22 µm; Millipore, Watford, UK). S. aureus Newman (gifted by Dr. Angelika Gründling, Imperial College London, UK) and B. cereus NCIMB 9373 were resuscitated on MH agar at 37 • C from 15% glycerol (v/v) stocks kept at −70 • C, and maintained thereafter at 4 • C.
Preparation of Bacterial Suspensions
Typically, bacterial suspensions were prepared from cultures that were inoculated with 3-5 colonies into 5 mL MH broth in universal bottles and incubated (37 • C, 150 rpm) until late exponential phase (determined by measuring the absorbance at 600 nm of the culture and comparing to growth curves constructed for each species; approximately 12 h). Next, bacterial cells were harvested by centrifugation (2000× g, 10 min, 4 • C), washed twice with PBS (for 1 L: 8 g of NaCl, 0.2 g of KCl, 1.78 g of Na 2 HPO 4 ·2H 2 O, 0.24 g of KH 2 PO 4 ; pH 7.4), and re-suspended to the desired CFU/mL in MH broth or PBS. The CFU/mL of the suspensions were checked by serially diluting 10 µL in PBS (in duplicate), plating on MH agar, incubating overnight (37 • C, 24 h), and performing CFU counts.
Assessing Antibacterial Potency
MIC values were determined by broth micro-dilution according to Clinical and Laboratory Standards Institute protocol [15]. Briefly, EPA in MH broth was serially diluted in flat-bottomed 96-well microtitre plates to final well concentrations of 4,8,16,32,64,128,256, and 512 mg/L (100 µL per well). Five microliters of bacterial suspension at 1 × 10 7 CFU/mL (prepared in PBS as described in Section 4.2) was used to inoculate each well. Plates were sealed with Parafilm, incubated (37 • C, 24 h), and the lowest concentration that prevented bacterial growth visible to the naked eye was determined to be the MIC. Control wells containing either MH broth only or the volume of ethanol equal to the greatest volume in a test well were also inoculated; a non-inoculated MH broth well was also included. MBC was determined according to Clinical and Laboratory Standards Institute protocol [16] by plating 20 µL from each well showing no visible growth at 24 h on to MH agar and incubating these plates for colonies to form (37 • C, 24 h). Contents from individual wells were spread across a quarter of an agar plate and, as no attempt was made to wash away residual EPA, the effect of carryover preventing the formation of colonies cannot be dismissed. The lowest concentration of EPA that killed ≥99.9% of the initial inoculum was determined to be the MBC. MIC and MBC values were determined from duplicated series of wells.
Killing Kinetics
The times required for EPA at 128 mg/L to kill 5 × 10 5 CFU/mL from exponential phase cultures of B. cereus and S. aureus were determined. Briefly, 200 µL of EPA at 128 mg/L in MH was prepared and dispensed into an Eppendorf tube, while control wells received an equal volume of carrier solvent (2.56 µL ethanol). Then, 10 µL of a cell suspension (at 1 × 10 7 CFU/mL and prepared as described in Section 4.2) was added to each tube, before the contents were mixed by inversion and then incubated statically at 37 • C. At 15 min, 30 min, 1 h, 2 h, and 4 h, the CFU/mL in each tube was determined by serial dilution and plating of 10 µL of suspension as described in Section 4.2. Geometric means and standard errors of these values were calculated from quadruplicate trials. The experiment was repeated in PBS to determine whether active bacterial growth was necessary for the killing activity of EPA.
Selection of Bacterial Strains with Reduced Susceptibility to EPA
To investigate the possibility to select experimentally for strains with reduced susceptibility to EPA quickly, bacteria were serially passaged in the presence of sub-inhibitory concentrations of this fatty acid. Briefly, an MIC plate for each bacterium was prepared as described in Section 4.3, except that the final well concentrations of EPA were 16, 32, 64, and 128 mg/L. After 24-48 h incubation, 5 µL from the well showing growth at the greatest concentration of EPA was used to inoculate the wells of a new MIC plate set up such that the greatest EPA concentration was double that of the concentration in the well from which the inoculum was taken. Meanwhile, the remainder of the well contents were stored at −70 • C in a cryogenic tube with 15% glycerol (v/v). This process was continued for 13 passages for each species of bacterium. Finally, the MICs against EPA of each passage isolate and the original parent strain were determined as described in Section 4.3, once the cultures had been recovered from cryogenic stocks by culturing on MH agar (37 • C, 24 h) as described in Section 4.1.
Leakage of A260-Absorbing Material from Bacterial Cells
To assess bacterial membrane perturbation and increasing membrane permeability, leakage of 260-nm absorbing material was quantified from B. cereus and S. aureus cells in suspension after exposure to increasing concentrations of EPA for 30 min, according to a protocol modified from Carson et al. [17]. These measurements were performed concomitant with bacterial viability assessments by plating cell suspensions on agar. For this, EPA (solubilized in ethanol) was added to PBS and made up to 90 µL to give 16, 32, 64, 128, 256, and 512 mg/L (final volume concentrations after addition of inoculum below), while control tubes contained 90 µL PBS with ethanol concentrations corresponding to each of the respective EPA-containing tubes. Two negative control tubes contained PBS only (no EPA or ethanol). For 10 µL from each tube, A260 was determined on a NanoDrop 1000 spectrophotometer (ThermoScientific, Wilmington, DE, USA) and each of these values for the tube solutions served as the 'blank' when readings were to be taken again from each tube at 30 min. After this, to each tube was added 10 µL of bacterial suspension at 1.5 × 10 10 CFU/mL, which had been prepared in PBS as described in Section 4.2, except that the cells were derived from a 500-mL shake flask culture (37 • C, 150 rpm, 24 h). Immediately, one of the negative control tubes was sampled to determine CFU/mL and the A260 of sterile-filtered supernatant. CFU/mL was determined by serial dilution and plating of 10 µL of suspension as described in Section 4.2, while the remaining 80 µL of the suspension was centrifuged (2000× g, 10 min). Then the supernatant was collected and passed through a 0.22-µm syringe filter (4 mm; Sterlitech, Washington, DC, USA), before the A260 of this filtrate was measured on the NanoDrop against its respective 'blank'. Meanwhile, all other tubes were incubated (37 • C, 30 min). After incubation, the CFU/mL of unfiltered suspension and A260 of filtered suspension were determined for each tube as described above, however CFU/mL counts were performed only for the remaining negative control, each EPA-containing tube, and the tube containing the greatest volume of carrier solvent. Note that as the control incubations in the presence of carrier solvent (ethanol) showed the presence of only negligible quantities of A260-absorbing material in cell-free filtrates (data not shown), these A260 values were not subtracted from the A260 value of each respective EPA treatment reading. This experiment was repeated twice more, though CFU/mL was determined for only one of these further trials.
Author Contributions: Andrew P. Desbois and Phuc Nguyen Thien Le conceived and designed the experiments; Phuc Nguyen Thien Le performed the experiments; Andrew P. Desbois and Phuc Nguyen Thien Le analyzed the data; Andrew P. Desbois contributed reagents/materials/analysis tools; Andrew P. Desbois and Phuc Nguyen Thien Le wrote the paper.
Conflicts of Interest:
The authors declare no conflict of interest. | 7,243.6 | 2017-11-01T00:00:00.000 | [
"Biology"
] |
Exploring Early and Late Toxoplasma gondii Strain RH Infection by Two-Dimensional Immunoblots of Chicken Immunoglobulin G and M Profiles
Toxoplasma gondii is an intracellular apicomplexan parasite infecting warm-blooded vertebrate hosts, with only early infection stage being contained with drugs. But diagnosis differencing early and late infection was not available. In the present investigation, 2-dimensional immunobloting was used to explore early and late infections in chickens. The protein expression of T. gondii was determined by image analysis of the tachyzoites proteome separated by standard-one and conventional two-dimentional gel polyacrylamide electrophoresis (2D- PAGE). Pooled gels were prepared from tachyzoites of T. gondii. A representative gel spanning a pH range of 3-10 of the tachyzoite proteome consisted of 1306 distinct polypeptide spots. Two-dimensional electrophoresis (2-DE) combined with 2-DE immunoblotting was used to resolve and compare immunoglobulins (Igs) M & G patterns against Toxoplasma gondii strain RH (mouse virulent strain). Total tachyzoite proteins of T. gondii were separated by two-dimensional gel electrophoresis and analyzed by Western blotting for their reactivity with the 7 and 56 days post-infection (dpi) SPF chicken antisera. Different antigenic determinant patterns were detected during analysis with M and G immunoglobulins. Of the total number of polypeptide spots analyzed (1306 differentially expressed protein spots), 6.97% were identified as having shared antigenic polypeptide spots on immunoblot profiles with IgG and IgM antibodies regardless the time after infection. Furthermore, some of the immunoreactive polypeptide spots seemed to be related to the stage of infection. Interestingly, we found natural antibodies to toxoplasmic antigens, in addition to the highly conserved antigenic determinants that reacted with non-specific secondary antibody; goat anti-chicken IgG antibodies conjugated with horseradish peroxidase. In conclusion, unique reactive polypeptide spots are promising candidates for designation of molecular markers to discriminate early and late chicken infection.
Introduction
Toxoplasma gondii is an intracellular apicomplexan parasite that infects a wide range of warmblooded vertebrate hosts. The definitive hosts are members of the Felidae family including domestic and wild (feral) cats. A wide variety of vertebrates can serve as intermediate hosts including chickens. T. gondii-infected chickens are good indicators for environmental contamination with oocysts from cat feces because of their feeding habits [1][2][3]. T. gondii also has been known to infect many different birds, including chickens, ducks, turkey, and ostriches [4 -11]. It has been proposed that infected chickens might function as T. gondii reservoirs and an important source of Toxoplasma infection [3,6,7]. Based chiefly on the detection of specific anti-Toxoplasma antibodies; several techniques were used for serodiagnosis including immunofluorescence antibody test (IFAT), immunosorbent agglutination assay (ISAGA), enzymelinked immunofiltration assay (ELIFA), modified agglutination test (MAT), latex agglutination test (LAT), direct aglutination test (DAT), indirect hemagglutination (IHA), enzyme linked immunosorbent assay (ELISA), sabin feldman dye test (SFDT), enzyme-linked immunosorbent assay (ELISA), and immunoblotting (IB) [12,13]. Immunoblotting techniques and enzyme immunoassays have evolved tremendously for the detection of the presence of antibodies against most of the infectious agent-specific antigens in animal and human sera [14]. The combination of toxoplasmic antigens electrophoresis under denaturing conditions, an electrotransfer, and a specific antibody examination has been exploited to compare the immunological patterns of mothers, fetuses, and infants [13,15,16]. The combination of the 2-DE with immunoblotting (IB) technique, namely immunoproteomics revealed many distinct antigens compared with conventional SDS-PAGE (1-DE) and its immunoblotting assay. Insight into host immunological responses against pathogen proteins has been reported by a large number of investigators using two-dimensional gel electrophoresis (2-DE) combined with antigenic proteomes [17]. The proteome and antigenic proteome (immunoproteome) have been used to explore relationships between two isolates of Neospora caninum (KBA-2 and VMDL-1) [18], identification of strain-specific antigens of Toxoplasma gondii [19], characterization of the expressed proteins of T. gondii [20,21,22], Fasciola hepatica [23], Schistosoma japonicum [24], Ascaris suum [25], and even evaluation of cross-reactivity between tachyzoites of N. caninum and T. gondii [26]. Chicken antisera raised against the rapidly dividing tachyzoite stage (invasive stage) were used in an enzyme-linked immunosorbent assay (ELISA) and Western blot (immunoblot) analysis to obtain a more detailed picture of the diagnostic polypeptide spots (molecular markers) for more precise serodiagnosis of recent and late Toxoplasma-infected chickens.
Ethics Statement
Animal experiments were conducted in accordance with the guidelines of Beijing the Municipality on the Review of Welfare and Ethics of Laboratory Animals approved by the Beijing Municipality Administration Office of Laboratory Animals (BAOLA) and under the protocol (CAU-AEC-2010-0603) approved by the China Agricultural University Animal Ethics Committee. All experimental procedures were also approved by the Institutional Animal Care and Committee of China Agricultural University (The certificate of Beijing Laboratory Animal employee, ID: 15883) from Sigma-Aldrich, USA. Immobilon-P membranes were from Millipore (Millipore, China). Immobiline DryStrip, pH 3-10 nonlinear, 18cm; immobilized pH gradient gel (IPG) buffer and 2-D Quant Kit were from Amersham pharmacia Biotech AB, Uppsala, Sweden. Superenhanced chemiluminescent substrate (ECL) was from Shanghai Yubo Biological Technology Co, Ltd. Broad range molecular weight protein standards were from Bio-Rad; USA. All other chemicals were reagent grade.
Experimental chickens
Two-week-old specific pathogen free (SPF) Arbor Acre (AA) broiler chicks were purchased from Beijing Arbor Acres Poultry Breeding Co., Ltd. They were housed in isolators and fed with a pathogen-free diet and water. The climatic conditions, lighting program, and chicken fodder and water were manually-operated and the chicks were cared for in agreement with the approved guidelines of the Institutional Animal Care and Committee of China Agricultural University. A total of thirty; 30-day-old chicks were randomly allocated into two groups each consisting of 10 and 20 birds. The first group consisting of chickens was served as control. The second group with 20 chickens was subcutaneously infected with 5x10 6 live tachyzoites of T. gondii strain RH. The chickens were housed in two different isolators for the entire experiment, with food and tap water provided ad libitum. Chickens were exposed to a 12 h/12 h light/ darkness regimen at 25°c. The chickens were not abstained from food and water before CO 2 euthanasia.
Blood collection and serum samples
Blood samples from experimentally infected (test) and control specific pathogen free (SPF) chicks were collected at 7 dpi (days post-infection) and 56 dpi. All the blood samples obtained from the brachial vein were allowed to clot and then centrifuged at 3000 rpm for 20 minutes; sera were aspirated, dispensed into aliquots and stored at -20°C.
Pooled sera
Equal volumes of 9 Toxoplasma gondii-infected and 5 control chicken sera collected at individual dates were pooled according to collection date.
Each pool was aliquoted and the aliquots were designated 7 dpi, 56 dpi and control pooled sera respectively.
Sample preparation and electrophoresis
Parasite propagation and purification. Tachyzoites of T. gondii strain RH were obtained from the peritoneal cavity of 4-day infected inbred female mice as follows: The mice were euthanized by cervical dislocation and sprayed with 70% ethanol. The outer skin of the peritoneum was removed to expose the inner skin lining of the peritoneal cavity. A peritoneal lavage with 5 ml of PBS was recovered with a syringe to collect the parasites, passed through a 27-gauge needle, and the tachyzoites were purified by sieving through 3-mm-pore-size polycarbonate filters (Millipore, China). The tachyzoite-containing filterate was centrifuged at 100 ×g for 10 minutes at 4°C to eliminate peritoneal cells and debris. In order to collect the Toxoplasma tachyzoites, the tachyzoite-containing supernatant then was centrifuged at 200 ×g for 10 minutes at 4°C, and the pellet was washed thrice in PBS [27,28]. The tachyzoites from the same batch of samples were harvested, purified, washed and kept aliquots in -80°C for experimental use.
One-dimensional polyacrylamide gel electrophoresis. The protein in lysis buffer (Trisbase, pH 9.6) was mixed with loading buffer at a ratio 1:5 and then boiled for 5 minutes before loading. The protein was separated using 12% gels according to Amersham protocols. The running gels were stained using 0.1% Coomassie brilliant blue R-250 in 50% methanol and 10% glacial acetic acid for 30-60 min, and then destained in 10% and 7% glacial acetic acid.
The detailed procedure for silver staining gel is described below. Preparation for two-dimensional gel electrophoresis (2-DE). T. gondii strain RH Tachyzoites were obtained from the peritoneal cavity of 4-day infected inbred female mice and protein preparations was recovered according to [28] with minor modifications as follows: Protein was prepared by rapid freezing and thawing 3 times using liquid nitrogen to disrupt tachyzoites in lysis buffer containing 7 M urea, 2 M Thiourea, 4%(W/V) CHAPS, 1%(W/V) DTT, 1mM PMSF and 0.5%(V/V) immobilized pH 3-10 gradient strips (IPG) buffer, and dissolved in 40 mM Tris-base, pH 9.6. The protein concentration was determined by 2-D Quant Kit and used at concentrations of 100μg and 300μg for standard-one and conventional two-dimentional gel polyacrylamide electrophoresis to be stained with Coomassie brilliant blue R-250. For silver staining of two-dimensional gel electrophoresis, 200μg of protein was used.
Proteins were separated according to their isoelectric charge at 500 V for 1 hr, 1000 V for 1hr and 4500 V for 10 hrs at a constant temperature of 20°C; proteins were separated according to their isoelectric charge. IPG strips were stored at -20°C until use. The IPG strips were equilibrated for 1 hr in a reducing buffer (6 M Urea, 87% v/v Glycerol, 64.8 mM DTT, 2%w/v SDS, 0.04% Bromophenol blue and 1.5 M Tris-HCl, pH 8.8) and then followed by 1 hr in an alkylation buffer (6 M Urea, 87%v/v Glycerol, 135 mM iodoacetamide, 2% w/v SDS, 0.04% Bromophenol blue and 1.5 M Tris-HCl, pH 8.8). The equilibrated IPG sample strips were subjected to 12.5% vertical SDS-PAGE overnight at 30 mA. Broad range molecular weight protein standards were included for all protein samples. Gels were stained with Coomassie brilliant blue R-250 after fixation in 10% methanol and 7% acetic acid for 1 hr. The gels were destained twice for 1-2 hrs in 10% methanol and 7% acetic acid.
Silver staining was done essentially as previously described by [30]. After electrophoresis, gels were fixed for 2 hrs in an appropriate volume of fixing solution {(50% ethanol (or methanol), 12% acetic acid and 0.05% formalin)}. The gel was washed in 20% ethanol for 20 min after discarding the fixing solution and then incubated for 2 min in sensitizing solution (0.02% (w/v) sodium thiosulfate (Na 2 S 2 O 3 ).
Next, the gels were washed twice for 1 min each, in deionized water, and incubated in cold silver staining solution {(0.2% (w/v) silver nitrate (AgNO 3 ) containing 0.076% formalin)} for 20 min to allow the silver ions to bind to the polypeptide spots. In the final step, the gels were rinsed in deionized water for 20-60 sec and then in the developing solution {(6% (w/v) sodium carbonate (Na 2 CO 3 ), 0.0004% (w/v) sodium thiosulfate (Na 2 S 2 O 3 ) and 0.05% formalin)}. The reactions were terminated by adding 12% acetic acid.
Immunoblot analysis. The separated polypeptide spots from 2-DE gels were transferred to Immobilon-P Transfer Membrane (Millipore, China) for 90 min at 18 V on a Trans-blot semi-dry Transfer Cell TM (Biorad) in semi-dry transfer buffer (48 mM Tris and 2.93 g glycine); pH 9.2 containing 20% methanol. The membranes were rinsed in methanol for 3 min and then washed twice with PBS-T buffer; pH 7.4 (8 mM sodium phosphate, 2 mM potassium phosphate, 140 mM NaCl, 2.7 mM KCl and 0.5% v/v Tween) for 30 s each. The blots were quenched overnight at 4°C with 1%v/v fish gelatin in PBS-T. The blotted membranes were incubated with anti-Toxoplasma gondii RH strain SPF chicken sera diluted 1:500 in 1%v/v fish gelatin for 1 hr at ambient temperature under constant agitation. After 3 washes in PBS-T for 15 min, the membranes were incubated with goat anti-chicken IgG (H+L chain specific) antibodies conjugated with horseradish peroxidase diluted 1:2000 in blocking buffer for 1 hr at ambient temperature under constant agitation. Membranes were washed three times with PBS-T buffer for 15 min each and one time with PBS for 10 min, then treated with two different substrate systems; superenhanced chemiluminescent substrate (ECL) plus according to the manufacturer's instructions; the blots were exposed to X-Ray film for 30-60 s. Analysis of the 2D-immunoblotting images was carried out with PDQuestTM 2-D Analysis Software; (BIO-RAD).
Results
In order to rule out environmental factors that could influence gene products, all protein preparations were conducted from the same batch of T. gondii tachyzoites for all 1D and 2D gels and blots, and the experiments were run in triplicate to avoid experimental bias and random errors. As shown in Fig. 1, the protein profile of the tachyzoite protein of T. gondii strain RH was resolved by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and stained with Coomassie brilliant blue (CBB) and silver staining methods. Figs. 1A and 1B displayed differential staining sensitivity.
Although CBB stain is more convenient than the silver stain, the latter is more sensitive than CCB stain. In addition to the multi-step procedure of the silver staining method, highly expressed proteins were visualized as dark brown periphery with yellow center (i.e. volcano or donut-shaped) that can lead to problems during qualitative and quantitative analysis as in Fig. 2A. The more intense CBB and silver stain patterns of different bands that were resolved by SDS-PAGE were good indicators of the presence of more than one polypeptide in the bands at the same molecular weight or of over-expression of the same polypeptides (unpublished data) or of relative abundance of those particular polypeptides. High-resolution twodimensional polyacrylamide gel electrophoresis (2-D PAGE) combining with the isoelectric focusing and SDS-polyacrylamide gel electrophoresis provides much better resolution than either procedure alone. The procedure separates the complex mixtures of protein extracted from biological samples according to charge (pI) by isoelectric focusing (IEF) in the first dimension and according to size (MW) by SDS-PAGE in the second dimension followed by visualizing with mass spectrometry (MS)-compatible stains (Fig. 2B). Pooled gels were prepared from tachyzoites of T. gondi strain RH. A representative gel spanning a pH range of 3-10 of the tachyzoite proteome consisted of 1306 distinct polypeptide spots.
The appearance of spot trains of differently modified and charged variants of the same polypeptide spots is pictured below (Fig. 2B). As shown in Fig. 2A, spots with yellow centers and dark boundaries could lead to problems during qualitative and quantitative analysis by image analysis software.
Immunological evaluations of the whole tachyzoite antigens of T. gondii strain RH were conducted. The 2-D immunoblots were probed with immune and non-immune SPF chicken sera with recent and late toxoplasmosis. Western blotting of the 2-DE gels using pooled control sera as primary antibodies and anti-chicken IgG as secondary antibodies revealed a total of 15 immunoreactive polypeptide spots (Fig. 3).
As illustrated in Fig. 4, when tachyzoite antigens of T. gondii strain RH were separated by 2-DE and electroblotted onto Polyvinylidene fluoride (PVDF) before being probed with secondary antibodies; 4 immunoreactive polypeptide spots were revealed.
The T. gondii strain RH antigenic polypeptide spots eliciting the immunoglobulin G (IgG) and IgM antibody responses were studied by using 7 dpi and 56 dpi T. gondii-infected specific pathogen free (SPF) chickens. A total of 91 shared reactive polypeptide spots were detected by using IgG and IgM antibodies, which were of lowest interest value with respect to the discrimination between early and late infection (S1 Fig.). S1 Table provides the isoelectric point and molecular weight results of shared immunogenic polypeptide spots obtained with antibodies specific for IgG 56 dpi, IgG 7dpi, IgM 56 dpi and IgM 7dpi obtained from the PDQuestTM 2-D Analysis Software.
Moreover, IgG-Toxoplasma 7 dpi and 56 dpi antibodies reacted mainly with 128 polypeptide spots (S2 Fig.); however 155 polypeptide spots reacted only with IgG 56 dpi (Fig. 5). The restricted number of antigenic polypeptide spots (i.e. 20) reacting with IgG is of great diagnostic value for late infection (Fig. 6). From the data in S2 Fig, Figs. 5 and 6, the isoelectric point and molecular weight were depicted as illustrated in S2 Table, Tables 1 and 2 The serological profile of antigenic components in the IgM Toxoplasma antibody response was different from that of the IgG response, albeit some characteristic features were persistently observed (S3 Fig, Figs. 7 and 8). As pictured below, 145 shared IgM immunoreactive polypeptide spots were revealed by using a pool of 9 sera from 7 dpi and 56 dpi T. gondii-infected SPF chickens. However, 65 and 76 unique antigenic polypeptide spots reacted with IgM Toxoplasma antibodies from 7 dpi and 56 dpi SPF chickens respectively. The results of 2D-immunoblotting gels (S3 Fig, Figs. 7 and 8) that were accomplished with the aid of PDQuestTM 2-D analysis software are depicted in S3 Table, Tables 3 and 4 respectively.
Comparative analyses of the immunologically resolved, immobilized and reactive polypeptide spots of T. gondii that have been detected by IgM and IgG Toxoplasma antibodies from experimentally infected SPF chickens are summarized below (Table 5).
Further analysis of the 2-DE immunoblot profiles revealed that the signal was slightly more intense at 7 dpi than 56 dpi. This observation might be related to antibodies avidities occurring during the course of infections. From our unpublished data, the IgG antibody titers assayed by modified agglutination test (MAT) to T. gondii RH strain-infected chickens started to increase by 1 week after subcutaneous infection and peaked between the third and fourth weeks, and subsequently antibody titres declined slightly.
Discussion
The infectious tachyzoite stage of T. gondii RH strain is the disease-causing stage in the life stage of T. gondii. Infection of SFP chickens with the T. gondii RH strain induced production of Toxoplasma-specific antisera which were exploited to find specific molecular markers for more Diagnosis of Toxoplasma gondii Strain RH-Infected Chickens Using 2DI precise serodiagnosis of different stages of infection (i.e. recent versus late Toxoplasma infection). The protein expression profile of T. gondii was determined by image analysis of the tachyzoites proteome separated by standard-one and conventional two-dimentional gel polyacrylamide electrophoresis (2D-PAGE), and the macro-and micro-scale gels of the tachyzoite proteome were stained with Coomassie brilliant blue and the high sensitive silver stain. Coomassie brilliant blue is more convenient, reproducible and an endpoint procedure compared with the multi-step silver stain procedures. Furthermore, variations in the efficacy silver staining for some proteins were reported by Morozov, et al. in 1986 [31], so this variation together with protein load variations (300μg of protein for Coomassie brilliant blue R-250 versus 200μg of protein for silver staining) could account for other differences in the visual data occurring between the two stains. The close proximity of molecular weight bands that bear the same charge and the possibility for the presence of more than one different polypeptide in the same band in the electrophoretic profile of the T. gondii RH strain resolved by macro-scale SDS-PAGE technique led to our use of a more highly sophisticated micro-scale separating method (2D SDS-PAGE). For this purpose, pooled gels were prepared from tachyzoites of T. gondii, and a representative gel spanning a pH range of 3-10 of the tachyzoite proteome consisted of 1306 distinct polypeptide spots. More than 163 and 150 protein spots from T. gondii strains RH and KI-1 tachyzoites, in corresponding order, were detected by 2-DE within a pH range of 3-10 after silver staining [32]. A high-resolution 2-DE gel separation over pH ranges 4-7 and 6-11 was also exploited to distinguish over 1000 polypeptides spots [20], and in a separate study, 1,227 protein spots of T. gondii soluble tachyzoite antigens were resolved through fractionation by 2-DE at a pH range of 3-10 [33]. These differences could be due to sample preparation and minor differences that affect the intensities and numbers of polypeptide spots in the two-dimensional gels.
The tachyzoite immunogenic polypeptide spot analysis recognized by specific humoral immune responses has important implications for immunodiagnosis, immunotherapy and vaccination strategies. Two-dimensional electrophoresis (2-DE) combined with 2-DE Table 4. T. gondii strain RH tachyzoite proteins (Fig. 8 immunoblotting was also used to resolve and compare M and G immunoglobulin patterns of the Toxoplasma gondii strain RH (mouse virulent strain). The subcutaneous route of acquisition of T. gondii strain RH appeared to be the reason the immunoglobulin A (IgA) antibody response was of low interest. Nevertheless, amongst the 1306 resolved polypeptide spots, 91 common spots were reacted with T. gondii IgM and IgG antibodies regardless of the course of infection. Furthermore, some of the immunoreactive polypeptide spots appeared to be related to the stage of infection. During the early stage of infection (i.e. 7 days post-infection), 55 and 155 of unique polypeptide spots reacted with T. gondii IgM and IgG antibodies, respectively. However, 76 and 20 unique polypeptide spots were reacted with T. gondii IgM and IgG antibodies recovered from the late stage of infection (i.e. 56 days post-infection) in corresponding order. The unique polypeptide spots are of special interest for discrimination between early and late infections, and the early unique polypeptide spots appear to be good early infection markers. However, some of late stage spots could be good markers to discriminate late infections. Naturally occurring immunoglobulin (Ig) G antibodies to T. gondii strain RH were also observed in a pool of control sera collected from SPF chickens. Our present findings agree with those observed in previous studies [34][35][36], and our results are also consistent with a previous report [37] describing the presence of naturally occurring immunoglobulin M antibodies to T. gondii in Japanese populations. The existence of IgM and IgG antibodies in humans infected with T. gondii was described in the previous work [38,39]. Further supporting evidence for the presence of natural antibodies of IgM and IgG classes against killed tachyzoites comes from fluorescence or electron microscopy studies showing localized intense staining of tachyzoites [40][41][42]. Moreover, goat anti-chicken IgG (H+L chain specific) antibodies conjugated with horseradish peroxidase detected 4 polypeptide spots. These spots may contain some highly conserved antigenic determinants.
In summary, an implication of our findings is that unique reactive polypeptide spots are promising candidates for the formulation of molecular markers to segregate early and late chicken infections. Furthermore, the findings of our study together with those we are currently undertaking provide information regarding a wide variety of warm-blooded vertebrate hosts. The common unique determinants can be used to develop universal chimeric molecular markers for detection of all serologically positive warm-blooded vertebrate hosts and to differentiate between different toxoplasmosis infection stages. Table. T. gondii strain RH tachyzoite proteins (S1 Fig.). Isoelectric point and molecular weight of shared immunogenic polypeptide spots using antibodies specific for IgG 56 dpi, IgG 7dpi, IgM 56 dpi and IgM 7dpi. (DOC) S2 Table. T. gondii strain RH tachyzoite proteins (S2 Fig.). Isoelectric point and molecular weight of shared immunogenic polypeptide spots using antibodies specific for IgG 56 dpi and 7dpi. (DOC) S3 Table. T. gondii strain RH tachyzoite proteins (S3 Fig.). Isoelectric point and molecular weight of shared polypeptide spots of 2-DE separated T. gondii strain RH tachyzoite proteins using antibodies specific for IgM 56 dpi and IgG 7 dpi. (DOC) | 5,318.6 | 2015-03-24T00:00:00.000 | [
"Biology",
"Medicine"
] |
Statistically unbiased prediction enables accurate denoising of voltage imaging data
Here we report SUPPORT (statistically unbiased prediction utilizing spatiotemporal information in imaging data), a self-supervised learning method for removing Poisson–Gaussian noise in voltage imaging data. SUPPORT is based on the insight that a pixel value in voltage imaging data is highly dependent on its spatiotemporal neighboring pixels, even when its temporally adjacent frames alone do not provide useful information for statistical prediction. Such dependency is captured and used by a convolutional neural network with a spatiotemporal blind spot to accurately denoise voltage imaging data in which the existence of the action potential in a time frame cannot be inferred by the information in other frames. Through simulations and experiments, we show that SUPPORT enables precise denoising of voltage imaging data and other types of microscopy image while preserving the underlying dynamics within the scene.
Here we report SUPPORT (statistically unbiased prediction utilizing spatiotemporal information in imaging data), a self-supervised learning method for removing Poisson-Gaussian noise in voltage imaging data.SUPPORT is based on the insight that a pixel value in voltage imaging data is highly dependent on its spatiotemporal neighboring pixels, even when its temporally adjacent frames alone do not provide useful information for statistical prediction.Such dependency is captured and used by a convolutional neural network with a spatiotemporal blind spot to accurately denoise voltage imaging data in which the existence of the action potential in a time frame cannot be inferred by the information in other frames.Through simulations and experiments, we show that SUPPORT enables precise denoising of voltage imaging data and other types of microscopy image while preserving the underlying dynamics within the scene.
Recent advancements in voltage imaging and calcium imaging have enabled recording of the population activity of neurons at an unprecedented throughput, which opens up the possibility of a system-level understanding of neuronal circuits [1][2][3] .To investigate causality within neuronal activities, it is essential to record the activities with high temporal precision.Unfortunately, the inherent limitation in the maximum number of photons that can be collected from a sample in a given time interval dictates the inherent trade-offs between imaging speed and signal-to-noise ratio (SNR) 4,5 .In other words, increasing the temporal resolution in functional imaging data inevitably results in a decrease in the SNR.The decrease in SNR not only hinders the accurate detection of the neurons' locations but also compromises the timing precision of the detected temporal events, which nullifies the increase in temporal resolution.Fortunately, all functional imaging data have high inherent Article https://doi.org/10.1038/s41592-023-02005-8 follows is how we can implement an accurate statistical model that allows us to accurately predict each pixel value under such conditions.
To this end, we propose SUPPORT (statistically unbiased prediction using spatiotemporal information in imaging data), a self-supervised denoising method for functional imaging data that is robust to fast dynamics in the scene compared to the imaging speed.SUPPORT is based on the insight that a pixel value in functional imaging data is highly dependent on its spatiotemporal neighboring pixels, even when its temporally adjacent frames alone fail to provide useful information for statistical prediction.By learning and using the spatiotemporal dependence among the pixels, SUPPORT can accurately remove Poisson-Gaussian noise in voltage imaging data in which the existence of the action potential in a time frame cannot be inferred from the information in other frames.We demonstrate the capability of SUPPORT using diverse voltage imaging datasets acquired using Voltron1, Voltron2, paQuasAr3-s, QuasAr6a, zArchon1, SomArchon and BeRST1.The analysis of the voltage imaging data with simultaneous electrophysiological recording shows that our method preserves the shape of the spike while reducing the statistical variance in the signal.We also show that SUPPORT can be used for denoising time-lapse fluorescence microscopy images of Caenorhabditis elegans (C.elegans), in which the imaging speed is not faster than the worm's locomotion, as well as static volumetric images of Penicillium and mouse embryos.SUPPORT is exceptionally compelling for denoising voltage imaging and time-lapse imaging data, and is even effective for denoising calcium imaging data.Finally, we developed software with a graphical user interface (GUI) for running SUPPORT to make it available to the wider community.
Central principle of SUPPORT
The central principle of SUPPORT is to perform denoising based on a statistical prediction model with minimal bias by exploiting all available information in both spatial and temporal domains (Fig. 1a).A functional imaging dataset y is considered a realization of a random variable that is drawn from p (y) = p (x) p (n|x) , where x and n are the clean signal and the zero-mean Poisson-Gaussian additive noise, respectively (that is, y = x + n).In this setting, the noise in each pixel is independent in both time and space (that is, ∀(i, k) ≠ ( j, l) , p (n i,k ) = p (n i,k |n j,l ) , where i, j and k, l are temporal and spatial indices, respectively, where the signal is not (that is, ∀ (i, k, j, l) , p (x i,k ) ≠ p (x i,k |x j,l ) ).The dependency among x i,k encodes the spatiotemporal structure of the data x (that is, p(x)), which can be learned using a statistical prediction model, whereas the spatiotemporal independence of n makes it impossible to predict.The prediction model can be implemented as a neural network that predicts a pixel value x i,k using its spatiotemporal neighboring pixel values by solving the following optimization problem 20,21 : where L(•,•) is the loss function defined as the L p distance between the inputs, f θ denotes the neural network parameterized by θ and Ω i,k denotes the spatiotemporal neighboring pixels of y i,k excluding itself.Evaluating this loss function requires the ground truth x, which is inaccessible, but the zero-mean property of the noise allows us to replace x i,k with y i,k for self-supervised training 21 : For the implementation of the network f θ (Ω i,k ), we devised a network architecture that automatically satisfies the requirements (Fig. 1b,c and Supplementary Figs. 1 and 2).For the prediction of x i,k , redundancy in the sense that each frame in a dataset shares a high level of similarity with other frames apart from noise, which offers an opportunity to denoise or distinguish the signal from the noise in the data [6][7][8][9] .
Denoising is a type of signal processing that attempts to extract underlying signals from noisy observations based on previous knowledge of the signal and the noise 10 .The fundamental property of noiserandomness-does not allow for exact recovery of the signal, so we can only reduce statistical variance at the cost of increasing statistical bias (that is, an absolute deviation between the mean denoising outcome and the ground truth).In other words, denoising is a statistical estimation of the most probable value based on our previous statistical knowledge of the signal and the noise.Unfortunately, for any given noisy observation, the exact corresponding probability distribution functions (PDFs) of the signal and the noise are almost never known.Therefore, all denoising algorithms start with setting the signal model (that is, PDF of signal) and noise model (that is, PDF of noise), either explicitly or implicitly, and their accuracy determines the denoising performance.
The most common approach starts with applying linear transforms, such as the Fourier transform and the wavelet transform, to noisy observations 11,12 .Then, a certain set of coefficients that corresponds to a small vector space is preserved, while others are attenuated to reduce statistical variance.This is based on a signal model in which the signal is a random variable drawn from the small vector space, whereas noise is drawn from the entire vector space.An implicit yet important assumption here is that the basis used for the linear transform maps the signal component sharply onto a relatively small and known set of coefficients.When the assumption is not met, denoising leads to a distortion of signals or an increase in statistical bias.Such bias can be reduced by loosening the assumption (for example, the signal is drawn from a larger vector space), but then the variance is increased.
Therefore, building a good signal model that is strong enough to reject noise while being accurate enough to avoid bias is the most critical step in denoising.Previous efforts have focused on finding a handcrafted basis that empirically matches the given data 13 .Some have shown higher general applicability than others 14 , but no universal basis that performs well across different types of data has been found, mainly because of the differences in their signal models and noise models 15 .This has led to the idea of using a basis learned directly from the dataset for denoising 6,16,17 .However, these methods still suffer from high bias, as their ability to reduce variance relies on the strong assumption that the data can be represented as a linear summation of a small number of learned vectors.
Recently, the convolutional network has emerged as a strong alternative to existing learning-based image denoising algorithms 18 .The high representational power of convolutional networks allows for learning nearly arbitrary signal models in the image domain, resulting in low bias in denoising outcomes without sacrificing variance 19 .Owing to its high representational power and the high inherent redundancy in functional imaging data, convolutional networks have shown enormous success in denoising functional imaging data [7][8][9] .As a key aspect, these methods learn the signal model from noisy data in a self-supervised manner [20][21][22][23] , so the need for 'clean' images as the ground truth for training is alleviated.
Both DeepCAD-RT 7 and DeepInterpolation 9 are based on the assumption that the underlying signal in any two consecutive frames in a video can be considered the same, whereas the noise is independent when the imaging speed is sufficiently higher than the dynamics of the fluorescent reporter 7,9 ; the networks are trained to predict the 'current' frame using the past and future frames as the input.Unfortunately, this assumption breaks down when the imaging speed is not sufficiently faster than the dynamics, and the bias in the denoising outcome is increased.This is becoming increasingly prevalent due to the development of voltage indicators [24][25][26][27][28] and calcium indicators with extremely fast dynamics 29 .In that regard, the question that naturally Article https://doi.org/10.1038/s41592-023-02005-8its spatiotemporal neighbor Ω i,k excluding y i,k is taken as the input while preserving the spatial invariance.The current frame y i is fed into a convolutional network that has a zero at the center of the impulse response (Fig. 1b,c); the zero at the center of the impulse response indicates that the pixel value y i,k cannot affect the network's prediction of x i,k (refs.20,30), which is attained by convolution layers and dilated convolution layers with zeros at the center of the kernels.These layers offer a fractal-shaped receptive field that grows exponentially with depth, enabling the network to integrate information from a large number of neighboring pixels (Supplementary Fig. 2).In addition, temporally adjacent frames are fed into a U-Net 31 to extract the available information from the temporally adjacent ones (Supplementary Fig. 1).The outputs from the two convolutional networks are integrated by the following convolutional layers.This architecture 'forces' the network to make a prediction xi,k by using its spatiotemporal neighbor The major difference between SUPPORT and DeepCAD-RT 7 or DeepInterpolation 9 , which can also denoise functional imaging data
Article
https://doi.org/10.1038/s41592-023-02005-8 through self-supervised learning, is that DeepCAD-RT and DeepInterpolation learn to predict a frame given temporally adjacent other frames, whereas SUPPORT learns to predict each pixel value by exploiting the information available from both temporally adjacent frames and spatially adjacent pixels in the same time frame.When the imaging speed is not sufficiently faster than the dynamics in the scene (Fig. 1a), the signal at different time points becomes nearly independent (for example, the existence of the action potential in a time frame cannot be inferred from the information in other frames).In such a case, the major assumptions of the signal models in DeepCAD-RT and DeepInterpolation are violated, which leads to high bias in the denoising outcome.In comparison, SUPPORT relies on the spatiotemporal pixel-level dependence of the signal rather than frame-level dependence, and each pixel value is estimated based on all available information, including its spatially adjacent pixels in the same time frame.
Performance validation on simulated data
For the quantitative evaluation of SUPPORT's performance, we first validated it on synthetic voltage imaging data, which were generated using a NAOMi simulator 32 .We generated multiple datasets with a frame rate of 500 Hz with different spike widths, ranging from 1 to 9 ms (ref.33), to verify how the performance of SUPPORT changes as the dependence between the activity in adjacent frames is diminished.The simulation parameters, including spike frequency, dF/F 0 , noise level and level of subthreshold activity, were chosen to match the experimental voltage imaging data acquired using Voltron 24 (Methods).Finally, Poisson and Gaussian noise were added to the generated videos.Further details can be found in the Methods section.We applied SUPPORT, DeepCAD-RT 7 and penalized matrix decomposition (PMD) 6 to the synthetic datasets and compared the results.The signals were separated from the backgrounds in the denoised videos (Methods) to compare their accuracy in recovering the time-varying signal (Fig. 2a and Supplementary Video 1).Qualitative comparisons of the results from the dataset with a spike width of 3 ms showed that the denoising outcome from SUPPORT was nearly identical to the ground truth.DeepCAD-RT successfully reduced the variance in the video, but also attenuated the neuronal activity.This was expected because the method was designed for removing noise in calcium imaging data, which has much slower dynamics.PMD showed better performance in preserving neuronal activities, in part because it did not discard the current frame for denoising, but it introduced visible artifacts in the images.
To quantify the performance of each denoising method, we calculated the peak SNR (PSNR) of the denoised videos and calculated the Pearson correlation coefficient between the voltage traces extracted from the clean video and the denoised video.The voltage traces were extracted from 116 cells (Methods).In terms of PSNR, all methods showed substantial enhancements compared to noisy images for every spike width (Fig. 2b and Supplementary Figs.3-5): noisy (1 ms, 4.57 dB; 9 ms, 15.43 dB), SUPPORT (1 ms, 35.94 dB; 9 ms, 43.08 dB), DeepCAD-RT (1 ms, 30.90 dB; 9 ms, 39.05 dB) and PMD (1 ms, 32.07 dB; 9 ms, 38.61 dB).However, in terms of the Pearson correlation coefficient, only SUPPORT (1 ms, 0.885; 9 ms, 0.991) showed improvement compared to noisy images (1 ms, 0.593; 9 ms, 0.942) for every spike width (Fig. 2c and Supplementary Fig. 6).DeepCAD-RT (1 ms, 0.190; 9 ms, 0.984) and PMD (1 ms, 0.554; 9 ms, 0.983) showed improvement only when the spike width was larger than 5 and 3 ms, respectively, which verifies the importance of exploiting spatially adjacent pixels in the same time frame.We note that this inconsistency between the two metrics stems from the fact that the Pearson correlation coefficient is affected only by the time-varying component of the signals, whereas PSNR is largely determined by the static component.
For further comparison, we analyzed the voltage traces at the single-pixel (Fig. 2d) and single cell levels (Fig. 2e).Only the single-pixel voltage traces from SUPPORT retained the spike waveforms (Fig. 2d), whereas the spikes were buried under the noise level in the single-pixel voltage traces from the noisy video.DeepCAD-RT and PMD reduced the variance in the single-pixel voltage traces, but the spikes were still not detectable due to the bias introduced by their signal models.The single cell voltage traces showed similar results (Fig. 2e and Supplementary Figs.7-9), although the difference was less dramatic than the single-pixel traces, as the SNR was improved by averaging multiple pixel values.SUPPORT was able to reduce variance without distorting the waveforms for every spike width.In comparison, the spikes were not detectable in the results from DeepCAD-RT and PMD when the spike width was under 3 ms.It should be noted that the performance of both DeepCAD-RT and PMD was better for larger spike widths, but for different reasons.DeepCAD-RT estimates the current frame given temporally adjacent frames, so the prediction becomes more accurate when the dynamics are slower.PMD attempts to find a low rank approximation of a given matrix that is supposedly closer to the ground truth, so a temporally long event is less likely to be 'ignored' as its contribution to the approximation error is higher.
Denoising single-neuron voltage imaging data
To validate SUPPORT's capability to denoise experimentally obtained voltage imaging data while retaining the spikes, we applied SUPPORT to in vivo single-neuron voltage imaging data with simultaneous electrophysiological recordings.The dataset contained light-sheet microscopy images of a single neuron in the dorsal part of the cerebellum of a zebrafish expressing Voltron1 with simultaneous cell-attached extracellular electrophysiological recording.Electrophysiological recordings were taken at a sampling rate of 6 kHz, and light-sheet imaging was performed with a frame rate of 300 Hz (ref.24).
In the raw data, both the spatial footprint and temporal traces of the neuron were severely corrupted by Poisson-Gaussian noise.We compared temporal traces extracted from the raw video and the denoised video using SUPPORT, DeepCAD-RT and PMD, along with the electrophysiological recording.Spike locations from the electrophysiological recordings were extracted (Methods) and visualized as black dots for a visual aid (Fig. 3a,b).After denoising with SUPPORT, the temporal trace showed a much lower variance compared to the temporal trace of the raw data while preserving the spikes (Supplementary Figs. 9 and 10).In comparison, while the temporal variance in the denoising outcome acquired using DeepCAD-RT was low, the spikes were no longer visible in the traces, which implies that the signal modeling in DeepCAD-RT substantially increased the bias.The temporal trace from PMD was nearly identical to that from the raw video, which indicates that PMD had limited impact on both bias and variance.
After we applied SUPPORT to enhance this data, not only did the neuronal activity become clearly visible in the images, but the spatial footprints of the activity also showed high consistency with the corresponding neuronal shape (Fig. 3c and Supplementary Video 2).Representative frames from the raw and denoised data show that SUPPORT removed the noise very effectively, while the activity was preserved.
For further comparison, we extracted single-pixel fluorescence from the cell membrane pixels and found that the average single-pixel SNR was strongly enhanced with SUPPORT (14.46 dB) compared to DeepCAD-RT (12.21 dB) and PMD (13.46 dB) (Fig. 3d).The spatiotemporal diagram, which visualizes the voltage transients of each 2 × 2 binned pixel, also verified that SUPPORT successfully reduced the variance while preserving the spikes at the pixel level (Fig. 3e).
Next, we tested the capability of SUPPORT to recover subthreshold activity of neurons using wide-field microscopy images of a single neuron in cortex layer 1 of a mouse brain expressing Voltron1 with simultaneous cell-attached extracellular electrophysiological recording (Fig. 4a).Electrophysiological recordings were taken at a sampling rate of 10 kHz, and imaging was performed at a frame rate of 400 Hz.
After denoising with SUPPORT, we found that even a single-pixel fluorescence trace faithfully reflected the subthreshold signal (Fig. 4b).
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https://doi.org/10.1038/s41592-023-02005-8 The average Pearson correlation coefficient, obtained by comparing the fluorescence traces with the electrophysiological recordings, of SUPPORT (0.51 ± 0.18) showed a 0.30 increase compared to the raw image (0.21 ± 0.12) (Fig. 4c).The power spectral density of the fluorescence traces from the denoised image was also consistent with that of the electrophysiological recordings.We confirmed the one-to-one correspondence between the fluorescence trace and the transmembrane potential using wide-field microscopy images of a single neuron in the brain slice from mouse cortex layer 2/3 expressing QuasAr6a (ref.34), which is known to possess high linearity (Fig. 4e).The one-to-one correspondence became evident after SUPPORT denoising (Fig. 4f).The average Pearson correlation coefficient between the fluorescence traces and the electrophysiological recordings increased from 0.18 ± 0.11 to 0.65 ± 0.22 after denoising (Fig. 4g).These results were in line with those from the simulation (Supplementary Fig. 11).
Additionally, we found that SUPPORT precisely revealed the traces from single pixels inside the soma (Supplementary Fig. 12) and along the dendritic branch (Supplementary Figs.13-15 and Supplementary Video 3), which indicates SUPPORT's suitability for studies involving voltage dependence along the neuronal processes 35 .Finally, SUPPORT was able to denoise in vitro cultured neurons labeled with a synthetic voltage dye, which indicates its suitability for designing voltage indicators (Supplementary Fig. 16).
Denoising population voltage imaging data
We applied SUPPORT to voltage imaging data that contained in vivo population neuronal activity in awake mouse cortex layer 1 expressing Voltron1 (ref.24) and zebrafish spinal cord expressing zArchon1 (ref.27).The mouse dataset was recorded with a wide-field fluorescence microscope with a frame rate of 400 Hz, and the zebrafish dataset was recorded with a light-sheet fluorescence microscope with a frame rate of 1 kHz (ref.36).
After applying SUPPORT to the voltage imaging data, we applied baseline correction (Methods).Despite the high noise level of the voltage imaging data, the neuronal structures became clearly visible after denoising (Fig. 5a,d, Supplementary Video 4 and Supplementary Fig. 17).The single-pixel SNR was improved by 9.11 dB on average (21.58 ± 1.62 dB for SUPPORT, 12.47 ± 0.89 dB for the raw data) for the mouse dataset (Figs.5b) and 6.32 dB (19.08 ± 2.07 dB for SUPPORT, 12.72 ± 0.67 dB for the raw data) for the zebrafish dataset (Fig. 5e).For further analysis, we extracted the voltage traces from manually drawn regions of interest (ROI) (Fig. 5c,f,g).In line with the results from the simulation and the single-neuron voltage imaging, the variance was greatly decreased, while the sharp voltage transients induced by spikes were preserved (Supplementary Figs.18-40).
We also extracted the neurons and corresponding temporal signals using localNMF 36 , which is an automated cell extraction algorithm, from the mouse and zebrafish datasets (Methods and Supplementary Fig. 41a,b).Owing to the improvement in SNR, we were able to automatically segment 42 neurons from the denoised mouse data compared to 31 neurons from the raw data.For zebrafish data, 27 neurons from the denoised data and nine neurons from the raw data were extracted.We then measured the F 1 score between the ground-truth ROI and the extracted ROI across several intersection-over-union (IoU) threshold values.We quantified the area under F 1 score across the IoU curve, and there was a 1.6-fold improvement for mouse data (0.31 for denoised and 0.19 for raw data) and a 2.0-fold improvement for zebrafish data (0.43 for denoised and 0.21 for raw data) (Supplementary Fig. 41c).The extracted neuronal signal from SUPPORT also clearly shows spikes, while the signal from the raw data shows high variance (Supplementary Fig. 41d), which indicates that SUPPORT facilitates the automated analysis of large-scale population voltage imaging data.
It was shown that SUPPORT could denoise other population voltage imaging data with different regions and voltage indicators, indicating its suitability for the routine use of population voltage recordings (Supplementary Figs.18-40, 42 and 43).Finally, we observed that SUPPORT trained on single population voltage imaging data accurately denoised another population voltage imaging data without fine-tuning (Supplementary Fig. 44), which demonstrates its generalizability.
Denoising voltage imaging data with motion
The signal model of SUPPORT does not assume that objects in the images remain stationary, which allows for the possibility of denoising image data with motion.To verify this, we applied SUPPORT to synthetic, semisynthetic and experimental voltage imaging datasets with motion.
We first applied random rigid translation to the synthetic datasets generated using a NAOMi simulator as described in the previous section.The translation profile was created by drawing a sequence of random numbers from a zero-mean Gaussian distribution and filtering the sequence with a low-pass filter with a cut-off frequency of 5 Hz to mimic the motion induced by respiration and heartbeat.Subsequently, we applied SUPPORT to the dataset for denoising (Supplementary Figs.45 and 46).The traces extracted from the SUPPORT-denoised video showed reduced variance while maintaining the spikes (Supplementary Fig. 45d).Quantitatively, the SUPPORT-denoised image showed an improvement of 6.95 dB in the average SNR (31.23 ± 1.85 dB) compared to the noisy image (24.28 ± 0.02 dB), when motion on a scale larger than the size of the cell body was present (Supplementary Fig. 45e).Additionally, the root-mean-squared error (r.m.s.e.) was lowered by 0.0087 for the SUPPORT-denoised image (0.0074 ± 0.0014) compared to the noisy image (0.0161 ± 3.38 × 10 −5 ) (Supplementary Fig. 45f).We also found that altering the sequence of preprocessing steps (motion correction, photobleaching correction and SUPPORT) did not significantly affect the results (Supplementary Fig. 47).
Next, we applied random rigid translation, identical to that applied to the synthetic data, to the aforementioned in vivo single-neuron voltage imaging data with simultaneous electrophysiological recordings (Fig. 6a-c).We then applied SUPPORT for denoising and aligned the results for motion correction.The outcome was visually indistinguishable from the results obtained by applying SUPPORT to the motionless data (Fig. 6d).
Quantitatively, using simultaneously recorded electrophysiological recordings as ground truth, the SUPPORT-denoised image with motion on a scale comparable to the cell body size showed a substantial improvement of 0.46 in the average Pearson correlation coefficient (0.75 ± 0.12) compared to the raw image (0.29 ± 0.12) (Fig. 6e).Similarly, when using SUPPORT-denoised data without motion as ground truth, the average Pearson correlation coefficient showed an improvement of 0.57 for the SUPPORT-denoised image (0.95 ± 0.05) compared to the raw image (0.38 ± 0.19) (Fig. 6f).Additionally, the SNR was enhanced by 17.04 dB for the SUPPORT-denoised image (40.05 ± 0.44 dB) compared to the raw image (23.01 ± 0.51 dB) (Fig. 6g).
Finally, we evaluated SUPPORT using a voltage imaging dataset obtained from an awake mouse hippocampus expressing SomArchon 37 (Fig. 6h).This dataset contained natural motion with a scale comparable to the size of the cell body (Fig. 6i,j).Consistent with the findings from the synthetic and semisynthetic datasets, the variance was substantially reduced, while maintaining the distinct voltage transients associated with spikes (Fig. 6k).Furthermore, the single-pixel SNR showed an average improvement of 3.40 dB (17.30 ± 1.38 dB for SUPPORT, 13.90 ± 0.86 dB for the raw data) (Fig. 6l).
SUPPORT denoises imaging data of freely moving C. elegans
To assess the broad applicability of SUPPORT, we tested its capability to denoise three-dimensional time-lapse fluorescence microscopy images of C. elegans 38 , in which the differences among the frames came from the motion of the worm, which was not sampled with a sufficiently high imaging speed.The nuclei of all neurons in the worm were labeled using red fluorescent protein mCherry 39 under the H20 promoter.The volume images with 20 axial slices were recorded with spinning disk confocal microscopy at a volume rate of 4.75 Hz.
We denoised the video using SUPPORT, DeepCAD-RT and PMD in a plane-by-plane manner.We first compared the noisy data and the denoised results for a single axial slice.SUPPORT successfully denoised the images without any visible artifacts, whereas the denoising outcomes acquired using DeepCAD-RT and PMD suffered from motion-induced artifacts (Extended Data Fig. 1a and Supplementary Fig. 48), which again proves the importance of using an appropriate signal model for denoising.The difference between the SUPPORT output and the noisy input, which was expected to be white noise, did appear purely white.However, the difference between the outputs from DeepCAD-RT and PMD and the noisy input contains low frequency components that are highly correlated with the structure of the input image (Extended Data Fig. 1b).
In the consecutive frames shown in Extended Data Fig. 1c, the worm's locomotion is considerably faster than the imaging speed, which precludes the accurate prediction of the current frame based on adjacent frames.Nevertheless, SUPPORT successfully denoised the image without suffering from motion artifacts by incorporating information from neighboring pixels in the current frame.By contrast, DeepCAD-RT and PMD failed to predict the location of each cell, which was manifested as motion-induced artifacts in the images.The denoising outcome (Extended Data Fig. 1d, Supplementary Fig. 49 and Supplementary Video 5) demonstrates that SUPPORT can be used for denoising not only functional imaging data but also volumetric time-lapse images in which the speed of dynamics is faster than the imaging speed.
SUPPORT denoises volumetric structural imaging data
To demonstrate the generality of SUPPORT, we evaluated it on denoising volumetric structural imaging data in which no temporal redundancy could be exploited for denoising.SUPPORT was tested on two volumetric datasets that contained Penicillium imaged with confocal microscopy and mouse embryos imaged with expansion microscopy 40 .
Penicillium was imaged with two different recording settings to generate a pair of low-SNR and high-SNR volumes (Methods).
The volumetric images were denoised with SUPPORT regarding each z-stack as a time series.The qualitative analysis showed that SUPPORT was able to enhance the signal of volumetric structural imaging data, revealing the structures that were hidden by the noise (Extended Data Fig. 2a,b,e,f, Supplementary Fig. 50 and Supplementary Video 6).The fine structure of Penicillium was recovered with SUPPORT (Extended Data Fig. 2d), demonstrating the signal model's capability to learn statistics from a wide range of data.For the quantitative evaluation of SUPPORT with the Penicillium dataset, the Pearson correlation coefficients and SNR were measured by regarding the high-SNR image as a ground truth for each plane along the z axis (Extended Data Fig. 2c).The average Pearson correlation coefficient of SUPPORT (0.76 ± 0.07) showed 0.29 increments compared to the low-SNR image (0.47 ± 0.09) and the average SNR of SUPPORT (8.65 ± 0.62 dB) showed 5.98 dB increments compared to the low-SNR image (2.67 ± 0.51 dB).The qualitative and quantitative studies showed that SUPPORT is capable of enhancing not only time-lapse images but also static volumetric images.Thus, SUPPORT can be used in a wide range of biological research involving microscopic imaging.
Discussion
SUPPORT, a self-supervised denoising method, has demonstrated its ability to denoise diverse voltage imaging datasets acquired using Voltron1, Voltron2, paQuasAr3-s, QuasAr6a, zArchon1, SomArchon and BeRST1 (Supplementary Table 1).Thanks to its statistical prediction model that predicts a pixel value x i,k by integrating the information from its spatiotemporal neighboring pixels Ω i,k (that is, xi,k = f θ (Ω i,k )), it showed high robustness when faced with the fast dynamics in the scene.While this design allows SUPPORT to simultaneously achieve low bias and low variance, it still leaves room for fundamental improvement, as it does not exploit the information contained in y i,k .The reason y i,k was not exploited as an input is because it is used as the target in place of the ground truth for self-supervised learning; we cannot use y i,k as both the input and the target of the network, as the network will simply become an identity function.This means that the cost of truly exploiting all available information is to give up the self-supervised learning scheme that does not require ground truth.
It should be noted that SUPPORT is specifically designed to remove zero-mean 'stochastic' noise, which includes Poisson noise and Gaussian noise originating from photons, dark current and sensor readout.However, it is not capable of addressing 'deterministic' artifacts such as motion-induced artifacts, photobleaching or fixed-pattern noise.As a result, a specifically designed data processing pipeline is needed to process data containing such artifacts (Supplementary Fig. 47).
Denoising time-lapse imaging data in which a C. elegans exhibited rapid movement and a single volumetric image demonstrated that SUPPORT is not limited to denoising voltage imaging data; it can be used for denoising any form of time-lapse imaging data (Supplementary Figs.51-58 and Supplementary Videos 7-9) including calcium imaging in which the imaging speed is slow compared to the underlying dynamics or volumetric structural imaging data.This is an important finding, as it indicates that the data do not need to be low rank to be denoised using SUPPORT, which is often required by many denoising algorithms 6,41 .Also, SUPPORT could be trained with only 3,000 frames (Supplementary Figs.59 and 60), which would facilitate its general usage in many laboratories with common desktop settings, especially with our GUI-based SUPPORT (Supplementary Fig. 61).We also note that the performance of SUPPORT comes at the typical computational cost of 2 days of training time with an NVIDIA RTX 3090 GPU.Overall, its self-supervised learning scheme, robustness to fast dynamics, low variance in denoising outcomes and compatibility with motion make it a versatile tool for processing a wide range of image data.We expect that SUPPORT's core strategy, learning the statistical relationships between neighboring entities in an n-dimensional array, will extend beyond image denoising and be adapted to process a broader range of biological data.
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Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material.If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.To view a copy of this license, visit http://creativecommons. org/licenses/by/4.0/.© The Author(s) 2023 https://doi.org/10.1038/s41592-023-02005-8
SUPPORT network architecture
The architecture of the SUPPORT network consists of two subnetworks: two-dimensional (2D) U-Net and the blind spot network.2D U-Net exploits the information of the temporally adjacent frames.The input data are first separated into two blocks: (1) temporal neighboring frames and (2) the center frame.The temporal neighboring frames are concatenated in the channel dimension and passed through 2D U-Net.Then, the center frame and the output of 2D U-Net are concatenated in the channel dimension and passed through the blind spot network, which has a zero at the center of the impulse response.Finally, the outputs of 2D U-Net and the blind spot network are concatenated in the channel dimension and passed through 1 × 1 convolution layers.The overall architecture is illustrated in Supplementary Fig. 1a.
The 2D U-Net 31 consists of a 2D encoder, a 2D decoder and skip connections from the encoder to the decoder (Supplementary Fig. 1b).In the 2D encoder, there are four encoder blocks.Each block consists of a 3(x) × 3(y) convolutional layer, followed by a BatchNorm, a LeakyReLU and a 2(x) × 2(y) maximum pooling layer.In the decoder, there are four decoder blocks, each of which contains a bilinear interpolation followed by a 3(x) × 3(y) convolutional layer, a BatchNorm and a LeakyReLU.The skip connections link low-and high-level features by concatenating feature maps in the channel dimension.We designed 2D U-Net to take the previous 30 frames and next 30 frames as the input.For denoising structural imaging data, the previous ten frames and next ten frames were used as the input.
The blind spot network was designed to efficiently increase the receptive field of the network over computation (that is, memory and the number of multiply-add operations).A comparison to previous blind spot network designs 20,30 is shown in Supplementary Fig. 2. The blind spot network consists of (1) two sequential parts and (2) an aggregating part (Supplementary Fig. 1c).There are two sequential paths that use convolutional layers with kernel sizes of 3 × 3 and 5 × 5.Each sequential path consists of sequential blind spot convolutional layers with 'shortcut connections' (Supplementary Fig. 1c).The center value of the weight of the blind spot convolutional layer is masked as 0 to make the blind spot property.For the kernel size of 3 × 3, the dilation and padding are both set as 2 i for the ith layer to preserve blind spot properties for each feature after the layer.Similarly, for the kernel size of 5 × 5, the padding and dilation are set as 2 × 3 i .The shortcut connection links the input to the features by adding the input, passed by the 1 × 1 convolutional layer, to the intermediate features.In the aggregating path, all features after each layer in the sequential paths are concatenated in the channel dimension and then passed through three 1 × 1 convolutional layers to finally predict the signal.The receptive field of the blind spot network is illustrated in Fig. 1b, which shows the fractal-like pattern.
For the data in which structured noise can be predicted from the neighboring pixels, options to change the size of the blind spot were also implemented (Supplementary Fig. 51).To increase the size of the blind spot to p, we added additional dilation and padding of ⌊p/2⌋ for the last blind spot convolutional layers of two sequential paths.Also, only the final features of two sequential paths, rather than all intermediate features, were passed through the aggregating path.Overall, we adhered to the default network architecture (Supplementary Fig. 1) except for the following instances (Supplementary Table 2): (1) For structural imaging dataset, we reduced the size of temporal (or 'axial') receptive field to 21 due to the limited availability of the axial slices.(2) For dataset with motion, we increased the network capacity by multiplying the number of channels in the U-Net by a factor of four.(3) For dataset with correlated noise on neighboring pixels, we increased the size of the blind spot.
Training SUPPORT network
The network was trained on Pytorch 1.12.1 and CUDA 11.3 with an NVIDIA RTX 3090 GPU and an Intel Xeon Silver 4212R CPU.For the loss function, the arithmetic average of L1-loss and L2-loss was used.As a preprocessing step, each input video was normalized by subtracting the average value and dividing by the standard deviation.Patches with a size of 128(x) × 128(y) × 61(t) were extracted from the input video with an overlap of 61(x) × 61(y) × 1(t).If the spatial dimension of the data was smaller than 128, we reduced the patch size to match the spatial dimension of the data.Then, random flipping and rotation by integer multiples of 90° were used for data augmentation.A batch size of 16 was used by default.An Adam optimizer 42 with a learning rate of 5 × 10 −4 without weight decay was used for gradient-based optimization.To ensure reproducibility, random seeds for all relevant libraries, NumPy and PyTorch, were fixed at 0. The network was trained for 500 epochs, with each epoch containing a loop through all patches by default.The loss values were tracked for every gradient update to monitor the training procedure.Training SUPPORT for processing the zebrafish dataset that had a size of 1,024(x) × 148(y) × 24,000(t) took 47 h for 14 million gradient updates.The inference for the same dataset took 30 min.We note that overfitting was avoided by using 1,500 or more frames and training the network over an extended period did not lead to overfitting (Supplementary Figs.60 and 62).
For both training and inference, we used zero padding to match the input and output sizes, which had minimal impact on the results (Supplementary Fig. 63).
Synthetic voltage imaging data generation
Simulating synthetic voltage imaging data includes the pipeline of first generating clean video (ground truth) and then adding Poisson and Gaussian noise.To generate a realistic spatial profile that resembles neurons in a mouse brain, we used a NAOMi 32 simulator that was originally developed for simulating a two-photon calcium imaging dataset.The code was modified to generate voltage transients instead of calcium transients as temporal components.We generated five different videos with 15,000 frames and a frame rate of 500 Hz with different spike widths, ranging from 1 to 9 ms.The constructed voltage signals were matched to the parameters of Voltron.Every other parameter was set as default apart from increasing the simulated field of view twofold.The noisy video was generated by adding Poisson and Gaussian noise.To add Poisson noise to the images, we first normalized the input images and multiplied them by 1,000, and then used each pixel value as the parameter (that is, mean value) of the Poisson distribution.Thereafter, Gaussian noise with a mean of 0 and a standard deviation of 5 was added to the images.Finally, negative values were truncated to 0.
In vivo simultaneous voltage imaging and electrophysiology
The data from simultaneous structured illumination fluorescence imaging and patch-clamp electrophysiological recordings of single-neuron activity were recorded with mouse cortex L2/3 pyramidal neurons using a digital micromirror device or spatial light modulator with a frame rate of 1,000 Hz.Voltron2 and QuasAr6a were expressed using in utero electroporation.NDNF-Cre± mice ( JAX catalog no.028536) of 6 weeks to 8 months were used for in vivo QuasAr6 voltage imaging.All procedures involving animals were in accordance with the National Institutes of Health guide for the care and use of laboratory animals and were approved by the Institutional Animal Care and Use Committee (IACUC) at Harvard University.https://doi.org/10.1038/s41592-023-02005-8
In vitro single-neuron voltage recording
We prepared primary rat hippocampal neurons cultured on a 35 mm glass bottom dish (P35G-1.5-14-C,MatTek).At 9 days in vitro, neurons were stained with a voltage-sensitive dye (BeRST1, 2 μM) dissolved in an imaging solution containing 140 mM NaCl, 3 mM KCl, 3 mM CaCl 2 , 1 mM MgCl 2 , 10 mM HEPES and 30 mM glucose (pH 7.3) for 15 min, and then rinsed with a fresh imaging solution before optical imaging 28 .Time-lapse imaging of spontaneous neural activity was acquired using an inverted microscope (Eclipse Ti2, Nikon) equipped with a ×40 water-immersion objective lens (numerical aperture (NA) 1.15; MRD7710, Nikon), while maintaining the sample temperature at 30 °C.For excitation, an LED (SOLIS-623C, Thorlabs) with a bandpass filter (ET630/20x, Chroma Technology) was used at an irradiance of 20 mW mm −2 at the sample.Emission was passed through a dichroic mirror (T660lpxr, Chroma Technology) and an emission filter (ET665lp, Chroma Technology), and was collected by an sCMOS camera (Orca Flash v.4.0,Hamamatsu) at a 1-kHz frame rate with 4 × 4 binning and subarray readout (361 × 28 pixels) for a duration of 25 s.All the animal experiments were performed according to the Institute of Animal Care and Use Committee guidelines of Seoul National University (Seoul, Korea) (SNU-220616-1-2).
In vivo simultaneous calcium imaging and electrophysiology
A craniotomy over V1 was performed, and neurons were infected with adeno-associated virus (AAV2/1-hSynapsin-1) encoding jGCaMP8f.At 18-80 days after the virus injection, the mouse was anesthetized, the cranial window was surgically removed and a durotomy was performed.The craniotomy was filled with 10-15 μl of 1.5% agarose, and a D-shaped coverslip was secured on top to suppress brain motion and leave access to the brain on the lateral side of the craniotomy.The mice were then lightly anesthetized and mounted under a custom two-photon microscope.Two-photon imaging (122 Hz) was performed of L2/3 somata and neuropil combined with a loose-seal, cell-attached electrophysiological recording of a single neuron in the field of view.Temporally fourfold downsampling was held to the data to reduce the sampling rate before the analysis.After excluding some outlier recordings with a low correlation between calcium signal and action potentials, an ROI was manually drawn around the neuron, and fluorescence traces were extracted from the mean signal of the ROI in the temporal stack.All surgical and experimental procedures were conducted in accordance with protocols approved by the IACUC and Institutional Biosafety Committee of Janelia Research Campus.
Volumetric structural imaging of Penicillium
For the volumetric structural imaging of Penicillium, the specimen was imaged using a point-scanning confocal microscopy system (NIS-Elements AR v5.11.01,C2 Plus, Nikon) equipped with a ×16 0.8 NA water dipping objective lens (CFI75 LWD 16X W, Nikon).The imaging was performed using a 488 nm excitation laser with a laser power of 0.075 mW for the low-SNR image and a laser power of 1.5 mW for the high-SNR image.The frame rate was 0.5 Hz for 1,024 × 1,024 pixels with a pixel size of 0.34 μm and each volume consisted of 1,000 z-slices with a z-step size of 0.1 μm.
Expansion microscopy of mouse embryos
Mouse embryos were isolated on day 15.5 of pregnancy in C57BL/6J mice and fixed with ice-cold fixative (4% paraformaldehyde in 1× phosphate buffered saline) for a day at 4 °C.Fixed mouse embryos were embedded in 6% (w/w) low-gelling-temperature agarose and then sliced to a thickness of 500 μm with a vibratome.Embryo slices were then processed for anchoring, gelation, Alexa Flour 488 NHS-ester staining, digestion, decalcification and expansion according to the previously described whole-body ExM protocol 40 .Following a 4.1-fold expansion of the embryo slices in the hydrogel, the sample was attached to cover glass and imaged using a confocal microscope (Nikon Eclipse Ti2-E) with a spinning disk confocal microscope (Fusion v.2.1.0.34,Dragonfly 200; Andor, Oxford Instruments) equipped with a Zyla 4.2 sCMOS camera (Andor, Oxford Instruments) and a ×10 0.45 NA air lens (Plan Apo Lambda, Nikon).The z-stack images were obtained with a z-step size of 1 μm for intestine and bone, and 0.5 μm for tail.All animal experiments involving mouse embryos conducted for this study were approved by the IACUC of KAIST (KA-2021-040).
The larvae were paralyzed by bath incubation with 0.25 mg ml −1 of pancuronium bromide (Sigma-Aldrich) solution for 2 min (ref.47).After paralysis, the larvae were embedded in agar using a 2% low melting point agarose (TopVision) in a Petri dish.The dish was filled with standard fish water after solidifying the agarose gel.Specimens were imaged using a point-scanning confocal microscopy system (NIS-Elements AR v.5.11.01,C2 Plus, Nikon) equipped with a ×16 0.8 NA water dipping objective lens (CFI75 LWD 16X W, Nikon).The imaging was performed using a 488 nm excitation laser (0.15-0.75 mW).All animal experiments involving zebrafish conducted for this study were approved by the IACUC of KAIST (KA-2021-125).
Imaging spontaneous neurotransmission
Primary cultures of rat hippocampal neurons were obtained from embryonic day 18 Sprague-Dawley fetal rats and plated onto glass coverslips that were precoated with poly-d-lysine.Neurons were transfected with SF.iGluSnFR A184V (Addgene catalog no.106199) or iGABASnFR F102G (Addgene catalog no.112160) using calcium-phosphate method, along with SynapsinI-mCherry to serve as a presynaptic bouton marker.Transfected hippocampal neurons at day 16 in vitro were placed in a perfusion chamber (Chamlide, LCI) and mounted onto the 35 °C heating stage of an inverted microscope (IX71, Olympus) equipped with a ×40 oil-immersion objective lens (UPlanApo, ×40/1.00).The imaging was conducted in Tyrode's solution (136 mM NaCl, 2.5 mM KCl, 2 mM CaCl 2 , 2 mM MgCl 2 , 10 mM glucose, 10 mM HEPES; pH 7.4; 285-290 mOsm) containing 1 μM tetrodotoxin to block action potential firing.A total of 12 trials were obtained, each consisting of 500 frames captured at a frame rate of 100 Hz (iGluSnFR) or 50 Hz (iGABASnFR), using an Andor Sona-2BV11 sCMOS camera (Andor) driven by MetaMorph Imaging Software (Molecular Devices) with a binning of 2 and a cropped mode of 110 × 110 pixels.All the animal experiments were performed according to the Institute of Animal Care and Use Committee guidelines of Seoul National University (SNU-220525-4).
Baseline and activity decomposition of voltage imaging data
For visualization, the data were decomposed into the underlying baseline and neuronal activity.The baseline estimation was performed using the temporal moving average.Window length was chosen in accordance with the recording rate for the data.For the data that only required photobleaching correction, b-spline fit was used to estimate baseline without using the moving average (Fig. 5a).For the positive-going voltage indicators (zArchon1, QuasAr6a, paQuasAr3-s, SomArchon), the activity component was acquired by subtracting the estimated baseline from the data.For the negative-going voltage indicators (Voltron1, Voltron2), the activity component was acquired by subtracting the data from the estimated baseline.
Spike detection for F 1 score calculation
To calculate spike detection accuracy, we measured the F 1 score for a given dF/F 0 threshold.The spikes were detected through the following steps: (1) calculating dF/F 0 from the fluorescence trace, https://doi.org/10.1038/s41592-023-02005-8 (2) hard-thresholding the dF/F 0 trace and (3) finding local maximum locations.The dF/F 0 threshold refers to the threshold value used in step (2).In simulated data, clean voltage traces were used to obtain ground-truth spike locations.In experimental data, electrophysiological recordings were used as the ground truth.For subthreshold analysis, we calculated Pearson correlation coefficients between electrophysiological recording and single-pixel voltage traces in the subthreshold regime.
Cell detection in neuronal populations imaging data
For voltage imaging data, the SGPMD-NMF pipeline was applied to detect ROI and corresponding temporal signals, which is available on GitHub (https://github.com/adamcohenlab/invivo-imaging).In the pipeline, detrending based on b-spline fitting and demixing based on localNMF were used without additional denoising.For the mouse cortex data, detrended data was flipped before the demixing step by subtracting the data from the maximum value of the data, since the data were recorded with Voltron1, which is a negative-going voltage indicator.After extraction, we removed nonneuronal spatial components with the following simple heuristics: (1) reject if the number of pixels in the component is smaller than α, (2) reject if the width or height of the component is larger than β and (3) reject if the width/ height is not in (γ, δ).
For mouse cortex data, only the first heuristic was used, with α set as 10, where the size of the neurons was small in the data.For zebrafish data, all heuristics were used, with α = 100, β = 50, γ = 0.5 and δ = 1.5 (Supplementary Fig. 41).
Cellpose 48 was applied to a single frame image of SUPPORTdenoised video to detect cells (Supplementary Fig. 55).All parameters were set to default except 'flow' and 'cellprob', which were set by empirical values that best fit the data.
Real-time intravital imaging in anesthetized mouse
H2B-GFP ( Jackson Laboratory, Stock No. 006069) and mTmG ( Jackson Laboratory, stock no.007676) mice were purchased from the Jackson Laboratory.Flowing red blood cells in various tissues of the offspring of H2B-GFP crossbred with mTmG were imaged using a confocal and two-photon microscope (IVM-CMS, IVIM Technology Inc.).For real-time intravital imaging, mice were anesthetized using an intramuscular injection of a mixture of Zoletil (20 mg kg −1 ) and Xylazine (11 mg kg −1 ).Red blood cells fluorescently labeled by far-red fluorophore DiD (Thermo Fisher) were intravenously injected through the tail vein.To image ear skin, the right ear of the anesthetized mouse was gently attached to transparent coverslip with saline water [49][50][51] .To image kidney, a 15 mm incision was made on both the skin and the retroperitoneum and then the kidney was gently exteriorized with round forceps.The exposed kidney surface was covered by transparent coverslip 52,53 .A wet gauze soaked in warm saline was placed between the kidney and the underlying tissue to reduce motion artifacts [54][55][56] .To image muscle, a 10 mm incision was made on thigh skin and then muscle was exposed and covered by transparent coverslip 57 .A high NA water-immersion objective lens (CFI75 Apochromat 25XC W, NA 1.1, Nikon) was used, and 488, 561 and 640 nm lasers were used to excite green fluorescent protein (GFP), mT and DiD, respectively.All animal experiments involving live anesthetized mice conducted for this study were approved by the IACUC of KAIST (KA-2021-058, KA-2022-010).
Fig. 1 |
Fig. 1 | SUPPORT can be applied to functional imaging data with a fast dynamics indicator.a, SUPPORT's self-supervised learning scheme and previous methods that exploit temporally adjacent frames for denoising functional imaging data with slow and fast dynamics indicators.Functional imaging data are represented by green and red surfaces, which indicate the receptive field and prediction target area, respectively.b, Noisy frames are fed into the SUPPORT network and output the denoised image.Red tiles indicate the receptive field of the SUPPORT network, which uses spatially adjacent pixels in the same frame.c, Impulse response of the SUPPORT network on the current frame.The magnified view is presented on the right side.Response value of the center pixel is 0, which forces the network to predict the center pixel without using it.d, In vivo population voltage imaging data.The left shows the raw data and the right shows the SUPPORT-denoised data.Baseline and activity components are decomposed from raw data and SUPPORT-denoised data.The baseline component with gray colormap and activity component with hot colormap are overlaid.Magnified views of the boxed regions are presented below at the time points near spikes.Consecutive frames of two spikes (t = 0.2650 and 2.2325 s).
Fig. 2 |
Fig. 2 | Performance validation on simulated data.a, Synthetic population voltage imaging data.From left to right are the clean, noisy, SUPPORT, DeepCAD-RT and PMD denoised data.Baseline and activity components are decomposed from the data.The baseline component with a gray colormap and activity component with a hot colormap are overlaid.Magnified views of the boxed regions are presented underneath with the consecutive frames of the spiking event (t = 0.222 s).Scale bar, 40 μm.b, PSNR of the baseline-corrected data before and after denoising data with different spike widths.Clean data were used as the ground truth for PSNR calculation.c, The left shows a box-and-whisker plot showing Pearson correlation coefficients before and after denoising data with different spike widths.The right shows a line chart showing average Pearson correlation coefficient before and after denoising data with different spike widths.Two-sided one-way analysis of variance with Tukey-Kramer post hoc test was used.n = 116 for each test, which represents the number of neurons (NS, not significant, *P < 0.1, **P < 0.01, ***P < 0.001).d, Single-pixel fluorescence traces extracted from baseline-corrected data.From top to bottom: clean, noisy, SUPPORT, DeepCAD-RT and PMD denoised data.The left shows each single-pixel trace occupies each row.The right shows three representative single-pixel traces visualized with different colors.e, Single cell fluorescence traces near spiking event extracted from baseline-corrected data.From top to bottom: clean, noisy, SUPPORT, DeepCAD-RT and PMD denoised data.From left to right: changing spike widths of 1, 3, 5, 7 and 9 ms. Articlehttps://doi.org/10.1038/s41592-023-02005-8
Fig. 3 |
Fig. 3 | Denoising single-neuron voltage imaging data.a, Simultaneous electrophysiological recording and voltage imaging data.From top to bottom: electrophysiological recording, raw, SUPPORT, DeepCAD-RT and PMD denoised data.Detected spikes from electrophysiological recordings are marked with black dots.Traces from voltage imaging data were extracted using a manually drawn ROI.b, Enlarged view of the green region in a. c, Three representative frames indicated on b with green arrows for raw and denoised data.Baseline and activity components are decomposed from raw data and denoised data.The baseline component with a gray colormap and the activity component with a hot Article https://doi.org/10.1038/s41592-023-02005-8
Fig. 4 |
Fig. 4 | Recovering subthreshold activity in voltage imaging data.a, Raw and SUPPORT-denoised images of four neurons in mouse cortex layer 1 expressing Voltron1 are shown after baseline correction.Scale bars, 5 μm.b, Electrophysiological recording and single-pixel traces extracted from raw and SUPPORT-denoised data.Spike regions are detected from electrophysiological recording data and excluded in subthreshold analysis.c, The left shows box-and-whisker plots showing Pearson correlation coefficient between electrophysiological recording and single-pixel fluorescence traces in subthreshold region.The right shows box-and-whisker plots showing average Pearson correlation coefficients before and after denoising.A two-sided paired-sample t-test was used: cell 1, n = 1,842; cell 2, n = 675; cell 3, n = 2,610; cell 4, n = 506 and average, m = 4, where n represents the number of pixels and m represents the number of cells.d, Power spectral density of electrophysiological recording and single-pixel fluorescence traces of raw and denoised data.
e,
Raw and SUPPORT-denoised images of eight neurons in the brain slice from mouse cortex L2/3 expressing QuasAr6a are shown after baseline correction.Scale bars, 10 μm.f, Relationship between transmembrane potential and dF/F 0 .Average and standard deviation of dF/F 0 values are calculated for corresponding voltage values.Average points are drawn as solid lines and areas between average + standard deviation and average-standard deviation are filled.g, The left shows box-and-whisker plots showing Pearson correlation coefficient between electrophysiological recording and single-pixel fluorescence traces in subthreshold region.The right shows box-and-whisker plots showing average Pearson correlation coefficients before and after denoising.A two-sided paired-sample t-test was used: cell 1, n = 3,289; cell 2, n = 3,157; cell 3, n = 3,458; cell 4, n = 3,516; cell 5, n = 2,214; cell 6, n = 599; cell 7, n = 1,240; cell 8, n = 427 and average, m = 8, where n represents the number of pixels and m represents the number of cells (**P < 0.01, ***P < 0.001).
Fig. 5 |
Fig. 5 | Denoising population voltage imaging data.a, Images after baseline correction from mouse dataset.The top shows the baseline-corrected raw data.The bottom shows the baseline-corrected SUPPORT-denoised data.Boundaries of two ROI are drawn with cyan lines.Scale bar, 40 μm.b, Distribution of the SNR for all pixels from raw and SUPPORT-denoised data after baseline correction, n = 65,536.c, Traces from raw and SUPPORT-denoised data extracted from two ROI in a. Traces for the smaller temporal region are plotted on the right.The enlarged temporal region is colored blue and brown.d, Images from the zebrafish dataset.Baseline and activity components are decomposed from raw
Fig. 6 |
Fig. 6 | Denoising voltage imaging data with motion.a, Representative frames of raw video and SUPPORT-denoised videos without and with motion after baseline correction.Motion was synthetically applied to the images of neurons in mouse cortex L2/3 expressing QuasAr6a, simultaneously recorded with electrophysiology.Scale bars, 5 μm.b, Representative frames of a spatially expanded view of cell 1 in a at the timings indicated by red arrows in c.From left to right: frames at 604, 955, 2,214 and 3,521 ms.From top to bottom: raw video, SUPPORT-denoised video without motion and SUPPORT-denoised video with motion.Scale bar, 5 μm.c, Line plot showing the x and y direction motions in the micrometer scale.d, Electrophysiology trace and single-pixel fluorescence traces extracted from the videos.From top to bottom: electrophysiology, raw video, SUPPORT-denoised video without motion and SUPPORT-denoised video with motion.Scale bar, 500 ms.e, Box-and-whisker plot showing Pearson correlation coefficients between fluorescence traces and electrophysiology, before and after denoising.×5 indicates a five times higher motion compared to ×1. n = 5, which represents the number of cells.f, Box-and-whisker plot showing Pearson correlation coefficients between ground-truth image (SUPPORT-denoised image without motion) and images with motion before and after denoising.n = 5, which represents the number of cells.g, Box-and-whisker plot showing SNR acquired by comparing ground-truth image and images with motion before and after denoising.n = 5, which represents the number of cells.h, Representative frames of raw video and SUPPORT-denoised videos after baseline correction.The images show a neuron expressing SomArchon in the hippocampus of an awake mouse.Scale bar, 3 μm.i, Representative frames in h at the timings indicated by red arrows in j.From left to right: frames at 2,018, 17,203, 29,618 and 50,025 ms.Scale bar, 5 μm.j, Line plot showing x and y directional motions in the micrometer scale.k, Traces extracted from a single cell in raw video and SUPPORT-denoised video.Temporally expanded traces from the brown area on the left are shown on the right.l, Histogram of SNR from the raw video and SUPPORT-denoised video. Articlehttps://doi.org/10.1038/s41592-023-02005-8
Extended Data Fig. 1 |
SUPPORT denoises freely moving Caenorhabditis elegans imaging data.a, Images of freely moving C. elegans.From left to right: Noisy, SUPPORT, DeepCAD-RT, and PMD denoised data.Inset shows the intensity profile along the dashed line.Magnified views of the boxed regions are presented underneath.b, Pixel-wise difference between denoised data and noisy data.Squared norm of Fourier transform of each difference are shown in the lower images.Inset shows the logarithm of the squared norm of Fourier transform against the distance to the origin.c, Magnified views of the red boxed region in a at consecutive neighboring time points.Magenta lines were set on the left side of the brightest neuron in the noisy data.From top to bottom: Noisy, SUPPORT, DeepCAD-RT, and PMD denoised data.d, Noisy volume and denoised volume are depth coded and presented.Magnified views of the boxed regions are presented on the right.Extended Data Fig. 2 | SUPPORT denoises volumetric structural imaging data.a, Representative axial slice from low-SNR, SUPPORT-denoised, high-SNR volumes of Penicillium.b, Magnified views of the yellow boxed region in a at multiple axial locations.Axial location of a corresponds to 3.37 μm.c, Box-andwhisker plot showing Pearson correlation coefficient and signal-to-noise ratio for axial slices.A two-sided paired-sample t-test is used, N = 381, which represents the number of planes along the z-axis (***: p-value < 0.001).d, Intensity profiles of the cyan dashed line in a. e, Example frame of bone of a mouse embryo after expansion for the raw data (top) and denoised image using SUPPORT (bottom).f, Raw (top) and denoised image (bottom) of intestine of a mouse embryo.e-f, Length scales are presented in pre-expansion dimensions. | 13,939.8 | 2023-09-18T00:00:00.000 | [
"Computer Science",
"Engineering",
"Physics"
] |
Research on Black-Litterman Index Enhancement Strategy——Based on the Ledoit-Wolf Compression Estimation Method to Optimize the CSI 500 Index Enhancement Strategy
Financial risks may often lead to significant losses. A reasonable capital management model can prevent financial risks and enhance financial services to the real economy. The Black-Litterman model can reduce risks through asset allocation. This paper uses the Black-Litterman model to construct an enhanced strategy applied to the CSI 500 Index, and selects the backtest from December 1, 2019 to December 1, 2021. Through the strategy backtest, it can be found that: whether it is considered or not Transaction costs, using analysts’ consensus target price as the input point of view of the BL model, can provide excess returns for the index enhancement strategy under relatively stable conditions within the sample interval, and improve the sharpness ratio, information ratio, maximum drawdown, etc. Within the risk-return parameters. In order to solve the problem of model instability and extreme values of configuration weights in the first step, this paper adjusts the covariance based on the Leodit-wolf compression estimation, thereby optimizing the exponential enhancement model. The backtest results showed that although the volatility and maximum drawdown of the optimized enhanced index model increased slightly, it showed a higher excess return rate and information ratio. Therefore, the BL model optimized based on the compression estimation method can make the model applicable to a wider range, and can be extended to large-scale assets and multi-asset allocation, so that investors have more choices in quantitative investment strategies.
Introduction
Recently, China's A shares have continued to fluctuate, and the difficulty of investment has increased significantly. At the same time, the CSI 500 Index and other stock indexes that ha not received much attention from investors in the past ushered in a round of long-term structural market. The outstanding excess returns of related stock indexes, the CSI 500 continued strong private equity index enhancement strategy has once again heated up. As of July 2021, the CSI 500 Index has significantly outperformed the Shanghai and Shenzhen 300 Index by more than 14 percentage points, which has attracted the attention of investors. In order to study how to obtain profits through reasonable asset allocation in the structured market, an index enhancement strategy can be considered. The index enhancement strategy using the quantitative method can effectively increase the return on the basis of simple passive investment. Therefore, this paper focuses on the volatility of the CSI 500 to study the strategy of increasing the index.
The difficulties to be overcome for quantitative investment methods from theoretical application to actual application include, but are not limited to, the reverse engineering of some business models and the constant change of parameters according to the market environment. The Black-Litterman model is a semi-open quantitative asset allocation method. The main structure of the model is in Black&Litterman (1990) has been fully explained, but the setting of its parameters has not yet reached a consensus. But it is also the flexibility of this model setting that gives the BL model the possibility of multiple financial scenarios, and it can be optimized by adding other models and parameter settings. This paper optimizes the BL model by using the Leodit-wolf The compressed estimation method can optimize the covariance matrix. From the above review, it can be seen that in the use of BL model construction index enhancement strategy, no scholar has used the compressed estimation method to optimize the BL model.This paper draws on Leodit and Wolf to optimize the BL model to overcome problems such as extreme weights based on the covariance compression estimation method. Based on the optimized BL model, based on Zhu(2012), Zhou(2017), Fu(2018) and other scholars' index enhancement quantitative strategy, constructing the CSI 500 index enhancement strategy. In this paper, by constructing the Shrinkage Estimator of the covariance matrix, the problem of the irreversibility of the sample covariance matrix and the excessive estimation error is solved.The outliers in the sample covariance matrix actually bring a lot of estimation errors. Using unprocessed sample covariance matrix for combinatorial optimization will lead to poor weight distribution. The larger the condition number of the covariance matrix, the less stable it is. The condition number of sample empirical variance is generally relatively high, and the covariance of the Ledoit-Wolf compression estimation method can greatly reduce the condition number of the covariance, which is also one of the purposes of most compression methods in practical applications.
Combining the viewpoints of the above-mentioned scholars, it can be seen that in the use of BL model construction index enhancement strategy, no scholar has optimized its stability and weight extreme values. Therefore, the main contributions of this paper are as follows: First, use the compression estimation method to adjust the covariance of the BL model to optimize the CSI 500 index enhancement strategy, which can overcome the instability of the original index enhancement strategy model and extreme weights, etc. Question. Second, by constructing an index enhancement strategy, it is possible to conduct quantitative research on the CSI 500 index with a structural market this year, providing quantitative investors with a richer selection of quantitative strategies. Third, the application of Black-in index investment strategies There are not many empirical studies on the litterman asset allocation model. The strategy simulation of the litterman asset allocation model can further prove the feasibility of the model application.
CSI 500 Index Analysis
The CSI 500 Index is composed of the top 500 stocks ranked by the total market value after excluding the constituent stocks of the Shanghai and Shenzhen 300 Index and the top 300 stocks in total market value from all A shares. It comprehensively reflects the market value of a group of small and medium-sized stocks in the Chinese A-share market. The company's stock price performance. The CSI 500 Index experienced huge fluctuations from December 1, 2017 to December 1, 2021, with a maximum retracement of 2,200 points and a maximum increase of 3,200 points. Beginning in 2019, the CSI 500 Index has experienced a wave of structural rise, so it has attracted the attention of more institutional investors and individual investors. The CSI 500 Index is divided into 10 sectors, namely energy constituents, raw material constituents, industrial constituents, optional constituents, consumer constituents, pharmaceutical constituents, financial and real estate constituents, information constituents, communication constituents and Public constituent stocks. According to Wind's data, there are currently 499 stocks. Therefore, this paper will carry out the weighting ratio based on 10 sectors, and adjust the positions of 499 stocks according to the criteria for judging growth stocks.
For the CSI 500 Index, the current methods for index enhancement mainly include: (1) Refinancing enhancement, that is, strengthening by lending index constituent bonds and charging corresponding fees; (2) IPO enhancement, namely The excess returns obtained by purchasing the latest stocks or convertible bonds when listed; (3) Enhancement using quantitative methods. The first two methods are profitable through efficient capital operations or insufficient market pricing, but their strategic capacity is constant when the market gradually tends to equilibrium.
Shrinking. The quantitative strategy is closer to the nature of index enhancement: by judging the possible excess return opportunities of individual bonds, they are over-allocated in a quantitative way. The BL method provides a model reference for the realization of the quantitative index enhancement strategy, so this paper chooses the CSI 500 index as the index target of the study.
Theoretical Basis of the Black-litterman Model
For BL model parameter estimation, Litterman & Winkelmann (1996) discussed the estimation method of the covariance matrix, and gave a new covariance matrix estimation method suitable for a large number of asset classes and high-frequency financial time series data, which made up for the lack of big data computing power at that time Shortcomings in computational science. He&Litterman (2002) believes that the uncertainty of investors' opinions is almost the same as the uncertainty of the overall market, so he sets the opinion error matrix as , So now there is only that needs to be determined subjectivel，The value range of the judgment should be within the interval of 0-0.05. Idzorek (2004) proposed a method to quantify parameters , which is . Moreover, the confidence in the opinion error matrix can be converted into a confidence level by adding the ratio of the posterior allocation and the prior market equilibrium weight after the investor's opinion is added. Based on the quantitative parameter determination method of preset index deviation and excess return certainty, this paper constructs a quantitative passive allocation framework for index enhancement strategies.
Construction of Asset Allocation Model Based on Black-litterman
The BL model follows the standard assumptions of Markowitz's asset allocation theory in terms of investor http://ibr.ccsenet.org International Business Research Vol. 15, No. 2;2022 63 utility, and the representative investor utility function is: w is the weight vector of the class asset n . u is the market return vector corresponding to the class of assets n . is the investor's risk aversion coefficient. is the covariance matrix of of the returns of the class asset n . Both and can be obtained by a variety of different estimation methods.
The BL model's first a priori estimate of the rate of return on assets is not the average of historical data, but is obtained from the equilibrium asset size when the market clears. Assume that the proportion vector of n types of assets in the current market or in an index is mkt w ，Formula (1) can be used to reversely find the asset excess Another scalar is defined to describe investors' trust in a priori excess based on market equilibrium, as follows: The posterior market equilibrium excess return rate can be obtained: The corresponding posterior asset allocation weight can be obtained by the inverse calculation of equation (4.2): At this point, we have obtained the BL optimal asset allocation based on various asset information and investor subjective judgments in the comprehensive market equilibrium. However, for index enhancement applications, the economic significance of the parameters needs to be clear and defined.
1.The degree to which the scalar deviates from the exponential configuration. According to formula (4.4), when 0 , there is () ER . Thus according to formula (4.5), we c an get * mkt ww . Therefore, the degree to which the BL enhanced configuration result deviates from the exponential weight can be determined by controlling the size of the scalar.
2.Opinion credibility matrix -Diagonal matrix expression of opinion percentage confidence.It is generally believed that the confidence of an opinion is independent of the relative benefits of the opinion, and the historical correctness of an opinion can be used as an unbiased estimate of its certainty. According to the relevant principles of the Bayesian method,when the degree of confidence in the opinion→100%, that investors believe the future market rate of return will definitely change according to the direction and magnitude of their judgment, there would be 0 .In addition, in general, it can be assumed that the greater the volatility of the return on assets at the point of view, the more difficult and inaccurate the judgment of its future return. So it can use ' : as the value of the diagonal element of the i -th row of the matrix,which can meet the above two characteristics. Where i c is the confidence probability of the investor for the i -th viewpoint, the value range is 0 to 1. i P is the row vector of the i -th row of the P matrix.
3. -Risk aversion coefficient matching asset class. The formula for calculating the risk aversion factor of general investors proposed by Idzorek (2004) what kind of asset is used as the market standard asset and how to determine the risk-free rate of return.
This paper believes that the appropriate market standard asset can be selected as the CSI 500 Index itself, and the risk-free rate of return is the instantaneous yield to maturity of one-year treasury bonds. According to the above modeling steps of the BL model, first, the implicit equilibrium return needs to be required. The risk-free interest rate adopts the one-year treasury bond's instantaneous yield to maturity level of 2.301%. The data needed for inverse optimization are shown in Table 1 to Table 5.
CSI 500 Index Strengthening Strategy Construction
The basic market data selects the daily market data from December 1, 2017 to December 1, 2021, as well as the daily market data of the sample period, total market value data and index weight indicators. The risk-free interest rate level is selected when the exchange is the most liquid Yield to maturity of 1-year Treasury bonds. Some indicators need to be set as follows: 1.Consistent target price setting. This paper selects the unanimous target price of the researcher in the Wind terminal as the investor's point of view of individual stock income. Compared with financial data, analysts know that the target price has a higher update frequency, and the calculation of the conversion from the target price to the excess return is relatively clear. The timeliness of the analyst's consensus target price is one month in the future. Assume that the analyst's unanimous target price for the i -th stock one month later is t T yuan and the actual price is t A yuan, then the quantitative analyst's historical view confidence is: The rolling time window here is the past 24 months. Therefore, there will be no over-fitting fallacy that uses future data in advance. According to consistent target price data and confidence data, opinion matrix P and opinion credibility matrix can be formed.
The average return rate of the researcher's unanimous target price from December 1, 2017 to December 1, 2021 can be obtained: 2. Tracking error and no short selling setting. The tracking error range of index-enhanced products on the Chinese market will be agreed to be between 200 and 800 basis points. After many experiments, the tracking error can be controlled within this range. The reasonable value range is 0.0001 to 0.001.According to Hu(2019), the backtest result is 0.0005 in the actual backtest. Because the short-selling mechanism in my country's market is not perfect, and index-enhanced products generally do not adopt a long-short strategy, the minimum asset exposure of individual stocks in the backtest investment portfolio is restricted to 0%.
3. Strategy rebalance. The rebalancing frequency of the index enhancement model is set to not once a month, and the strategy sample is updated from the existing investment portfolio to the posterior optimal asset distribution calculated by the BL model. The transaction cost of rebalancing is based on the closing price of the stock at the end of the day, considering the two situations of no transaction cost and fixed ratio transaction cost.
According to the Black-litterman and the above settings, the relevant parameters of the model can be calculated as shown in Table 2 to According to the above optimal allocation weights, construct the CSI 500 Index enhancement strategy, carry out the fund purchase ratio according to the weights, and set a half-year adjustment of individual stocks in each sector. The basis of the adjustment is based on whether the stock meets the definition of growth stocks Adjust positions, buy or hold if the above indicators are met, and do not buy or sell short if they are not met. The basis for judging growth stocks is shown in Table 6: Through the above-mentioned model solution and position adjustment strategy setting, the CSI 500 Index enhancement strategy has been established.
Strategy Implementation and Backtest Results
The CSI 500 Index enhancement strategy is implemented through Python using the relevant functions in the Pandas, Windpy and WindAlgo packages. The backtest start time is December 1, 2017, and the end time is December 1, 2021. CSI 500 Total Return Index.
Backtest Results of BL Index Enhancement Strategy without Considering Transaction Costs
As shown in Figure 4-1, compared with the basic CSI 500 index, the BL index enhancement model that uses analysts' consistent target price information has a continuous and relatively stable excess return rate, with an annual return rate of approximately 33.05%, and the index The tracking error of the years is 0.50%, indicating that the strategy has a relatively good positive return enhancement. The Beta value of the BL index enhancement model is 0.83, which shows that compared with the CSI 500 index, this strategy exposes less systemic risks. The smaller maximum backtest of 34.01% can also illustrate this feature.
Backtest Results of BL Index Enhancement Strategy Considering Transaction Costs
In the operation of actual index-enhanced products, the transaction cost brought about by repositioning is an expenditure that must be considered, and it will form a drag on product performance in the long run. Based on the BL index enhancement strategy that considering transaction costs, for repositioning transactions, each transaction cost is increased by two thousandths, assuming that repositioning is carried out every six months.
The backtest results are shown in Figure 4.2. It can be clearly seen that due to the existence of transaction costs, the benefit advantage of the BL index enhancement strategy relative to the CSI 500 index has been narrowed.
Solving the Covariance Matrix Based on the Leodit-wolf Compressed Estimation Method
The usual maximum likelihood estimation of covariance can be regularized using shrinkage methods. Ledoit and Wolf proposed in 2004 to calculate the asymptotically optimal shrinkage parameters by minimizing the MSE criteria, resulting in the Ledoit-Wolf covariance estimation method named after them.
Using the Ledoit-wolf compression method to estimate, a biased estimator that can converge faster and the empirical covariance estimator are combined through the compression coefficient. The new covariance loses a certain degree of unbiasedness but achieves faster convergence. . In fact, as long as it is guaranteed that the estimated amount of superposition is biased, there is generally no limit to its selection. To understand the optimal compression strength from a geometric point of view, the compression estimator is the orthogonal projection of the true covariance matrix on the line connecting the sample covariance and the compression target. In the actual calculation, we can use the identity matrix as the superimposed biased matrix. The new covariance matrix is: The compression factor in the formula can be obtained by minimizing the loss between the new covariance and the empirical covariance. is the compression target, and the unit matrix can be used in actual calculations. S is the sample covariance matrix. This method is more suitable when the covariance matrix has more characteristic variables and fewer sample observations.
The key to the compression estimate lies in the determination of the compression strength, which can be estimated through a certain loss function. Ledoit&Wolf (2003) uses the distance between the covariance compression estimator and the true covariance matrix as the loss function. The distance is measured by the Frobenius norm, that is, the optimal compression strength can be solved by The minimum value of the formula is obtained: Under the Forbenius norm loss function, Ledoit and Wolf obtained the asymptotically optimal linear combination of the identity matrix and the sample variance matrix. They gave the selection method of 1 and 2 , pointing out that the two are only determined by the following four items: p is the number of samples, k is the number of parameters, k I is the kk unit matrix, and the others are operational variables. A new covariance matrix can be calculated based on the above model.
Estimation of Optimization Model Based on Leodit-wolf Compression Estimation Method
Based on the principle analysis of the above covariance matrix, this part of the software uses Python and loads the Ledoit-Wolf package to realize the Ledoit-Wolf compression estimation of the covariance matrix. Table 5.1 shows the covariance calculated by the compressed estimation method:
Implementation of Optimized CSI 500 Index Enhancement Strategy and Backtest Results
According to the optimized CSI 500 index enhancement strategy model, as in the previous section, it is implemented through Python using the relevant functions in the Pandas, Windpy and WindAlgo packages. The backtest start time is December 1, 2017, and the end time is December 1, 2021. Table 5.3, compared to the unoptimized BL index enhancement strategy that does not consider transaction costs and the basic CSI 500 index, the optimized BL index enhancement model has a higher excess return rate, and the annualized return rate is about It is 36.60%, which is 1.43% higher than before optimization. The information ratio has been increased from 1.97 to 2.05. The Beta value is 0.79. Compared with the CSI 500 Index, this strategy also exposes fewer system risks.
However, the maximum retracement of the strategy has increased from 35.04% to 35.72%, and the volatility has increased from 57.88% to 59.81%, indicating that the risk of the optimized strategy has slightly increased. Based on the optimized BL index enhancement strategy considering transaction costs, for repositioning transactions, each transaction cost is increased by two thousandths, assuming that repositioning is carried out every six months. The backtest results are shown in Figure 5.2. It can be clearly seen that due to the existence of transaction costs, the benefit advantage of the BL index enhancement strategy over the CSI 500 index has also been narrowed.
Conclusion
This paper uses the relevant data of the CSI 500 Index from December 1, 2017 to December 1, 2021, and innovatively uses the Ledoit-Wolf compression estimation method to optimize the Black-Litterman model to construct the CSI 500 index enhancement strategy. According to the strategy backtest results of the BL CSI 500 Index enhancement strategy, the results are as follows: The index enhancement strategy optimized with the Ledoit-Wolf compression estimation method has a higher excess return rate and information ratio, that is, it can be better than the performance of the performance benchmark CSI 500 Index. But at the same time there is a higher volatility and a maximum retracement, so the optimized strategy corresponds to a higher risk.
(2) On the whole, the Black-litterman-based CSI 500 index enhancement strategy before and after optimization can achieve excess returns compared with the CSI 500 index, and has a higher Sharpe ratio, information ratio and smaller Maximum drawdown. Therefore, the index 0.00 0.50 Performance benchmark (CSI 500) Optimized BL index enhancement strategy enhancement strategy performs well, which can bring excess returns to investors within the sample range and reduce risks to a certain extent.
(3) It can be seen from the results that using the researcher's consistent target price as the rate of return input condition can effectively improve the risk-return parameters of the asset portfolio, so that the index enhancement strategy constructed by the Black-Litterman model has better performance than the benchmark. The BL model can perform well. Adapt to the index enhancement scenario.
The CSI 500 index enhancement strategy based on the Ledoit-Wolf compression estimation method to optimize the Black-Litterman quantitative model performed well in the backtest, so the author makes the following suggestions: 1. It is reasonable to add other valid viewpoints to the Black-litterman model. With the development of my country's financial market, there will be more and more quantitative investment based on indexes. Therefore, the Black-litterman model can be used reasonably to obtain excess returns. The viewpoint matrix in this paper adopts the consistent target price of Wind researchers. In actual application, in addition to the researcher's consistent target price as the input condition of the rate of return, it can also be input into the model based on subjective but not quantifiable information such as public opinion information. To deal with the impact of macroeconomic and stock market fundamental changes on the strategy.
2. When constructing a quantitative model, suitable optimization methods should be found according to the possible defects of the model. For example, the covariance of the Black-litterman model used the historical covariance matrix estimation method in previous researches. In practice, the model is prone to instability and extreme values of configuration weights are often encountered, but no measures have been taken. Optimize it.
The use of optimization based on the Ledoit-Wolf compression estimation method can broaden the application scenarios of the Black-litterman model. Therefore, when building a quantitative model and setting parameters, the model must be adjusted through sufficient mathematical operations and empirical backtesting, and effective and rapid model adjustments must be made in accordance with changes in the market and changes in the underlying assets of the application.
3. Quantitative investment strategies should consider strategies with high scalability. Priority is given to building a highly versatile asset allocation framework model. The BL model has a good effect on the enhanced allocation of a single asset with a representative index, such as stocks, bonds, commodities, etc. A highly versatile asset allocation framework can make the strategic logic of quantitative investment institutions more malleable, the depth of optimization will be higher, and the strategy development will have more synergistic effects. | 5,812.8 | 2022-01-26T00:00:00.000 | [
"Economics",
"Business"
] |
Design of Optimized Wavelet Packet Algorithm to Improve Perception of Sensorineural Hearing Impaired
A novel optimized wavelet packet algorithm is proposed to improve the perception of sensorineural hearing-impaired people. In this work, we have developed optimized wavelet packet along with, biorthogonal wavelet basis functions using MATLAB Code. Here, we have created eight bands based on auditory filters of quasi octave bandwidth. Evaluation was carried out by conducting listening tests on seven subjects with bilateral mild to severe sensorineural hearing loss. The speech material used for the listening test consisted of a set of fifteen nonsense syllables in VCV context. The test results show that the proposed algorithm improves the recognition score, speech quality and transmission of overall feature specifically over the unprocessed signal. The response time also reduces significantly.
Introduction
For sensorineural hearing impaired people, the auditory filters are wider than normal in increased spectral masking [1].Masking proceeds primarily at peripheral level of ear and splitting of speech into two complementary signals thereby presenting them dichotically to diverse ears which might help in reducing the effect of increased masking in persons with sensorineural hearing impairment with residual hearing [1]- [3].Our ear uses wavelet transform while analyzing sound, at least in the very first stage [4].The wavelet transform is used in signal processing, due to the capability of wavelet transforms to existing a time-frequency (or time-scale) repre-sentation of signals as the wavelet transform uses a variable-width window (narrow at high frequencies and wide at low frequencies).
Wavelet analysis is equivalent to a bank of band pass filters.The wavelet filter bank allows a better representation of both the temporal and the place pitch in the speech signals.Nogueira et al. [5] have designed a WP filter bank and incorporated it into a commercial ACE (Advanced Combinational Encoder) strategy for speech processing in cochlear implants.Averaged results of speech intelligibility tests have shown that the mixed WP filter-bank leads to significantly better speech perception performance than the fast Fourier transform (FFT) as used in the commercial ACE strategy.Yao, J. et al. [6] investigated the application of an improved signal processing method called bionic wavelet transform (BWT).Authors have concluded that application of the BWT in cochlear implants has a number of advantages, including improved recognition rates for vowels and consonants, reduction in the number of channels in cochlear implant, reduction in the average stimulation duration of words, better noise tolerance and higher speech intelligibility rates.Abhjit Karmarkar et al. [7] have proposed a criterion to select the optimal wavelet packet based on the Zwicker's model critical band structure.Authors obtained optimal WP tree for different sampling frequencies and results are compared with other CB motivated WP trees.M. T. Kolte et al. [8] showed that the modified wavelet packets algorithm based on auditory critical bandwidth, resulted the relative improvements in recognition scores for processed scheme of wavelet packets were 3.33% to 22.23%.
The objective of our work is to minimize the effect of spectral masking in sensorineural hearing impaired with better perception using minimum number of channels.Modified wavelet algorithm using ten bands is proposed in [8].In this investigation, we have developed optimized wavelet packet algorithm biorthogonal wavelet family using MATLAB Code.We have created eight bands based on auditory filters of quasi octave bandwidth.[9] [10].Four alternate bands are combined for even-odd dichotic presentation.The inverse wavelet packet transform were used to produce speech components from the wavelet packet representation.Wavelet coefficients are being employed in order to synthesize the speech components.
The paper is planned into four sections.Section 1 introduces the need of the proposed system and also reviews the different techniques proposed by the different researchers to overcome various problems related to the hearing impaired using wavelet transform.Section 2 discusses the design of optimized wavelet packet.Section 3 includes listening tests for evaluation.Listening test results and discussion are presented in section 4. Section 5 concludes this paper.
Optimized Wavelet Packets
The handling scheme is developed as spectral splitting with optimized wavelets packets based on eight frequency bands as the performance by hearing-impaired subjects saturated around eight channels, while performance by normal-hearing subjects is sustained to 12 -16 channels in higher background noise [11].The number of channels desired to obtain high levels of speech understanding is still the subject of discussion [12].MATLAB code was developed based on optimized wavelet packet with biorthogonal wavelet functions.Biorthogonal wavelets chosen such that symmetry and exact reconstruction are possible using FIR filters.The inverse wavelet packet transform was used to synthesize speech components from the wavelet packet representation.To produce the speech component, wavelet coefficients are used.
The wavelet packet decomposition produces generic analysis signals that give richer signal analysis.The nodes of wavelet packet decomposition are known as wavelet packet atoms.Each wavelet packet atom is indexed by three parameters namely: scale, position and frequency.Unlike conventional wavelet transform, which is employed on low pass bands iteratively, the wavelet packet analysis is employed on both low pass (approximations) and high pass (details) sub bands.The conventional wavelet transform can offer (n+1) possible ways to analyze signal when the "n" decomposition levels are utilized.For wavelet packet analysis, for "n" level decomposition, it yields ways to encode the signal [13]- [15].A generic wavelet packet analysis is shown in the Figure 1.
In the notation W j,n where, j stands for scaling factor and n denotes frequency parameter, the representative equations are given by ( 1) and (2).
In optimized wavelet packet, we have applied discrete wavelet transform at first level of decomposition and wavelet packet for further three levels to obtain eight bands having quasi octave bandwidth.For each level, we have applied biorthogonal family with same order of decomposition.Following Figure 2 shows optimized wavelet packet tree.
Following Table 1 shows that all the eight band in alternate fashion for even-odd index with centre and pass band frequency for each band in KHz.
The stepwise workflow of the new approach of optimized wavelet packet is presented in the following algorithm.
Pseudo Algorithm
• Read audio input signal x(n) of length N.
• Perform wavelet packet decomposition of x(n) up to level 4 as directed in Figure 1.
• Construct the optimized wavelet packet tree by rejoining following nodes of the original tree T: 11, 12, 13, and 14 and 9, 10, 5, 6.Thus optimized tree will have only eight nodes as shown in Figure 2. • Selectively reconstruct the optimized wavelet tree to get two output signals-one for left ear and other for right ear, as follows: -In optimized tree, make all four approximate coefficients nodes numbered 15, 17, 9, and 5, zero while keeping detail coefficients nodes as it is and reconstructed the tree.-In optimized tree, make all four detail coefficients nodes numbered 16, 18, 10, and 6, zero keeping approximate coefficients nodes as it is and reconstructed that tree.
Listening Tests for Evaluation
The assessment was carried out by conducting listening tests on seven subjects with bilateral mild to severe sensorineural hearing loss.The speech material used for the listening test consisted of a set of fifteen nonsense syllables in VCV context with consonants /p, b, t, d, k, g, m, n, s, z, f, v, r, l, y/ and vowel /a/ as in "farmer".
Responses were tabulated in the form of confusion matrix and response time was also been recorded.Confusion matrices were used for calculating recognition scores and relative transmitted information.Further, the consonants were clustered according to the articulatory features [16] and the contribution of different features was analyzed.The features selected for this study were voicing
Listening Tests Results and Discussion
Listening tests were conducted to measure three performance parameters that are recognition score, response time and information transmission analysis.Comparative analysis of these parameters for processed and unpro-Table 1.Eight bands for odd-even presentation.cessed signal was evaluated.The detailed analysis of these results is shown in following subsections.
Recognition Score
Figure 3 provides percentage recognition scores (%) acquired from the confusion matrix.For the impaired subjects, the recognition score for unprocessed signal varies from 48.33% to 90%, and for processed signal recognition score varies from 53.33% to 93.33%.The average values observed as 66.17% and 74.58% for unprocessed and processed signals.The average relative improvement observed was 8.40%.Figure 4 shows the graphical representation of relative improvement in percentage recognition scores with respect to unprocessed signal.
Response Time
Response time is the time interval between speech materials presented dichotically to subjects and the response given by subjects.The response time for unprocessed signal varies from 4.08 to 8.6 seconds, and for processed signal, it varies from 3.9 to 8.2 seconds.The relative decrease in response time varies from 4.65% to 44.20%.The observed average value for processed signal was 5.01 Sec. Figure 5 shows the comparative the results for unprocessed and processed signals.
Information Transmission Analysis
Relative information transmission is used to measure the transmission performance in the context of specific features.The overall information transmitted and information transmitted for specific features were obtained for all subjects.The average overall information transmitted for Bi-ortho filter was observed as 78.62% for unprocessed signal and 85.31% for processed signal.The average relative improvement in overall information transmission observed as 6.69%.The contribution of all the six features to overall improvement was indicated by information transmission analysis.In addition, the improvement observed for the place feature.Since, the place information is linked with frequency resolving ability of auditory process, the effect of spectral masking has been reduced.Relative information transmitted for consonantal features is given in Table 2 and plotted in
Conclusion
An optimized wavelet packet using biorthogonal family based on auditory critical bandwidth is designed and implemented in the MATLAB.The experimentation results shows that signal processing scheme resulted in improvement in overall speech reception quality and significantly, improvement was recorded in recognition scores.Response time reduces significantly showing reduction in load on perception process.The contribution of all the six features to overall improvement was indicated by information transmission analysis.In addition, the improvement was observed for place feature.Since the place information is linked to frequency resolving capacity of auditory process, the effect of spectral masking has been reduced.
(voiced: /b d g m n z v r l y/ and unvoiced: /p t k s f/), place (front: /p b m f v/, middle: /t d n s z r l/, and back: /k g y/), manner (oral stop: /p b t d k g l y/, fricative: /s z f v r/, and nasals: /m n/), nasality (oral: /p b t d k g s z f v r l y/, nasal: /m n/), frication (stop: /p b t d k g m n l y/, fricative: /s z f v r/), and duration (short: /p b t d k g m n f v l/ and long: /s z r y/).
Figure 6
shows relative decrease in response time.Response time reduces significantly showing reduction in load on perception process.
Figure 3 .
Figure 3. Comparative results of percentage recognition scores of unprocessed and processed signal.
Figure 4 .
Figure 4. Relative Improvement in % with respect to unprocessed signal.
Figure 5 .
Figure 5. Comparative result of response time of unprocessed and processed signal.
Figure 6 .
Figure 6.Relative decreases in response time.
Figure 7 .
Figure 7. Information transmitted for overall feature.
Figure 8 .
Figure 8. Information transmitted for continuance feature.
Figure 9 .
Figure 9. Information transmitted for duration feature.
Figure 11 .
Figure 11.Information transmitted for manner feature.
Figure 13 .
Figure 13.Information transmitted for place feature.
Table 2 .
Relative information transmitted for consonantal features. | 2,643.2 | 2016-02-15T00:00:00.000 | [
"Computer Science"
] |
Enhancing Performance of GIS on Cloud Computing
Cloud computing provides a way of determining dynamically scalable and virtualized resources as a service over the Internet. GIS is a technology, which could use Cloud Computing for distributed parallel processing of a large set of data, store and share the results with users around the world. GIS is beneficial and works well when it be available to everyone, everywhere, anytime and with downcast fee of minimal sized in terms of technology and outlay. Cloud Computing used to portray and help users to use GIS applications in an easy way. This paper will study some example of a data structure like a K-d tree and Quad trees of GIS application and compare between them when storing these data structures on Cloud computing, the paper also portrays the results of the study of data structure on cloud computing platforms to retrieve data from cloud computing. The paper provides an application for “finding neighborhood from existing data stored. Keywords—Cloud Computing; GIS; Kd-tree; Quadtree
I. INTRODUCTION
Geographical information system (GIS) is a group of Tools that analyzes, stores, manages, captures and presents visual data that are associated with geographical locations‖ this assumes a definition of the acronym of GIS [11].GIS or geospatial information studies play a prominent role in many fields and widely adopted nowadays.In another view, it is any information system merging of statistical analysis, cartography hardware, software, and special types of DB (huge size-different shapes -…) and data to provide information and present the result of all these operations.GIS used in decision -making as in public health [12] which describe the relation between distribution diseases and concentration vary in different locations for making best possible decision by using spatial relations between it, visualizing the data to produce information and processing these data.In addition, in a pilot project designed to explore the potential for an information tool and educate sector engagement model to benefit the sector and its communities in the transport corridor to the north of Brisbane.By allowing participants, community, government and non-government organizations (NGO) to access information at a regional level to assist with decision making and the evaluation of shared cross-sector service provision and planning initiatives.[15] Over a few decades, efforts made to upgrade applications of GIS in order to provide huge spectrum services to the users through the globe.For example, but not limited to, application of integration, GIS and hydrology, by monitoring of Surface water and Groundwater resources is dependent on dynamic and static parameters of these water systems as well as meteorological data sets.All this information is large in volume and spatial as well as temporally varying in Nature.[13] Another one of using GIS in watershed management.By studying the basic characteristic of watershed likes, drainage network and flow paths derived from readily available Digital Elevation Models (DEMs) and USGS's National Hydrography Dataset (NHD) program.[14].Cloud computing has emerged as a paradigm to deliver on demand resources (e.g., infrastructure, platform, software, etc.) to customers similar to other utilities (e.g., water, electricity and gas).[16] Cloud Computing can be used across the challenges in GIS applications.GIS is a complete System of Hardware, Software, and Spatial Data (topographic, demographic, graphic image, digitally...) performs processing and analysis operations on those data to produce reports, graphics, statistics, and controls geographic data processing workflows.[1] [8]
II. PREVIEW ON DIFFERENT GIS DATABASES
The GIS has a special natural due to the large amount of data, the way of storing this data, and the experts who deal with it.The recent emergence of cloud computing brings new possibilities in service deployment.Services deployed in environments that made to scale up or down as required, with the service provider only charged for actual usage.Many types of database can be used for storing the spatial data like Quad tree, R tree and K-d tree I will look for those types as a background.
A quad tree is a tree data structure used to represent a picture successively in deeper level represented the best subdivisions of picture areas.Each node represents and links to the quadrant of its parent.A process of subdividing an image matrix into four quadrants parts recursively until every part has unique color fills up the tree.A Quad tree is trees whose nodes are either leaf (no children) or have four children Fig 1 show the shape of quad tree structure.The children are arranged one, two, three, and four.The region of the quad tree describes a piece of space in two dimensions (like X and Y) by dividing the region into four equal quadrants, sub quadrants, and so on with each leaf (which mean the node is the last one) node containing data corresponding to a specific sub region.Each node in the tree must have exactly four children, or have leaf node.[17] The region quad tree is not strictly a ‗tree' as the positions of subdivisions are independent of the data.They precisely called 'tries'.A region quad tree with a depth of n (number of levels) used to represent an image consisting of 2n × 2n pixels, where each pixel value is zero or one [2].The advantage of the quad tree lies in reducing the complexity of the intersection process by enabling the pruning of certain objects or portions of objects from the query.The disadvantage of quad tree, it must planed scope beforehand.[18] Fig. 1.Quad tree structure Rtree is a real extension of B-trees (Comer 1979), which refers to binary search tree, in that a node can have more than two children, unlike self-balancing binary search trees, the Btree optimize for systems that read and write large blocks of data.B-trees are a good example of a data structure for external memory.A B -tree commonly used in databases and file systems.B-tree does not need rebalancing as frequently as other self-balancing search trees, but may waste some space [19].The R tree (Rectangle tree) is a data structure, use in multiple dimensions.Which is heightbalanced tree [2].It consists of two levels of storage, medium and last node (leaf node).The stats of last nodes and medium nodes stored the data objects built by gathering rectangles at the lower level.The collected data in rectangle shape as shown in Fig 2, which illustrate the structure of the R tree.The nodes can be covered, overlapping, or completely disjoint, no assumption about their properties.The Minimum Bounding Rectangles (MBRs) of the actual data objects assume stored in the last node of the tree.Each medium node is associated with some rectangle, which completely encloses all rectangles that correspond to lower level nodes.[3] Fig. 2. R tree structure k-d tree (short for k-dimensional tree) is a spacepartitioning data structure for organizing points in a kdimensional space.k-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g.range searches and nearest neighbor searches).k-d trees are a special case of binary space partitioning trees [20].k-dtree also used in computer vision and machine learning algorithms consists of finding nearest neighbor matches to high dimensional vectors that represent the training data.[21].However, a key problem of data driven tree structures is the capability of data update.Each point insertion or deletion requires the modification of large parts of the actual tree structure.[22] Fig. 3. k-d tree structure
III. PREVIOUS WORK
To implement spatial applications efficiently requires the use of spatial data structures, which used to store data objects that linked with location and an important class of data structures used in computer graphics, geographic information systems, and many other fields.
To improve performance of K-d tree and Quad tree have different shapes.For example, the building of the data structure which represent in the using of mathematical mean by using median of data [9].Another shape of improving performance, in this paper the author use the same data structures K-d tree and Quad tree addition to Tile arrays and by ignoring the unnecessary objects, the time of retrieving data is decreased as in [10] IV.METHODOLOGY We have one database but with different data structure.Actually, we use hash tables and multidimensional array.
A hash function is any function that used to map data of arbitrary size to data of fixed size.The values returned by a hash function called hash values, hash codes, hash sums, or simply hashes.One use is a data structure called a hash table, widely used in computer software for rapid data lookup.Hash functions accelerate table or database lookup by detecting duplicated records in a large file.Hash functions used in hash tables, to find out a data record (a dictionary definition) given its search key (the headword).Specifically, the hash function used to plane the search key to an index.The index gives the address in the hash table where the suitable record should be stored.Hash tables, sequenced, used to implement associative arrays and dynamic sets.[23] Typically, the domain of a hash function (the set of possible keys) is larger than its range (the number of different table, indexes), and so it will plan several different keys to the same index.Therefore, each slot of a hash table is associated with (implicitly or explicitly) a multi of records, rather than a single record.For this reason, each slot of a hash table often called a -bucket,‖ and hash values called -bucket indices.‖The hash function only hints at the record's locationit tells where we can start looking for it.Still, in a half-full table, a good hash function will typically decrease the search down to only one or two entries.Hash table used in many applications like an approximate nearest neighbor.
Searching in large databases has become popular owing to its computational and memory efficiency.The famous hashing methods, e.g., Locality Sensitive Hashing (LSH) and Spectral Hashing (SH), construct hash functions based on random or principal projections.[4].The complementary hashing approach, is an approach used hash table, which is able to balance the precision and recall in a more effective way.The key idea is to employ multiple complementary hash tables, which are learned sequentially in a boosting manner, so that, given a query, its true nearest neighbors missed from the active bucket of one hash table are more likely to be found in the active bucket of the next hash table.[5] Now we look for another type of data structure -multidimensional array.‖It is recognized in the past that, traditional database Management Systems (DBMSs) does not handle efficiently multi-dimensional data (which are geometrical shapes in our search) such as squares, Polygons, or even points in a multi-dimensional space.Multidimensional data arise in many applications, such as the most important fields: 1) Cartography, Maps could be stored and searched electronically answering efficiently geometric queries.www.ijacsa.thesai.org2) Computer-aided Design (CAD).
3) Computer vision and robotics.4) Rule indexing in expert database systems.[6].On some applications the focus on increase the memory storage and reduce the conflict of data access to use one dimensional array, but by use the automatic partitioning memory scheme for multidimensional arrays based on linear transformation to provide high data throughput of memory storage the experimental illustrate that saving in memory banks and digital signal processing (DSP).[7] The application starts as in Fig 8.The curves illustrate the numbers of search (X-axis) with the time in (microsecond).The curves represent that the biggest time the system taken is in the data structure of K-d tree(K-DT)which green one and next it the Quad tree(QT HT) with data structure in hash table represented by red one and the smallest one is the Quad tree in multidimensional array(QTMD ) in blue.
VI. CONCLUSION
Our goal is studying the performance of different kind of DB structure for GIS which storage in Cloud computing.The data type of GIS is huge and need to store in the data structure with a method to provide the performance goal:--Min.Mass storage.
-Min.Time search.So, during store data map we use two data structures:--K-d tree to store points.
-Quad tree to store regions.
We find that quad tree is more useful and can store large regions with small data as shown in Fig 14.The gauge of any query is the query time.We use 3 data structures to search in database Hash table (has a constant time -hash function‖) for regions, K-d tree (proportional to the length of the tree) query for XY points, and Multidimensional array (has constant time) to search for regions.As we say before we will treat with regions so we compare between hash table and multidimensional array.We find a multi dimensional array is the fastest one.The disadvantage of multidimensional array large memory size, but this memory is local on the computer not in the server.Maybe not as effective if the amount of divisions increase.The result illustrates that the data type of GIS should store in a -quad tree in multidimensional array‖ which give better performance than the two other types, K-d tree and Quad tree in the hash function.
Fig 4
Fig 4 illustrates the GUI of The application .It builds to display the performance of different types of GIS data structures, quad tree, and K-d tree.The application has the ability to search, add, delete, and update the points.In addition to, it has to division the map to different scale from 1 to 9 and prints the name of site beside the location on the tree.The application contains the ability to find the nearest neighbor from any record exits in DB.All the process occurs on the cloud computing on the internet.The database structures storage on the -SOMEE.com.‖The application can play online and off line.The database of application uploaded to the cloud computing which represented by SOMEE.COM as a hosting DB.The application loaded the database in the first running of application Fig 5 shows the time of searching in database.
Fig. 4 .
Fig. 4. GUI of the project Hash table, and a Multidimensional array storing the data in data structure, the application illustrates the time response in Fig 5 represents the search time in DB.
Fig. 5 .
Fig. 5. Search time in DB Fig 6 illustrates the division in (4) degree.Moreover, the red point is the result of search for the point under search and its location in the tree.
Fig. 6 .
Fig. 6.Snap shoot for the result on map
Fig. 8 .
Fig. 8. Start of the project We have 42 records which are the cities and famous place in Egypt, ID represent the index of location in DB Location name, x and y the coordinate of the location.
Fig. 9 .
Fig. 9. coordinates of point form Fig 8 gives the coordinate of the point when clicked on the map directly and also the index number of the location.V. RESULTS First, we select the name of city from location name and put it in the location in the first label and press -search‖ which bring the name of the location and display it on the map Fig 9 show the choosing process of -Kafr_Elshik‖ city from a database.The name of a city under the search -Kafr_Elshik‖ Fig 11 and Fig 12 shown the result of choosing process.Fig 13 shows the time response for the different type of database structures.
Fig. 14 .
Fig. 14. the map in quad tree division | 3,491.6 | 2015-01-01T00:00:00.000 | [
"Computer Science",
"Environmental Science",
"Geography"
] |
Development of a portable pulsed fast ⩾106 neutron generator based on a flexible miniature plasma focus tube
A plasma focus device is a laboratory fusion device that is used to produce pulsed neutrons for a few tens of ns duration. A compact plasma focus tube (volume ≈ 130 cm3) has been developed, and this was connected to a newly developed capacitor bank using 24 coaxial cables, each 10 m long. The capacitor bank was of compact size and consisted of four energy storage capacitors (each 6 µF, 20 kV, size: 20 cm × 20 cm × 30 cm). The peak discharge current of the capacitor bank was estimated to be 176 kA with a rise time of around 3.6 µs at maximum 4.8 kJ operation energy. The average neutron yield was observed to be maximum (3.1 ± 1.0) × 106 neutrons/pulse with a pulse duration of 15–25 ns at an operating energy of 2.7 kJ (15 kV) and deuterium gas filling pressure of 4 mbar. Long coaxial cables allow only the plasma focus head (neutron source) to be moved as per need, making this a portable pulsed neutron source that is useful in many applications, including in extreme conditions, such as in borehole logging applications for oil and mineral mapping. This report describes the various components of this portable neutron generator together with its neutron emission characteristics.
Introduction
Portable fast neutron generators (PFNGs) have been proven to be a technically as well as commercially viable alternative to conventional neutron sources, such as Pu-Be, Am-Be and 252 Cf, in many applications covering vast areas, including security [1][2][3], industry [4], environmental and geological fields [5], medical fields, especially in biophysics [6,7], and in boron neutron capture therapy [8] among others. * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Among the various PFNGs, compact light-ion acceleratorbased hermetically sealed tubes that use deuterium-deuterium (D-D) and deuterium-tritium (D-T) fusion reactions have found the most widespread use [8][9][10][11][12][13]. These accelerators generate neutrons of energies ∼2. 45 MeV and ∼14.1 MeV, respectively. This consists of a source able to generate positively charged ions, one or more devices to accelerate the ions, and a metal hydride target loaded with either deuterium or tritium or a mixture of the two. An alternative to this is the dense plasma focus (PF)device based [14] portable pulsed ∼2. 45 and ∼14.1 MeV neutron generator, which uses the same fusion reactions in D 2 and/or D-T mixture gases, respectively. Unlike in accelerator-based sealed neutron tubes, ions are selfaccelerated in the plasma focus device to high energies (a few keV to several hundred keV) due to its geometry and produce intense neutrons for a short duration (typically a few 10 s ns). The plasma focus device is simple in operation as well as economical as most of its components are either replaceable at a low cost or designed for long and repetitive operations.
Together with pulsed intense neutrons, the plasma focus device is a widely known pulsed source of ions, electrons and soft as well as hard x-rays. They have routinely been used for several applications, such as lithography [15], radiography [16], material processing and thin film depositions [17], irradiation on materials for the first wall of upcoming fusion reactors [18][19][20] and in biological and biomedicine research [21][22][23][24]. In view of this, plasma focus devices continue to be designed and developed with different geometries and with different radiation yields that, suitable for use in the above-mentioned applications.
Numerous portable pulsed neutron generators of neutron yield ∼10 6 neutrons/pulse or less based on the plasma focus device have been developed worldwide in different laboratories [25][26][27][28][29][30][31][32]. For example, Silva et al [25] reported a maximum neutron yield of (1.06 ± 0.13) × 10 6 neutrons/shot at 9 mbar filling pressure of D 2 gas in a very small and fast plasma focus device operated at ∼400 J. Similarly, Milanese et al [26] reported the design, construction and experimental study of a very small transportable dense plasma focus device with 125 J of energy as an intense, fast neutron source of yield ∼10 6 neutrons/pulse. In another report [27], a compact and portable pulsed neutron source was reported to generate an average neutron yield of (1 ± 0.27) × 10 4 neutrons/shot at 200 J of bank energy. Rout et al [28] designed and developed a compact and portable sealed-type PF device, which could generate 10 5 -10 6 neutrons/pulse at 200 J of bank energy for 150 discharges for a single filling. Neutron emission of more than 10 4 neutrons/shot from a table-top plasma focus device of size 25 cm × 25 cm × 50 cm at only tens of joules energy was reported by Soto et al [29]. Soto et al [33] reported on the neutron emission from the smallest plasma focus device in the world (size: ∼20 cm × 20 cm × 5 cm) operating only at 0.1-0.2 J. A total neutron yield of (100 ± 40) neutrons/pulse was reported to be produced using this device at an operating energy of 0.1 J (4.9 nF, 6.5 kV), which can further be increased if operated repetitively.
Portability in all the above-mentioned devices has been achieved mostly through the use of a compact capacitor bank operating at sub-joule to a few hundred joules with an appropriately matched plasma focus unit. A typical plasma focus unit consists of a pair of coaxial electrodes working as the anode and the cathode, and an insulator sleeve placed in between them at the bottom [14]. The cathode is either designed in a tubular shape or in the form of a squirrel cage consisting of multiple rods. The majority of the low-energy plasma focus devices have used a tubular-shaped cathode as it also works as the experimental plasma chamber, which helps in achieving the desired compactness in a portable neutron source. A compact and coaxial spark gap is generally used for fast transfer of the capacitor bank energy to the plasma focus unit. The overall dimension is minimized by connecting all three main components, i.e. the capacitor bank, the spark gap and the plasma focus unit, using parallel plate transmission lines in a compact and rigid geometry. Moreover, these devices are mostly operated with battery-powered supplies, making them suitable for use in those field applications where a low to moderate neutron yield is required. However, high electromagnetic noise generated during capacitor bank discharge has been an issue in applications that require a high signal-to-noise ratio (S/N) because of its proximity to the plasma focus unit. In addition, the capacitor bank and other associated high-voltage (HV) components of the portable plasma focus devices may not be compatible for use in extreme conditions, such as a neutron probe tool in borehole logging for deep geological surveys to find deep ore deposits and petroleum reservoirs [34,35], as high moisture among other factors severely effects its electrical operation in such conditions.
Taking into consideration the above-mentioned limitations, an electromagnetic-interference proof and HV safe pulsed neutron generator based on a flexible miniature plasma focus tube has been developed. A tubular-shaped miniature plasma focus tube of size 5 cm diameter × 16 cm length and weight around 1.2 kg has been connected to a compact capacitor bank of size around 40 cm × 40 cm × 30 cm using 10 m long commercially available RG213 coaxial cables. The long coaxial cables provide the desired flexibility to move the plasma focus tube to any specific location in 10 m radius, as well as to reduce the effects of EMIs, as the outer conductor of the cables also helps to partially screen the electromagnetic noise generated during the capacitor-bank discharge. Here, the plasma focus tube shall be at HV for only a short duration of a few microseconds, making this useful as a neutron probe tool in extreme conditions without any change in electrical characteristics and, in turn, neutron emission characteristics. Moreover, isolation of the plasma focus tube and the capacitor bank makes handling of the portable neutron generators safe from any electrical hazard, which was otherwise not possible with other available portable neutron generators, where the capacitor bank and the plasma focus unit were held together in a compact geometry. The present report includes a detailed description of the major components of the portable plasma focus device, i.e. the plasma focus tube design, the capacitor bank and the spark gap, followed by experimental observations of timeresolved and time-integrated neutron emission characteristics in the subsequent sections.
Experimental setup
A schematic and a photograph of the newly developed portable pulsed neutron generator are depicted in figures 1 and 2, respectively. The main components of the portable pulsed neutron generators are the capacitor bank, the triggerable spark gap switch and the plasma focus tube. All these components have been indigenously designed and developed. A compact DC HV power supply has been used to charge the capacitor bank to the desired voltage and to supply a fast negative trigger pulse to trigger and close the spark gap switch. All the electrical operations were performed remotely using a hand-held control unit.
The capacitor bank was assembled using four energy storage capacitors connected in parallel. The capacitors were custom-made for fast high-discharge current, thus were suitable for such applications. Each capacitor has a capacitance of around 6 µF and self-inductance of less than 30 nH. The size of each capacitor was around 20 cm × 20 cm × 30 cm (l × w × h). Each capacitor was tested for its operation at a maximum rated voltage of 20 kV before connecting them in parallel to form the capacitor bank. The HV terminals of all the capacitors were terminated on a common SS plate of size 26 cm × 26 cm × 1.2 cm (l × w × t). Over this plate, the triggerable spark gap switch was assembled in a compact coaxial geometry, as seen in figures 1 and 2. The spark gap switch was indigenously developed for operation at atmospheric air pressure. One end of the spark gap switch was screwed to the HV plate of the capacitor bank, and the other end was coupled to the plasma focus tube through the RG213 coaxial cables, as depicted in the schematic diagram of the setup (figure 1). The overall dimension of the spark gap switch was around 14 cm diameter × 6 cm height. The center pin trigger method was adopted to trigger and close the spark gap switch. To trigger the spark gap switch, an SS pin of 0.6 cm diameter was placed at the center of its top electrode and insulated from it using a 0.2 cm thick tube made of ultra-high molecular weight (UHMW) polyethene material. The spark gap electrodes were made out of SS304 material and its outer casing was made of UHMW. A dry compressed air flushing arrangement was made to clean the spark gap before and after operation. The overall size of the capacitor bank together with the spark gap was 40 cm × 40 cm × 36 cm (l × w × h) with a total weight of around 100 kg and it was placed over a movable trolley. The capacitor bank discharge current was delivered to the plasma focus tube using the RG 213 coaxial cables. Although the use of RG213 coaxial cables has various advantages, as described earlier, it must be noted that the lumped inductance and resistance of the RG213 coaxial cable are typically ∼250 nH m −1 and ∼6 mΩ m −1 , respectively [36]. Hence, heavy parallelization of the cables was used to obtain the overall inductance and resistance values in the range necessary for efficient plasma pinch formation. In total, twenty-four 10 m long RG213 coaxial cables were used to couple the capacitor bank and the plasma focus tube. Twenty-four cables were used to minimize the overall inductance of the setup, as well as to conveniently connect them in a compact geometry, similar to the existing 17 kJ plasma focus device of neutron yield ⩾10 9 neutrons/pulse [37]. Nevertheless, 48 RG213 coaxial cables (each 5 m long) were used in a 17 kJ plasma focus device. Further, the use of tubular geometry in the currently reported plasma focus device has made this more compact in size and lighter in weight compared to that of the squirrel-cage-geometry-based existing 17 kJ plasma focus device. The frequency of plasma focus operation in the newly developed device could be high (⩽5 min) compared to that of the existing 17 kJ plasma focus device (⩾15 min). As such, the newly developed plasma focus device has many advantages over the existing device in the form of enhanced transportability, enhanced flexibility, easy accessibility and improved repeatability.
All 24 RG213 coaxial cables from the capacitor bank were terminated coaxially over the plasma focus tube assembly at a pitch circle diameter of 10 cm, as shown in figure 1. The plasma focus tube consisted of an SS304 cathode in the form of a cylindrical tube and an SS304 anode in the form of a rod placed at its bottom center. The cathode also worked as the experimental chamber. The inner and outer diameters of the cathode were 3.4 cm and 5 cm, respectively. The overall length of the cathode was 16 cm with a total internal volume of around 130 cm 3 , excluding the anode. The diameter and the effective length of the anode were 1.2 cm and 10 cm, respectively. The anode at the tip was given a hollow shape to reduce its erosion due to melting and evaporation upon collision with the relativistic electrons produced post plasma focus disruption [38,39]. An alumina tube of 1.0 cm diameter was placed over the anode at the bottom as an insulator between the anode and the cathode. The insulator plays a crucial role in the plasma sheath formation during the initial gas breakdown phase. An insulator of appropriate dimension and with a smooth surface (free of surface defects, such as micro-cracks) results in a uniform plasma sheath in the initial breakdown phase, which subsequently results in strong plasma focus formation [40,41]. Out of the total length of 5 cm of alumina tube, the exposed length of around 1.5 cm was polished via a special technique using diamond paste to make it compatible for smooth and efficient plasma sheath formation [28]. The surface roughness of the insulator surface was reduced from a few micrometers to a few hundreds of nanometers after polishing. The insulator to the anode sealing was achieved through metal-insulator brazing at multiple locations [28]. A bellow-sealed Swagelok valve with quarter-inch end connectors was welded to the experimental plasma chamber for evacuation as well as filling of the deuterium gas. The overall size of the plasma focus head, including the plasma focus tube and associated assemblies, was around 16 cm diameter × 25 cm length with weight around 6.5 kg. All the important features of the plasma focus device are tabulated in table 1.
Multiple diagnostics were employed to measure electrical characteristics, such as the discharge current and its rise time, as well as neutron emission characteristics. The Rogowski coil was used to measure the derivative of the discharge current [42]. It was made in-house using the RG174 coaxial cable. The measured discharge current-derivative was integrated externally using a passive (RC) integrator to obtain the discharge current signal. An integrator with an appropriate time constant was chosen to avoid signal distortion and for high S/N. A factor of (0.2 ± 0.03) kA mV −1 was multiplied by the experimentally observed current to obtain the real current values. Measurements of time-resolved emission of neutrons were performed using a plastic scintillator detector (PSD) coupled to a photomultiplier tube. Two identical PSDs were used along the axial direction and in the radial direction to measure anisotropy in the time-resolved emission of neutrons. The PSD signals were also used to measure the energy of the neutrons in both directions using the time of flight technique. The D 2 gas filling pressure in the plasma focus tube was measured using an Edwards capsule dial gauge working in the range from 0.5 to 25 mbar. The time-resolved neutron signals through the PSDs and the dI/ dt signal were recorded using a digital storage phosphorous oscilloscope (1 GHz bandwidth and 5 GS s −1 ). To avoid pickup due to electromagnetic noise, all the signalrecording devices were kept inside a Faraday cage. The neutron yield was measured using a silver-foil-activation-based Geiger-Muller detector (SAD). The SAD detector was in situ calibrated using a radio-isotopic Pu-Be neutron source.
Results and discussion
Electrical parameters, such as static inductance, and the peak discharge current have been determined using a short-circuit method. For short-circuit current measurement, the plasma focus tube was filled with a high deuterium gas pressure (p) of 15 mbar and operated at a capacitor bank energy (E) of 2.7 kJ. An oscilloscope image of a typical short-circuit currentderivative waveform together with the current waveform and two PSD signals is shown in figure 3. The current-derivative waveform was observed to be of a simple underdamped L-C-R discharge, and its time-period was measured to be 14.3 µs. Using the short-circuit discharge current time-period (T 0 ), the inductance and the maximum peak discharge current were calculated using formulas described elsewhere [43]. The value of the inductance was calculated to be 215 nH. The maximum peak discharge current (I 0 ) deliverable to the plasma focus tube was calculated to be 132 kA at 2.7 kJ. During shortcircuit measurements, no radiation was produced, and hence no pulses were recorded in the PSDs.
The plasma focus tube was filled initially with low D 2 gas filling pressure (1-2 mbar) during the initial insulator conditioning shots [40,44]. After conditioning of the insulator surface during the initial few plasma focus discharges, a large dip was observed in the current-derivative waveform near the quarter time-period and, correspondingly, in the current waveform, as shown in figures 4(a) and (b). The dip is followed by a fast oscillatory structure, which could be due to reflections in the coaxial cables. The frequency of the oscillatory structure in the current-derivative waveform was observed to be (119 ± 17) ns, which was close to the calculated transit time (100 ns) for the 10 m long coaxial cable [36]. The slight variation in the frequencies could possibly be due to superposition of electromagnetic noise generated during fast pulsed electrical discharge of the capacitor bank [45]. An attempt was made to reduce the noise by using a triaxial cable to transport the Rogowski coil signal to the oscilloscope, but there was no visible effect on the oscillatory structures in the current-derivative signal. The noise is filtered out by externally integrating it using a passive integrator, as can be seen from the current signal. A clear dip in the current waveform can be seen in coincidence with the current-derivative waveform. Moreover, similar structures were also seen in the measured current-derivative and pinch voltage in the coaxialcable-based medium energy (17 kJ) plasma focus device, as mentioned earlier. The dip indicates the plasma focus formation. The shape of this dip is a signature of plasma focus characteristics and, in turn, neutron emission characteristics. Generally, a sharp and large dip indicates strong plasma focus and a high neutron yield, and vice versa. Two time-resolved pulses have been recorded in each PSD placed at 80 cm from the anode tip in the axial and the radial directions, as shown in figure 4(b). These pulses could be of hard x-rays and neutrons. The hard x-rays are bremsstrahlung radiations produced due to collisions of relativistic electrons with solid anode material post disruption of plasma focus because of rapid growth of instabilities (sausage, m = 0). The energies of the hard x-rays have been reported to be of a wide range, varying from a few keV to a few MeV [38,39]. The hard x-ray pulse was confirmed by placing one of the PSDs in a lead casing of 3 cm thickness in a few plasma focus shots. The x-ray pulse was observed to be either attenuated partially or fully cut-off, which could be possibly due to shot-to-shot variation in its energy spectrum. The hard x-ray pulse duration i.e. full width at half maximum (FWHM) was measured to be (16 ± 4) ns.
Opposite to electrons, deuterium ions move axially away from the anode and collide with the background deuterium gas atoms/molecules to produce neutrons via d(d, 3 He)n beamtarget fusion reactions [38,39,[46][47][48]. The neutrons produced here are monoenergetic. The neutron emission is confirmed by changing the PSD position in a few plasma focus shots. The peak-to-peak separation between the first and second pulse was found to change with the change in PSD position, which could be associated with the change in the flight time of the neutrons. The time-of-flight separation between the hard xrays and neutron pulse was used for the calculation of neutron energy, as described elsewhere [43]. The neutron energy along the axis was calculated to be (2.49 ± 0.23) MeV, whereas the same perpendicular to axis (radial) was calculated to be (2.03 ± 0.12) MeV. The neutron pulse duration (FWHM) was measured to be (20 ± 3) ns.
Optimum D 2 gas filling pressure at 2.7 kJ operation energy was determined by varying the D 2 gas filling pressure and simultaneously measuring the neutron yield at each filling pressure using the SAD detector placed in the radial direction at 30 cm distance from the plasma focus anode tip. The D 2 gas filling pressure was varied in the range of 1-6 mbar. At each filling pressure, six plasma focus shots were performed and the average neutron yield of all the plasma focus shots was calculated. The average neutron yield was observed to increase with the increase in filling pressure up to 4 mbar, and then it started decreasing with the further increase in filling pressure, as shown in figure 5.
A maximum average neutron yield of (3.1 ± 1.0) × 10 6 neutrons/pulse into 4π sr was observed in the radial direction at the optimum D 2 gas filling pressure of 4 mbar. A maximum neutron yield of (4.7 ± 0.3) × 10 6 neutrons/pulse was also observed at 4 mbar. This could well be the optimum pressure for the current geometrical and operational parameters of the plasma focus device. Considering the well-known anisotropic emission of neutrons in the plasma focus device, the neutron yield would further be greater by at least 30% in the axial direction than that observed in the radial direction [37,46]. The observed variation in neutron yield with filling pressure could possibly be due to the variation in the plasma/current sheath speed (v s ) in the axial acceleration phase, which varies as the inverse square root of the filling gas pressure (v s ∝ I 0 /ap 1/2 ; a: anode radius). Other possible reasons for neutron yield variation with D 2 gas filling pressure have been explained in detail elsewhere [43]. Nevertheless, more than 30% variation in neutron yield under the same operating conditions was observed, which could be due to poor shot-to-shot reproducibility of the plasma focus discharges. The possible reasons for this have been cited to be problems in the discharge initiation and the presence of contaminants in the discharge chamber among others [49,50].
Moreover, all the neutron-optimized Mather-type plasma focus, from small to large devices, has been reported to have practically the same values of the drive parameter (I 0 /ap 0 1/2 ; p 0 is the optimum filling gas pressure) and the energy density parameter (28E/a 3 ). The variation in the optimized neutron yield of different plasma focus devices could be due to the difference in the volume of the pinched plasma and its duration, which depend on the geometrical and operational parameters of the plasma focus device. Soto et al [51] listed the drive parameters for various neutron-optimized PF devices (operating at 0.1 J to 1064 kJ), and the values were found to be in the range from 68 to 95 kA cm −1 mbar −1/ 2 . Using this value, the optimized anode radius for the currently reported plasma focus device at optimum D 2 gas filling pressure of 4 mbar is calculated to be in the range from 0.69 to 0.97 cm. The anode radius (0.6 cm) chosen for the current plasma focus device is nearly the same as that of the value calculated above. The slight deviation in the chosen value of the anode radius from the optimized value could be due to differences in mass and current factors, which were not considered while comparing the drive parameter values of all the neutron-optimized devices, as reported by Lee et al [52,53]. The six-phase radiative LEE model code [53,54] was used to calculate the axial run-down time of the current sheath and the neutron yield over a wide range of deuterium gas filling pressures. The inputs used for the code were as follows: inductance (L 0 ) = 215 nH, capacitance (C 0 ) = 24 µF, cathode radius (b) = 1.7 cm, anode radius (a) = 0.6 cm, anode length (z 0 ) = 11.5 cm, resistance (r 0 ) = 3 mΩ, charging voltage (V 0 ) = 15 kV and three different deuterium filling pressures (p), i.e. 1, 4 and 6 mbar. The fitted model parameters were: f m = 0.03-0.035; f c = 0.3-0.35; f mr = 0.25; and f cr = 0.6. The anomalous resistance values used for fitting were 1.95-2 Ω with characteristic rise times and fall times of 90-150 ns and 40-80 ns, respectively. A typical simulated current waveform is plotted together with the measured current waveform at the above-mentioned filling pressures in figures 6(a)-(c). The simulated current waveform is found to be in good agreement with the measured current waveform in the axial phase as well as at the start of the radial compression phase, which are the main points of interest in the LEE model code. The model parameters at 4 mbar filling pressure have been used to determine the axial run-down time and the neutron yield for different D 2 gas filling pressures beyond 6 mbar and their variations are plotted in figure 7.
The computed neutron yield is also seen to vary with the D 2 gas filling pressure, similar to that which is experimentally observed. The maximum computed neutron yield is found to be 2.2 × 10 6 neutrons/shot at around 9 mbar of filling pressure, which is higher than the experimentally obtained optimum gas filling pressure. A possible reason for the vast difference between the experimentally obtained filling pressure and that obtained using the LEE model code could be the high current leakage and low snowplough efficiency due to the bad shape of the current sheath. Bruzzone et al [55] reported the measurements of the current leakage, i.e. the fraction of peak discharge current that actually flows through the current sheath structure as a function of the D 2 gas filling pressure, and found them to be filling-pressure dependent. They concluded that, among others, current leakage in the vicinity of the insulator and badly shaped current sheaths during the initial stages of the discharge can lead to irreproducible behavior and also can limit the useful operating pressure range of the device. Hence, to accurately determine the filling gas pressure range, the initial breakdown phase (gas breakdown, current sheath formation and detachment of the current sheath from the insulator surface) should be appropriately taken into account in the modeling of the plasma focus device [53,54]. Detailed investigations in very low energy plasma focus devices have shown that the current sheath remains attached for a period of time close to 20%-30% of the quarter period of the discharge, and the duration of the breakdown phase can be anywhere between 25% and 40% of the quarter period of the discharge [56]. This is due to the dependence of the breakdown phase duration on various parameters, such as the filling pressure, insulator material and its dimensions, and electrode dimensions [57]. The effect of the duration of the breakdown phase can be negligible on the duration of the axial acceleration phase and the radial compression phase in the medium and largesized plasma focus device when compared with its quarter discharge period, as may be the case with the reported plasma focus device. However, due to the compact size of the plasma focus tube (generally used with a low-energy capacitor bank) it might affect the current sheath characteristics (e.g. shape, thickness) and the current leakages, which subsequently affect the plasma focus device performance and the neutron yield.
Nevertheless, the majority of plasma focus devices, working from tens of joules to hundreds of kilojoules and with different geometrical and operational parameters, have experimentally obtained optimum filling pressure around 5 mbar, as seen with the reported device here [58]. Koh et al [59] reported a high-pressure operational regime of the plasma focus device. They used various combinations of filling gas pressures of deuterium, capacitor bank charging voltages, anode lengths and insulator sleeve lengths to optimize the neutron yield from the NX2 plasma focus device. They observed that at all the charging voltages for various combinations of anode and insulator sleeve lengths, there was an optimum filling pressure, which produced a maximum neutron yield. They argued from the beam-target fusion point of view (which is considered to be the dominant mechanism of neutron production in plasma focus devices) that below the optimum pressure, the number density of the deuterons accelerated in the axial direction was lower and thus resulted in a lower neutron yield. At pressures above the optimum pressure, the speed of the deuterons decreased during the post-pinch phase as it has to pass through dense ambient conditions, which will result in less efficient beam-target interaction, leading to a low neutron yield. This has also been observed experimentally using a medium-energy plasma focus device, where a higher number density of deuterium ions with high energies was measured at the optimum filling pressure for a charging voltage, which in turn resulted in a higher neutron yield compared to other filling pressures [60].
Moreover, the neutron yield was also estimated using the existing scaling laws [61]: Y n ∼ 1.7 × 10 −10 I 0 3.3 (I 0 in ampere) for neutron emission. The experimentally observed maximum neutron yield was found to be less than that estimated (1.3 × 10 7 neutrons/shot) at 132 kA peak current. The possible reason for the large difference between the experimentally observed and estimated neutron yield could be attributed to the use of a tubular cathode. The operation with the tubular cathode increases loading of the current sheath as well as the current leakage, which in turn reduces the neutron yield [62]. The relatively lower values of the mass and current factors obtained using the LEE model code also support this argument. Also, in operation with tubular cathodes, addition of impurities (due to back-reflected particles from the cathode wall) during the axial flow, may result in a substantial drop in temperature due to increased radiation loss, which is also consistent with the reduction in neutron output.
The neutron yield is estimated to increase further with an increase in capacitor charging voltage to its maximum design operating voltage, i.e. 20 kV (4.8 kJ, 176 kA), as per the above-mentioned scaling law for neutron emission. The neutron yield estimated to be produced at 20 kV of charging voltage is 3.47 × 10 7 neutrons/shot. Currently, D 2 gas needs to be refilled after every plasma focus shot due to the silicon o-ring gasket that is used for vacuum sealing in the plasma focus tube. The plasma focus tube is being sealed using brazing of insulator-metal joints at various locations, similar to the miniature sealed plasma focus tubes published elsewhere [28,30,32]. With this, once filled with D 2 gas, the plasma focus tube can be operated to produce neutrons for multiple shots over a long duration without needing to purge and refill the D 2 gas. Furthermore, the lengths of all the 24 coaxial cables are being increased beyond 10 m to make it feasible to use a neutron probe deeper in applications, such as borehole logging.
Summary and conclusion
A portable-head plasma focus device that is suitable for field applications, specifically for borehole logging applications, has been developed and characterized. The long coaxial cables and low weight of the plasma focus head provide the desired flexibility to move this to anywhere around a 10 m radius while keeping all the other components (e.g. capacitor bank, power supplies) stationary. Moreover, the capacitor bank was designed for operation at a maximum of 4.8 kJ, and strong plasma focus formation was observed, even at a lower operation energy of 2.7 kJ or below. Hence, there is further scope to increase the length of the coaxial cables and operate the capacitor bank at its maximum energy to obtain the same peak discharge current and hence to observe the neutron yield of the same order with enhanced flexibility. A maximum neutron yield of (4.7 ± 0.3) × 10 6 neutrons/pulse into 4π sr in the radial direction with a pulse duration of (20 ± 3) ns was observed at a D 2 filling gas pressure of 4 mbar and 2.7 kJ operation energy. The average neutron yield in the radial direction was observed to be maximum (3.1 ± 1.0) × 10 6 neutrons/pulse into 4π sr at 4 mbar filling pressure. The neutron energy along and perpendicular to the plasma focus device axis was calculated to be (2.49 ± 0.23) MeV and (2.03 ± 0.12) MeV, respectively. Higher neutron energy along the axis than that in the radial direction has been attributed to highly energetic/highfluence deuterium ions along the axis than that perpendicular to this in accordance with the beam-target fusion mechanism of neutron emission. This would have also contributed to the increase in neutron emission along the axis.
The plasma focus tube is further being modified into an allmetal sealed tube via brazing and welding at different joints that will make it feasible for multiple-shot operations over a long duration with single filling of the D 2 gas. This can also be filled with D-T mixture gas for enhanced neutron emission over a long duration without any change in device parameters. Moreover, all the components of the plasma focus device have been indigenously developed, and these were replaceable at a very low cost. The use of customized coaxial cables with low lumped inductance and resistance can help in reducing its overall weight further and improving the portability. Thus, its simple operation makes this a low-cost, low-maintenance alternative to complex and accelerator-based sealed portable neutron tubes, currently being used for the type of applications mentioned earlier.
Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors. | 8,187.2 | 2023-04-24T00:00:00.000 | [
"Engineering",
"Physics"
] |
Nerve and Arterial Supply Pattern of the Popliteus Muscle and Clinical Implications
Introduction The aim of this study was to investigate the nerve and artery supply and the tibial attachment of the popliteus muscle using anatomical methods. Methods Forty-four nonembalmed and embalmed extremities were dissected for this study. To measure the attachment area of the popliteus, the most prominent points of the medial epicondyle of the femur and the medial malleolus of the tibia were identified before dissection. A line connecting these two prominent points was used as the reference line, with the most prominent point of the medial epicondyle of the femur as the starting point. This study also investigated the area where the popliteus attaches to the bone and the points where nerves and arteries enter the popliteus muscle when it is divided into three equal parts in the coronal plane. Results The mean length of the reference line was 34.6 ± 2.1 cm. The origin of the popliteus was found to be at a distance of 16.6% to 35.2% on the tibial bone from the proximal region. The popliteus was innervated by only the tibial nerve in 90% of the cases and by the tibial and the sciatic nerves in the remaining 10% of the cases. The inferior medial genicular artery and the posterior tibial artery supplied blood to the popliteus in 90% and 65% of the cases, respectively. When the popliteus muscle was divided into three equal parts in the coronal plane, the nerve and the artery were found to enter the muscle belly in zones II and III and zones I and II in 92% and 98% of the specimens, respectively. Discussion. The anatomical investigation of the popliteus in this study will help identify patients with clinically relevant syndromes.
Introduction
The popliteus muscle (PM) is a small muscle that acts as a major posterolateral stabilizer of the knee joint, rotating the tibia medially under the femur under non-weightbearing conditions [1,2]. As the PM acts as an important factor in the movement and injury of the knee joint, anatomical studies have been conducted with a focus on the femoral attachment of the muscle [1,[3][4][5][6][7][8]. A study using magnetic resonance imaging analysis showed that the PM sulcus depth affected the rotational alignment with tendinitis [9]. The PM sulcus is also considered to be on the femoral side of the PM muscle. Although a morphological classification of the PM was recently performed [10], no studies on nerve innervations and blood supply were found.
Anatomy textbooks state that the tibial nerve innervates the PM [11,12]; there is also study showing that the tibial nerve innervates [2]. However, it is difficult to obtain information about the nerve supply and distribution from the tibial nerve to the PM in the popliteal region. Moreover, this cadaveric study was conducted as there is little information about the arterial supply.
Muscular spasticity is common in upper motor neuron syndrome. Injection treatment is applied as PM spasticity has been confirmed in many patients with in-toeing [2]. One of the treatment methods, botulinum toxin, is known to have a long-lasting effect when injected into a site where the neuromuscular junction is dense. It is also effective when injected near the motor entry point where the nerve enters the muscle belly [13]. Thus, a suitable injection site is thought to be the tibial region because the muscle belly is the upper portion on the tibial area on the posterior aspect. In this study, we speculated about the injection site of the PM based on the above reasoning. An alternative method is the accurate palpation of the PM, which is necessary for posture correction therapy. However, there is insufficient data on how to accurately palpate the PM.
Thus, the aim of this study was to investigate the nerve and artery supply of the tibial attachment of the PM using anatomical methods.
Materials and Methods
Twenty-three adult cadavers (13 males and 10 females, age range 45-95 years) donated to the medical university were dissected for this study. Two limbs showing evidence of prior surgery or injury around the popliteal region were excluded.
For the dissection procedure, the skin was removed to expose the fatty layer and superficial fascia, and then, the heads of the gastrocnemius were carefully cut to identify the PM and neurovascular structures surrounding the PM. Further careful dissection was performed to identify the nerve branches around the PM, and the artery entering the PM was traced. After dissection of the neurovascular structures around the PM, this study investigated the tibial attachment area and the entry points of the nerve and the artery when the PM muscle was divided into three equal parts in the coronal plane (Figure 1(a)). To measure the point of attachment of the PM in this study, the medial border of the tibia and the prominent point of the lateral epicondyle of the femur were divided into three parts at equal intervals (Figure 1(a)).
To measure certain variables, the most prominent points of the medial epicondyle of the femur (MEF) and the medial malleolus of the tibia MMT were identified before dissection. A line connecting the MEF and the MMT was used as the reference line, with the MEF as the starting point ( Figure 1(b)). The measurement variables were as follows: (1) The reference line between the MEF and MMT
BioMed Research International
A single observer obtained all measurements using a measuring tape and digital calipers (resolution 0.01 mm, CD-20PSX, Mitutoyo, Japan). The data were analyzed using SPSS version 23.0 (IBM SPSS Inc., Chicago, IL, USA). The present study was conducted in accordance with the principles of the Declaration of Helsinki. This study was approved by the Institutional Review Board of Korea National Sport University (IRB No. 20210722-115).
Results
The mean length of the reference line was 34:6 ± 2:1 cm. The attachment point of the PM was located at a distance of 16.6% to 35.2% along the tibial bone from the proximal region (Table 1). No significant differences were found in the reference line or between the right and left legs between males and females (p ≥ 0:05).
In 90% of the cases, the PM was innervated by the tibial nerve only, whereas the PM was innervated by the tibial nerve and the sciatic nerve in the remaining 10% of the cases (Figures 2 and 3). When the PM was divided into three equal parts in the coronal plane for the nerve division, zones II and III were distributed at 66.5% and 25.5%, respectively. The artery was distributed at 60.2%, 37.8%, and 2.0% in zones I, II, and III, respectively (Figure 1(a)).
Upon examination of the arteries that supplied blood to the PM, one to three arteries were found to supply blood. In this investigation, when the sum of the arterial frequencies was calculated, the inferior medial genicular artery was involved in supplying blood to the PM in 90.0% of the cases (Figure 4). In 65% of the cases, the posterior tibial artery was involved in supplying blood to the PM ( Figure 5). The blood supply to the PM was by the anterior tibial artery in 35.0% of the cases and by the popliteal artery in 5.0% of the cases (Figures 6 and 7, Table 2).
Discussion
The PM is a major stabilizer of the posterolateral knee region, and overactivity of the PM might lead to friction between the PM tendon, lateral femoral condyle, and the lateral meniscus. PM shortness is a common cause of lateral knee pain [14,15]. Immobilization could tighten the PM, resulting in strain following a twisting strike during weight-bearing. Identifying a PM lesion is challenging because the muscle is deeply situated and its pain is difficult to differentiate from that of the adjacent structures, such as the gastrocnemius, meniscus, and posterior cruciate ligament [16]. One study reported that PM syndrome was caused by an isolated PM due to compression of the neurovascular bundle. In this case, the patient felt calf pain and numbness in the posterolateral aspect of the calf and sole [17]. Because the PM and popliteal artery are adjacent to each other, the condition of this muscle affects the blood circulation of the popliteal artery. To date, few anatomical studies have been conducted on the blood supply of the PM. In this study, the blood supply of the PM was often found to be provided by the inferior medial genicular artery ( Figure 4). Blood supply is important for muscle recovery. Thus, adequate blood supply is necessary for the recovery of the PM as the legs are mostly in standing and working positions. In addition, anatomical studies on the arteries supplying blood to the PM will help increase the success rate The number and location of the motor entry points of the PM are also clinically interesting for effective muscle spasticity treatment. Earlier studies [2] reported an average of 2.2 motor entry points (range, 1-3) with the tibial branch as the origin of the innervating nerve for the PM and the nerve branch entering the PM on its superficial surface~1 cm distal to its superior border. In this study, the number of motor entry points ranged from 1 to 4. The most common cases had two motor entry points (47.6%), followed by one (33.3%) and three motor entry points (14.3%). Four motor entry points were found in 4.8% of the cases. In all cases in this study, the innervating nerve for the PM did not originate from the tibial nerve. In 10% of the cases, the PM was innervated by the tibial and the sciatic nerves (Figure 3), (Figure 2). In this study, as 66.5% of the motor entry points were distributed in zone II, zone II was considered to be the most effective injection point ( Figure 1). Next, we surveyed the results of previous studies examining the shape of the PM and the surrounding structures to which it is connected [1,16,17]. The PM was shown to have a triangular shape [2] and is attached to surrounding ligaments and meniscus [1]. A recent study investigated the shape of PM tendon and the surrounding structures it is connected to during its insertion to bone [10]. Another study examined the shape related to the lateral collateral ligament at the point where the PM is inserted [18]. In this study, we focused on how the origin site attaches to the bone and the nerve and the artery supplying the PM rather than the surrounding structures.
One method uses manual therapy for pain caused by PM shortness. A point situated between 16.6% and 35.2% of the distance from the MEF on the tibial bone was found to be suitable for palpation of the PM ( Table 1). Knowledge of the location of the origin of attachment of the PM to the tibia will be helpful in the treatment of muscle relaxation by applying appropriate pressure through manual therapy. Previous research [2] showed the shape of the PM but from a posterior view. There are structures superficial to the PM, such as the gastrocnemius, nerves, and vessels. Therefore, it is recommended to approach the PM by touching the bone at the medial border of the tibia. The results of this study suggest that setting the area between 20 and 30% along the medial border of the tibia would be optimal for manual therapy for tight PM (Table 1).
Conclusions
The present study showed that the tibial attachment area, nerve innervations, and blood supply of the PM could be considered constant anatomical characteristics. We propose that manual treatment targeting the PM be located 20-30% from the MEF along the tibial bone. In 90% of the specimens, the PM was innervated by the tibial nerve and received blood from the inferior medial genicular artery. When the PM was divided into three equal parts in the coronal plane, the nerve was found to enter the muscle belly in zones II and III in 92.0% of specimens, whereas the artery entered the muscle belly in zones I and II in 98.0% of specimens ( Figure 1). This finding will help understand the anatomy of the PM and its environment and treatment of syndromes involving the PM.
Data Availability
The underlying data supporting the results of our study can be found in the manuscript.
Anterior tibial a.
Sup
Post ⁎ Figure 6: The blood supply of the popliteus (asterisk) was by the anterior tibial arteries (arrows) in 35.0% of the cases. Artery % Anterior tibial a. and inferior medial genicular a. 25 Inferior medial genicular a. and posterior tibial a. 20 Inferior medial genicular a. 25 Popliteal a. and inferior medial genicular a. and posterior tibial a. 5 Posterior tibial a. and anterior tibial a. 5 Anterior tibial a. 5 Posterior tibial a. 15 5 BioMed Research International | 2,975 | 2022-01-10T00:00:00.000 | [
"Medicine",
"Biology"
] |
Plasticity in zwitterionic drugs: the bending properties of Pregabalin and Gabapentin and their hydrates
The hydrate forms of the zwitterionic drugs Pregabalin and Gabapentin show plastic bending in a single crystal, whereas the anhydrous equivalents are brittle. A close structural analysis attempts to justify such behaviour.
Introduction
In recent times, the classic idea of crystals as a brittle objects has been progressively abandoned (Dunitz, 1984). Observation of phenomena such as shearing (Reddy et al., 2005a) or bending (Reddy et al., 2005b) as well as martensitic (Zamir et al., 1994;Steiner et al., 1993;Ding et al., 1991;Etter & Siedle, 1983), super-elastic (Takamizawa & Miyamoto, 2014) and super-plastic (Takamizawa et al., 2018) transformations clearly show that organic crystals share many similarities with metallic and covalent inorganic analogues. Mechanical properties of molecular crystals are investigated and discussed with increasing frequency and those studies have attracted considerable attention (Reddy et al., 2010;Naumov et al., 2015). Aside from the understandable academic curiosity, mechanical properties are important for the manufacturing of crystalline solids into products. For example, in the pharmaceutical industry, good plasticity guarantees that microcrystalline drug substances can be readily manufactured into tablets without the addition of excipients (Thoorens et al., 2015;Chang & Sun, 2017).
A characteristic of molecular crystals is that they are held together by supramolecular interactions. It follows that crystal synthesis occurs in relatively mild conditions, whilst a supramolecular approach enables a certain degree of structure design (Desiraju, 1989;Etter, 1990;Moulton & Zaworotko, 2001). In this view, understanding how molecular features determine a crystal structure and, in turn, material properties would enable crystal engineering and properties design.
The rapid scientific advances of the past decades allow the confident prediction of how a given set of molecules will pack in a crystal structure (Reilly et al., 2016). On the other hand, a general theory is still missing to infer bulk chemical and mechanical properties from structures. Therefore, material development proceeds through the application of a series of practical rules, which often apply to specific types of materials (Lusi, 2018;Corpinot & Bučar, 2019).
The first attempts to rationalize the relationship between structure and mechanical properties in molecular crystals involved small aromatic molecules (Reddy et al., 2006b,a). In such materials, aromatic stacking and halogen or hydrogen interactions coexist in the same structure and extend along different crystallographic axes. Manipulation of face-indexed single crystals showed that bending occurred only perpendicular to the planes of the weaker interactions, whereas the stronger supramolecular bonds helped to preserve structural integrity in the other directions (Saha et al., 2018). Then, chemical anisotropy appeared as a requirement for plasticity and such features were thought to guarantee the realization of bendable single-and multi-component crystals (Krishna et al., 2016;Rao Khandavilli et al., 2017;Saha & Desiraju, 2017;Alimi et al., 2018;Nath et al., 2018). However, the discovery of plastic bending in the (quasi)-isotropic structures of dimethyl sulfone proves that alternative mechanisms might exist (Thomas et al., 2017).
Due to their relevance in manufacturing and processing, many studies of mechanical properties involve APIs (active pharmaceutical ingredients), which suggest that hydrate forms might have higher plasticity than their corresponding anhydrates (Sun & Grant, 2004;Liu et al., 2018;Fucke et al., 2012;Chang & Sun, 2017). In these cases, the mechanical properties were only observed at the microscopic level on polycrystalline powders, making the correlation between structure and properties elusive. In p-hydroxybenzoic acid (Sun & Grant, 2004) and uric acid (Liu et al., 2018), despite creating a rigid 3D hydrogen-bonded network, the inclusion of water enables the separation of zigzag chains that are interdigitated in the anhydrous forms (see Figs. S10 and S11 of the supporting information). Hence, increased plasticity was explained by the removal of a mechanical (or steric) obstacle to molecular movement, which was deemed necessary for plastic bending. Anhydrous theophylline shows a different story: hydrogen bonds, stacking and weak C OÁ Á ÁH bonds support the structure along the orthogonal crystallographic directions, and there is no mechanical interlock to prevent molecular movement (Fucke et al., 2012;Chang & Sun, 2017). In that view, crystals of theophylline should be highly plastic. Instead, plasticity is lower than in the hydrate form, which is characterized by 2D hydrogen-bonded networks that pack in an interdigitated zigzag fashion (see Fig. S12 of the supporting information). In the theophylline system, increased plasticity was attributed to the 'lubricant' action of water molecules that allows easier slippage of the 2D sheets. Ultimately, also in the case of hydrate forms, multiple mechanisms explain plastic bending and the observation of such a phenomenon on single crystals could give new insights into the role of water. This work reports on the mechanical properties in the anhydrous and hydrate forms of Pregabalin and Gabapentin (Fig. 1). Despite the similar crystal packing, the hydrate forms show superior plasticity, which results in macroscopic bending of single crystals whereas the anhydrous forms are brittle.
Experimental
Pregabalin (SPG) and Gabapentin (GP) were purchased from Flourochem. Methanol was purchased from Sigma-Aldrich and Milli-Q water was used for the experiments.
Crystallization of SPG: SPG crystals were obtained from commercially available SPG dissolved in methanol to saturation and left at room temperature for 2 days.
Crystallization of SPGH I: SPG was dissolved in pure water and crystallized at 280 K for 3-5 days to obtain good-quality crystals.
Crystallization of GP and GPH: GP and its hydrate crystals are reproduced by following the same procedure mentioned in the literature (Wang et al., 2017;Reece & Levendis, 2008).
Optical microscopy: single crystals of SPGH I and GPH were selected and bent with tweezers and a needle, the images were captured using an Olympus IX53 microscope under 4Â magnification.
IR spectroscopy: IR spectra for SPG and SPGH I were collected on a PerkinElmer Spectrum 100 F T-IR Spectrometer equipped with a PerkinElmer Universal ATR Sampling Accessory.
Raman spectroscopy: Raman spectra for SPG and SPGH I were collected on a Horiba Jobin Yvon LabRam Aramis spectrometer with a 532 nm laser source. The spectrometer was coupled with an Olympus BX40 confocal microscope with a CCD camera cooled by a thermoelectric Peltier device. Raman maps were processed using the LabSPEC 5 software package.
Powder X-ray diffraction: Powder X-ray diffraction data were collected on an Empyrean diffractometer (PANalytical, Philips) using Cu K 1,2 radiation ( = 0.1541 nm) at room temperature operated at 40 kV and 40 mA. The samples were scanned over the range 4-40 2 using a step size of 0.02 2 and a scan speed of 0.02 2 s À1 .
Differential scanning calorimetry: calorimetric measurements of SPG and SPGH I were performed on a DSC 214 Polyma, NETZSCH instrument. Typically, 3-5 mg of sample was accurately weighed into a hermetically sealed aluminium pan and heated to 250 C at a 10 C min À1 heating rate under a nitrogen gas flow of 40 ml min À1 .
Thermogravimetric instrument at a heating rate of 10 C min À1 under a nitrogen stream of 20 ml min À1 . X-ray crystallography: single-crystal data for SPGH I were collected at ambient temperature using a three-circle Bruker D8 Quest diffractometer with a sealed tube Mo anode, K radiation = 0.71073 Å and a Photon 100 detector. Singlecrystal data for SPGH II were collected at 150 K under a nitrogen-flow (Oxford Cryosystem) using a three-circle Bruker D8 Quest with microfocus Cu anode, K radiation = 1.5418 Å and a Photon 100 detector.
The data were integrated and corrected for absorption with the Bruker Apex Suite. The structure solution was obtained by direct methods and refined against all F 2 with the SHELX software interfaced though X-SEED (Barbour, 2001). Nonhydrogen atoms were refined anisotropically and hydrogen atoms were placed in calculated positions, refined using idealized geometries (riding model) and assigned fixed isotropic displacement parameters.
Results and discussion
Amino acids are an important class of biologically active molecules that exist as zwitterionic tautomers under neutral conditions. Among them, (S)-3-isobutyl--aminobutyric acid, or Pregabalin (SPG), is an anticonvulsant blockbuster drug. In the anhydrous P2 1 2 1 2 1 crystal, which has the refcode CIDDEZ (Venu et al., 2007) in the CSD (Groom et al., 2016), the zwitterion dipoles pack along the b axis generating a double layer that is coplanar to the (110) plane. The structure is supported by a 2D network of charge-assisted hydrogen bonds between the ammonium and carboxylate groups [ Fig. 2(a)]. As multiple layers stack on top of each other, the isobutyl groups interdigitate along the [001] direction. The crystals are brittle, as expected for mechanically interlocked structures.
Recrystallization of SPG in water at 280 K results in the monohydrate form SPGH I. Single-crystal analysis reveals a monoclinic C2 polar structure ( Table 1). The zwitterions are arranged along the [010] axis and are intercalated by water molecules so that the double molecular layers separate into parallel planes. At the same time, the molecules in each layer come closer together preventing interdigitation [ Fig. 2(b)].
SPGH I is unstable at room temperature, reverting to the anhydrous SPG phase in air (Fig. S6). As expected from the different crystal packing, the dehydration is associated with a loss of macroscopic crystallinity. SPGH I undergoes a polymorphic transition upon cooling below 150 K. The phase transition is reversible (enantiotropic) and occurs in a singlecrystal-to-single-crystal fashion, as demonstrated by variabletemperature single-crystal diffraction experiments. The packing of the low-temperature SPGH II phase is virtually identical to the high-temperature phase. The differences are limited to a reduced symmetry (Z 0 = 16) and a different arrangement of the hydrogen-bonded bridges with water [ Fig. 2(c)].
In molecular materials, the single-crystal-to-single-crystal reduction of symmetry on cooling is known. Often, such transformations assume the aspect of an order-disorder Figure 2 Schematic representation of the crystal packing of (a) SPG, (b) SPGH form I and (c) SPGH form II. Hydrogen bonding interactions are in green, selected hydrogen atoms have been omitted for clarity.
transition, whereby a certain thermal energy is required for a molecule to rotate or vibrate between symmetry-related crystallographic positions (Lusi & Barbour, 2013;Braga et al., 2018). Here, the change occurs between two fully ordered structures instead. In that view, the preserved crystallinity is evidence of the high plasticity of these phases, and suggests that the supramolecular bonds with water can be easily broken and reformed without affecting the rest of the structure. Indeed, crystals of SPGH I exhibit plastic bending on the application of a moment perpendicular to the c axis (Fig. 3). Hence, the bending mechanism involves the sliding of successive layers along the crystallographic b direction (Fig. 2). In order for this to happens, either the hydrogen bond between water and zwitterions or the dispersion forces between the non-polar-layer intermolecular bonds need to quickly break and reform; crystallographic studies cannot determine which are responsible for the bending.
GP is a molecular and pharmaceutical analogue of SPG. In GP, cyclopentane substitutes the isobutyl group but the supramolecular feature of the two molecules are essentially equivalent. Due to extensive polymorph screening, multiple anhydrous and hydrate forms of GP are reported (Braga et al., 2008;Reece & Levendis, 2008;Wang et al., 2017).
Like SPG, the structure of GP form (CCDC refcode QIMKIG) is dominated by 2D networks of charge-assisted hydrogen bonds. In the latter, the bulkier cyclopentane group prevents interdigitation of successive layers (Fig. 4). GP (CCDC refcode QIMKIG02) forms 1D chains (Reece & Levendis, 2008;Wang et al., 2017;Ibers, 2001;Vasudev et al., 2009), whereas the packing in the anhydrous form (CCDC refcode QIMKIG03) resembles those of the hydrate forms, GPH I and II (CCDC refcodes QIMKOM and QIMKOM02), and SPGH I and II, the zwitterionic groups being separated into two planes. Remarkably, despite structural similarities, only the hydrates undergo plastic bending, whereas all the anhydrous forms are brittle. This observation suggests that the intercalated water molecules, rather than the weak dispersion forces, are responsible for the observed plastic bending.
Conclusions
High plasticity is a desirable property that guarantees processability in crystalline drug materials. To date, different sets of factors have been identified as responsible for plastic crystals, but a universal supramolecular strategy to improve such a property is not recognized yet. For example, it was suggested that bending requires the anisotropic hierarchical distribution of strong and weak supramolecular interactions along perpendicular directions. On the other hand, interdigitation and crosslinked hydrogen bonds (mechanical and chemical interlocks, respectively) have been seen as detrimental for macroscopic plastic bending. At the same time, an increasing number of studies report that, at the microscopic level, hydrated forms exhibit higher plasticity than the anhydrous equivalents. In such phases, increased plasticity does not seem to correlate to a particular structural feature. This is also true for the two zwitterionic drugs SPG and GP. Here, plasticity occurs also at a macroscopic level, on large single Single crystals of SPGH I and GPH II before and after the mechanical deformation. The larger crystal faces are indexed. crystals, allowing a rationalization for such a phenomenon. Limited to the investigated systems, the alternation of 2D hydrogen-bonded networks and weak dispersive forces does not guarantee plastic deformation in the anhydrous crystals. In contrast, plasticity occurs in the hydrate forms even when mechanical and chemical interlocks are present. Therefore, in these instances the presence of water appears crucial. Many studies highlight the structural diversity possible for water molecules (Mascal et al., 2006;Infantes & Motherwell, 2002;Bajpai et al., 2016). We speculate that such promiscuity, together with the high mobility of these molecules, enables the quick rearrangement of the supramolecular interactions that are broken by mechanical stress.
Finally we note that SPG and GP are two examples of a wide class of amino acids with biological activity. As sustained by strong and directional charge-assisted hydrogen bonds, the molecular packing of SPG and GP is common to other zwitterionic -aminopropionic and -aminobutyric acids. Therefore, it would be of little surprise if those systems showed the same properties, and the reported observations could be valid for a wide class of drug substances.
Funding information
This work was conducted within the Synthesis and Solid State Pharmaceutical Centre (SSPC) and the Bernal Institute at the University of Limerick. The following funding is acknowledged: Science Foundation Ireland (grant No. 12/RC/2275; grant No. 15/SIRG/3577). | 3,276 | 2019-05-22T00:00:00.000 | [
"Materials Science"
] |
Working Stress Measurement of Prestressed Rebars Using the Magnetic Resonance Method
: Prestressed rebars are usually used to apply vertical prestress to concrete to prevent web cracking. The reduction of working stress will affect the durability of the structure. However, the existing working stress detection methods for prestressed rebars still need to be improved. To monitor the working stress of rebars, a magnetic resonance sensor was introduced to carry out experimental research. The correlation between rebar stress and the sensor’s induced voltage was theoretically analyzed using the magnetoelastic effect and magnetic resonance theory. A working stress monitoring method for prestressed rebars based on magnetic resonance was proposed. Working stress monitoring experiments were carried out for 16 mm, 18 mm, and 20 mm diameter rebars. The results showed that the induced voltage peak-to-peak value and the rebar prestress were nonlinearly correlated under different working conditions. Correlations between the characteristic indicators and the rebar working stress were obtained using nonlinear and linear fit. The cubic polynomial segmented fit outperformed the gradient overall linear fit, with the goodness of fit R 2 greater than 0.96. The average relative error values of working stress monitoring were less than 5% under different working conditions. This provides a new method for working stress measurement of vertical prestressed rebars.
Introduction
The prestressed concrete bridge is widely used in bridge construction because of its advantages of sizeable structural stiffness, smooth driving, and low maintenance cost [1]. Vertical prestressed rebar is used to provide vertical compressive stress to the reinforcement by post-tensioned method. The effect of vertical prestressed rebar can make the shear load capacity of the structure significantly increase by 95% [2]. However, the elongation of vertical prestressed rebar is slight during vertical prestressing tensioning in construction. Therefore, the prestress loss caused by rebar retraction is significant [3]. Furthermore, the loss of vertical prestress has an important influence on the principal tensile stress of the box girder web [4]. Once the vertical prestress is lost and the web cracks, the bridge structure's safety and durability will be affected [5][6][7]. Therefore, the vertical prestressed rebar working stress must be accurately monitored to ensure the structure's safety.
To avoid prestress detection affecting the structure's durability, nondestructive testing methods are usually used [8]. Commonly used methods are the strain method, electromagnetic resonance method, the stiffness method, the ultrasonic guided wave method, the eddy current method, and the magnetoelastic method. The strain method is based on the stress-strain relationship. The test is carried out by pasting electronic strain gauges or embedded sensors, and then converting the stress. Sawicki [9] successfully identified and improved the sensitivity of corrosion damage detection. The magnetoelastic sensor is also composed of the coil as the main component. To improve the sensor's sensitivity, Zhang [28] introduced the magnetic resonance theory into the magnetoelastic effect method. He proposed the resonance enhanced magnetoelastic method (REME) and verified the feasibility of this method for monitoring the stress of steel strands. However, as a hotrolled low-carbon steel structure, the rebar's section form, initial magnetization state, and stress-strain relationship differ from those of the steel strand, resulting in different stress identification. In addition, the advantage of small size of the magnetic resonance sensor meets the pre-embedded requirement of vertical prestressed rebar and can be applied in post-tensioned pipeline [29]. Therefore, monitoring the working stress of the rebar by REME needs further study.
Based on the existing research, this paper combined the magnetoelastic effect, electromagnetic induction law, and magnetic resonance effect. A working stress monitoring method for vertical prestressed rebar was proposed using the magnetic resonance sensor. Firstly, the relationship between sensor induced voltage and rebar stress was analyzed. Then, working stress monitoring experiments under different working conditions were carried out on rebars with different diameters. According to the experiment results, the nonlinear relationship between the induced voltage peak-to-peak values and the prestress was analyzed. Based on the experiment data, the correlation between the characteristic indicator and the rebar working stress was obtained by nonlinear fit and linear fit. According to the relationship, the working stress was accurately evaluated, and the feasibility of the proposed method was verified.
Theory
According to the Joule effect and the magnetization theory of ferromagnetic material, there is a functional relationship between the stress of rebar and the change in magnetic permeability [30,31]. In Equation (1), µ is the permeability of rebar, µ 0 is the vacuum permeability, λ s is the axial deformation constant, M s is the saturation magnetization, K u is the uniaxial magnetic anisotropy constant, H R is the excitation magnetic field, and θ 0 is the angle between the magnetic field and the easy magnetization axis [32].
A magnetic resonance sensor [28] was used to monitor the working stress of the rebar. The sensor's two coils are the excitation and induction coils. The coil is wound on the PVC skeleton, as shown in Figure 1. The equivalent circuit diagram [28] of the magnetic resonance sensor is shown in Figure 1. L T and L R are the inductance of the excitation coil and induction coil, respectively. C T and C R are the excitation and induction coil's compensation capacitors, respectively. u CT and u CR are the voltage of the compensation capacitor of the excitation coil and the induction coil. R T and R R are the internal resistance of the excitation coil and the induction coil, respectively. The voltage source is AC power, and the input voltage is u in . The millivoltmeter is regarded as a load connected in series with an induction coil, and its equivalent resistance is R L. According to Kirchhoff's voltage law [33], the self-impedance of the excitation coil and the induction coil is ZT and ZR, respectively, as shown in Equations (2) and (3). The loop current IR of the induction coil is shown in Equation (4), where j is the imaginary part of the complex number, Uin is the effective value of uin, ω is the angular frequency of uin, and M is the mutual inductance between the excitation coil and the induction coil. According to the coupled mode equation of LC coupled circuit [34], the relationship between coupling coefficient κ and mutual inductance M can be expressed as Equation (5); ω0 is According to Kirchhoff's voltage law [33], the self-impedance of the excitation coil and the induction coil is Z T and Z R , respectively, as shown in Equations (2) and (3). The loop current I R of the induction coil is shown in Equation (4), where j is the imaginary part of the complex number, U in is the effective value of u in , ω is the angular frequency of u in , and M is the mutual inductance between the excitation coil and the induction coil. According to the coupled mode equation of LC coupled circuit [34], the relationship between coupling coefficient κ and mutual inductance M can be expressed as Equation (5); ω 0 is the resonant frequency. .
A rebar with a cross-sectional area of A iron is placed in a magnetic resonance sensor. A air is the cross-sectional area of the nonmagnetic material between the coil and the rebar. The voltage source provides alternating current for the excitation coil. Under the action of alternating current, the excitation coil generates an excitation magnetic field [35,36]. The excitation coil and the induction coil are resonantly coupled. An excitation magnetic field of the magnetized rebar is generated in the induction coil. The magnetic field is expressed as H R , which has a functional relationship with the coupling coefficient κ, as shown in Equation (6). N R is the number of turns of the induction coil. l R is the effective magnetic circuit length of the induction coil. According to electromagnetic induction law, the induced voltage of the induction coil can be obtained by the magnetic flux in the area around the coil [37], as shown in Equation (7), where Φ is the magnetic flux around the area of the induction coil, and t is the time.
Combined with the electric power calculation formula, the excitation coil's input power P in and the millivoltmeter's output power P o as the load can be calculated, respectively. The results are shown in Equations (8) and (9). The transmission efficiency can be obtained as shown in Equation (10).
When the induction coil resonates, X R = 0, the transmission efficiency reaches the maximum, and the measured induced voltage is the highest. In the working stress monitoring experiment, the rebar is used as the core of the induction coil. The change of permeability of rebar caused by working stress also causes the induction coil's inductance change. After the inductance changes, the resonant frequency of the induction coil changes, as shown in Equation (11). When the resonant frequency of the induction coil deviates from the initial resonant frequency, the coil coupling coefficient κ and the sensor induced voltage are significantly reduced, thereby improving the sensitivity of the rebar working stress monitoring.
The above relationship is solved simultaneously to explore the internal relationship among stress, magnetism, and electricity. The change in stress will lead to the change of permeability of the rebar. The relationship between induced voltage and permeability can be simplified from Equations (7)- (12), where f(u CR ) is the function of induced voltage u CR representing permeability µ. The induced voltage u CR is related to the coupling coefficient κ. For a specific rebar and sensor, the relationship between the sensor's induced voltage and the rebar's working stress can be expressed as Equation (13); g(u CR ) is the function of the induced voltage u CR representing the working stress σ.
Through the above derivation, it can be found that the rebar working stress is related to the sensor's induced voltage. Therefore, the induced voltage of the magnetic resonance sensor can be used to evaluate the working stress of the rebar. To verify the feasibility of the magnetic resonance monitoring method (REME) for rebar working stress monitoring, rebar working stress monitoring experiments were carried out.
Experiment Design
Vertical prestressed tendons generally use rebar. To explore the relationship between rebar stress and sensor induced voltage, this paper uses the magnetic resonance sensor to carry out working stress monitoring experiments on rebar under different working conditions.
Experiment Equipment
A rebar working stress monitoring system was built to carry out the experiment, as shown in Figure 2. The experiment system comprised a universal testing machine, magnetic resonance sensor, signal generator, power amplifier, millivoltmeter, and computer. The maximum tensioning load of the universal testing machine is 100 tons. The universal testing machine was used to tension the rebar to different stress levels. In this experiment, a magnetic resonance sensor was used for working stress monitoring. The signal type for data analysis was induced voltage. The induced voltage peak-to-peak value was chosen as the electrical characteristic value characterizing the variation of the magnetic properties of the rebar with stress. The signal generator was connected to the excitation coil. The millivoltmeter was considered as a resistor connected to the induction coil. The signal generator generated an alternating excitation signal as a sine wave. The power amplifier was used to amplify the excitation signal power. The effective value of the induced voltage was measured by the millivoltmeter during the experiment. The value was transmitted and saved in the computer for further processing.
as the electrical characteristic value characterizing the variation of the magnetic properties of the rebar with stress. The signal generator was connected to the excitation coil. The millivoltmeter was considered as a resistor connected to the induction coil. The signal generator generated an alternating excitation signal as a sine wave. The power amplifier was used to amplify the excitation signal power. The effective value of the induced voltage was measured by the millivoltmeter during the experiment. The value was transmitted and saved in the computer for further processing.
Sensor and Specimen Preparation
A PVC tube with an outer diameter of 40 mm was used as the magnetic resonance sensor skeleton. The excitation and induction coil were wound with 0.25 mm-diameter enameled wire. The total number of turns of the excitation coil was 40 turns, and 1 layer was wound. The total number of turns of the induction coil was 1400 turns, and 10 layers were wound. The yield strength of HRB400 rebar is 400 MPa. HRB400 rebar is widely used in engineering projects. Rebar is a common ferromagnetic material with magnetoelastic effect [38,39]. The length of the sensor was 80 mm. The specimens were made of rebars with the yield strength of 400 MPa. To verify the applicability of the working stress monitoring method to different diameters of rebars, the specimens' diameters were made of 16 mm, 18 mm, and 20 mm. In actual engineering, the working stress of the rebar is lower than the yield strength. Therefore, the
Sensor and Specimen Preparation
A PVC tube with an outer diameter of 40 mm was used as the magnetic resonance sensor skeleton. The excitation and induction coil were wound with 0.25 mm-diameter enameled wire. The total number of turns of the excitation coil was 40 turns, and 1 layer was wound. The total number of turns of the induction coil was 1400 turns, and 10 layers were wound. The yield strength of HRB400 rebar is 400 MPa. HRB400 rebar is widely used in engineering projects. Rebar is a common ferromagnetic material with magnetoelastic effect [38,39]. The length of the sensor was 80 mm. The specimens were made of rebars with the yield strength of 400 MPa. To verify the applicability of the working stress monitoring method to different diameters of rebars, the specimens' diameters were made of 16 mm, 18 mm, and 20 mm. In actual engineering, the working stress of the rebar is lower than the yield strength. Therefore, the maximum design stresses are 50%, 70%, and 90% of the yield strength, respectively. There were 6 specimens of each diameter and a total of 18 specimens. The specimens were divided into three groups according to their diameter. Each rebar diameter yielded at 89 kN, 109 kN, and 155 kN in tension, respectively. The specimens were numbered as shown in Table 1, with D being the diameter of the rebar and P being the maximum stress-to-yield strength ratio. To ensure the reproducibility of the experiment results, two specimens with the same stress conditions were set up, numbered T1 and T2.
Loading Procedure
In the experiment, the magnetic resonance sensor was fixed in the middle of the rebar to avoid the magnetic field's influence at the rebar's end. The universal testing machine stretched the specimens. Loading and unloading were carried out with 3 kN as the starting and ending points to avoid instrument errors. The working stress of rebar does not reach its yield strength. Therefore, to ensure that no plastic deformation of the rebar occurs, the maximum stress levels were designed to be 50%, 70%, and 90% of the yield strength, and the step size was 10% of the yield strength. In practical engineering, the prestressed rebar will be initially tensioned to reduce the prestress loss. Therefore, the experiment was conducted with pretreatment of the rebars to simulate the initial tensioning during the construction phase. Then, the specimens were loaded and unloaded using the universal testing machine. The loading stage simulated the prestress application during the construction phase. The unloading stage was used to simulate the working stress during the operation phase. The loading and unloading speeds were both 0.2 kN/s. During the experiment, the excitation coil was excited with the initial resonant frequency of the induction coil (with rebar inside). Then, the induction coil resonated with the excitation coil. The excitation frequency and excitation voltage of each specimen are shown in Table 1. It can be seen that different diameters of rebars' excitation frequency and excitation voltage had some differences, but those of the same diameter were more stable. To ensure adequate deformation of the rebar and stability of the loading and test systems, the load was held for 30 s after each loading to the specified tension (each tension level). After the induced voltage was stabilized, the induced voltage peak-to-peak value of the induction coil was measured. The peak-to-peak induction voltage (Vpp) was repeated seven times, and the average value was taken to reduce the measurement error.
Experimental Results and Discussion
To study the relationship between the induced voltage peak-to-peak value and working stress, the loading and unloading experiment results with the maximum design stress of rebars with diameters of 16 mm, 18 mm, and 20 mm being 50%, 70%, and 90% of yield strength, respectively, were analyzed.
The Evolution Law of Induced Voltage with Working Stress
Due to the different diameters of the specimens, the tensile force during the data analysis was converted into stress to facilitate the control variable. To compare different groups of rebars with the same stress level, the stress to yield strength ratio was taken as the abscissa and expressed by T p . Considering the different initial magnetization states of different specimens, their initial induced voltage peak-to-peak values after pretreatment were different. Therefore, the starting point of each group of data was excluded from the initial value, and the increment of induced voltage peak-to-peak value (∆Vpp) was used as an indicator. As shown in Figure 3, ∆Vpp and rebar working stress are nonlinearly correlated. According to the magnetoelastic effect, the magnetization strength of the rebar changes when the stress changes. During the elastic stage, the force-induced magnetization is theoretically reversible. Therefore, during the unloading stage, the elastic strain recovery makes the reversible magnetization intensity recover. However, as shown in Figure 3, the induced voltage peaks did not fully recover when the rebar was unloaded to its starting value. This was because the plastic deformation generated by the rebar fabrication was not completely eliminated in the pretreatment stage. The magnetic domain structure was irreversibly rotated during loading, which resulted in irreversible magnetization.
tion is theoretically reversible. Therefore, during the unloading stage, the elastic strain recovery makes the reversible magnetization intensity recover. However, as shown in Figure 3, the induced voltage peaks did not fully recover when the rebar was unloaded to its starting value. This was because the plastic deformation generated by the rebar fabrication was not completely eliminated in the pretreatment stage. The magnetic domain structure was irreversibly rotated during loading, which resulted in irreversible magnetization. The corresponding ΔVpp-Tp curves were similar for each specimen. Therefore, the design stress range of 90% yield strength in each group of specimens was selected for further analysis. As shown in Figure 4, the relationship of the ΔVpp-σ was similar for the same stressing process for different rebars. During the loading stage, the ΔVpp decreased and then increased with the increase of working stress. During the unloading stage, the ΔVpp decreased and then increased with the decrease of working stress. The corresponding ΔVpp-σ curves in the loading and unloading stages were different. The same stress level in loading and unloading corresponded to two different ΔVpp. This was due to the hysteresis of the rebar as a ferromagnetic material after loading and unloading [40].
Unloading stage 0 50 100 150 200 250 300 350 400 The working stress loss stage corresponded to the unloading stage. Further analysis of the unloading stage was performed. The maximum stress level was taken as the starting The corresponding ∆Vpp-T p curves were similar for each specimen. Therefore, the design stress range of 90% yield strength in each group of specimens was selected for further analysis. As shown in Figure 4, the relationship of the ∆Vpp-σ was similar for the same stressing process for different rebars. During the loading stage, the ∆Vpp decreased and then increased with the increase of working stress. During the unloading stage, the ∆Vpp decreased and then increased with the decrease of working stress. The corresponding ∆Vpp-σ curves in the loading and unloading stages were different. The same stress level in loading and unloading corresponded to two different ∆Vpp. This was due to the hysteresis of the rebar as a ferromagnetic material after loading and unloading [40]. recovery makes the reversible magnetization intensity recover. However, as shown in Figure 3, the induced voltage peaks did not fully recover when the rebar was unloaded to its starting value. This was because the plastic deformation generated by the rebar fabrication was not completely eliminated in the pretreatment stage. The magnetic domain structure was irreversibly rotated during loading, which resulted in irreversible magnetization. The corresponding ΔVpp-Tp curves were similar for each specimen. Therefore, the design stress range of 90% yield strength in each group of specimens was selected for further analysis. As shown in Figure 4, the relationship of the ΔVpp-σ was similar for the same stressing process for different rebars. During the loading stage, the ΔVpp decreased and then increased with the increase of working stress. During the unloading stage, the ΔVpp decreased and then increased with the decrease of working stress. The corresponding ΔVpp-σ curves in the loading and unloading stages were different. The same stress level in loading and unloading corresponded to two different ΔVpp. This was due to the hysteresis of the rebar as a ferromagnetic material after loading and unloading [40]. The working stress loss stage corresponded to the unloading stage. Further analysis of the unloading stage was performed. The maximum stress level was taken as the starting The working stress loss stage corresponded to the unloading stage. Further analysis of the unloading stage was performed. The maximum stress level was taken as the starting point for comparison purposes. The starting point of each specimen was removed from the initial value. The increment of induced voltage peak-to-peak (∆Vpp) was used to characterize the working stress of the rebar, as shown in Figure 5.
There was a similar relationship between the ∆Vpp and working stress for rebars with different diameters. For specimens with the same diameter, due to the different composition and processing technology of different rebars, the force-induced magnetization law of rebars was different. Therefore, the reversible magnetization of each specimen was different, which made the ∆Vpp of different rebars different under the same working stress level. However, under different working conditions, the ∆Vpp-σ curve was similar. In the unloading stage, the ∆Vpp decreased first and then increased with the decrease of working stress. From the perspective of magnetic domain theory, it can be seen that the working stress had a more substantial influence on magnetization than the excitation magnetic field Buildings 2023, 13, 1416 9 of 17 at a greater working stress level. Therefore, magnetization would increase with the increase of stress at a greater stress level [41].
Buildings 2023, 13, 1416 9 of 17 point for comparison purposes. The starting point of each specimen was removed from the initial value. The increment of induced voltage peak-to-peak (ΔVpp) was used to characterize the working stress of the rebar, as shown in Figure 5. There was a similar relationship between the ΔVpp and working stress for rebars with different diameters. For specimens with the same diameter, due to the different composition and processing technology of different rebars, the force-induced magnetization law of rebars was different. Therefore, the reversible magnetization of each specimen was different, which made the ΔVpp of different rebars different under the same working stress level. However, under different working conditions, the ΔVpp-σ curve was similar. In the unloading stage, the ΔVpp decreased first and then increased with the decrease of working stress. From the perspective of magnetic domain theory, it can be seen that the working stress had a more substantial influence on magnetization than the excitation magnetic field at a greater working stress level. Therefore, magnetization would increase with the increase of stress at a greater stress level [41].
Comparing Figure 5a-c, it can be seen that under the same working stress level, the greater the design stress of different rebars in the same group, the lower the ΔVpp corresponding to the specimen. This was because when the design stress increased, the elastic strain generated by the rebar during the prestressing process increased, reducing the rebar's effective area. In addition, the more extensive range increased the magnetization range of the rebar. Therefore, in the unloading stage, the rebar simulated the working stress loss; when the working stress was lost to the same stress level, the ΔVpp measured by the specimen with high design stress was less. For each group of specimens, the turning point of the ΔVpp-σ curve was different, but it was concentrated at 135 ± 25 MPa. For the same group, the distribution of turning points was more concentrated. For example, the turning point of Group 2 was 157.19 MPa. In the same design stress of the same group, except for D20-P90-T1 and D20-P90-T2, the turning point of the ΔVpp-σ curve of other repetitive tests was the same stress level.
From the above analysis, it can be seen that the induced voltage peak-to-peak value was nonlinearly related to working stress. Therefore, to evaluate the working stress of prestressed rebar using the induced voltage peak-to-peak value, the mapping relationships between characteristic indicators and working stress were established by nonlinear fit and linear fit.
Relationship between Working Stress and the ΔVpp
Due to the measurement under different working conditions, the changing trend between the stress of prestressed rebar and the ΔVpp was basically the same. Therefore, a representative ΔVpp-σ curve was selected from three diameters for further analysis. Because the design stress of 90% yield strength included the stress process of 50% and 70% Comparing Figure 5a-c, it can be seen that under the same working stress level, the greater the design stress of different rebars in the same group, the lower the ∆Vpp corresponding to the specimen. This was because when the design stress increased, the elastic strain generated by the rebar during the prestressing process increased, reducing the rebar's effective area. In addition, the more extensive range increased the magnetization range of the rebar. Therefore, in the unloading stage, the rebar simulated the working stress loss; when the working stress was lost to the same stress level, the ∆Vpp measured by the specimen with high design stress was less. For each group of specimens, the turning point of the ∆Vpp-σ curve was different, but it was concentrated at 135 ± 25 MPa. For the same group, the distribution of turning points was more concentrated. For example, the turning point of Group 2 was 157.19 MPa. In the same design stress of the same group, except for D20-P90-T1 and D20-P90-T2, the turning point of the ∆Vpp-σ curve of other repetitive tests was the same stress level.
From the above analysis, it can be seen that the induced voltage peak-to-peak value was nonlinearly related to working stress. Therefore, to evaluate the working stress of prestressed rebar using the induced voltage peak-to-peak value, the mapping relationships between characteristic indicators and working stress were established by nonlinear fit and linear fit.
Relationship between Working Stress and the ∆Vpp
Due to the measurement under different working conditions, the changing trend between the stress of prestressed rebar and the ∆Vpp was basically the same. Therefore, a representative ∆Vpp-σ curve was selected from three diameters for further analysis. Because the design stress of 90% yield strength included the stress process of 50% and 70% yield strength design conditions, this paper selected specimens D16-P90-T1, D18-P90-T1, and D20-P90-T1 for discussion. In working stress monitoring, the working stress was unknown and needed to be evaluated based on the measured ∆Vpp. Therefore, the ∆Vpp was used as the abscissa and the stress converted by tension was used as the ordinate, which was recorded as Method 1. The σ-∆Vpp curves of D16-P90-T1, D18-P90-T1, and D20-P90-T1 are shown in Figure 6. yield strength design conditions, this paper selected specimens D16-P90-T1, D18-P90-T1, and D20-P90-T1 for discussion. In working stress monitoring, the working stress was unknown and needed to be evaluated based on the measured ΔVpp. Therefore, the ΔVpp was used as the abscissa and the stress converted by tension was used as the ordinate, which was recorded as Method 1. The σ-ΔVpp curves of D16-P90-T1, D18-P90-T1, and D20-P90-T1 are shown in Figure 6. As shown in Figure 6, during the unloading stage, the ΔVpp decreased first and then increased with the decrease of rebar working stress. Therefore, when the increase of the ΔVpp was observed, it could be considered that the working stress of the rebar had dropped to a low stress level relative to the design prestress. However, all three specimens had a ΔVpp corresponding to two different rebar prestress levels, and the mapping relationship between the ΔVpp and working stress could not be established. Therefore, the corresponding relationship between working stress and the ΔVpp variation under each stress level was discussed in sections.
The whole unloading stage bounded by the turning point can be divided into two sections: the high stress section and low stress section. Since the importance of the two sections was the same, it was necessary to evaluate the fit effect as a whole. The Taylor expansion of Equation (13) was carried out, the higher order term after the third order was ignored, and Equation (14) was obtained. The first, second, and third orders of the corresponding relationship between the ΔVpp and rebar working stress were discussed separately, as shown in Equation (15). The turning points of the corresponding curves of each specimen in Figure 6 were 119.37 MPa, 157.19 MPa, and 119.37 MPa, respectively. Taking the turning point as the dividing line, the three specimens were fitted to obtain the corresponding linear, quadratic, and cubic fit curves. Therefore, the goodness of fit (R 2 ) was used to evaluate the fit effect. The R 2 of each specimen was calculated based on two segmented data.
The R 2 is shown in Figure 7, demonstrating that as the order of fit increased, the R 2 approached one. The R 2 of cubic polynomial fit was higher than that of quadratic polynomial fit and linear fit, and its R 2 reached 0.98 on average. The cubic polynomial R 2 of the specimen D20-P90-T2 was as high as 0.99781, which was close to 1. In addition, when the order increased from three to four, there was little room for improvement in the R 2 . As shown in Figure 6, during the unloading stage, the ∆Vpp decreased first and then increased with the decrease of rebar working stress. Therefore, when the increase of the ∆Vpp was observed, it could be considered that the working stress of the rebar had dropped to a low stress level relative to the design prestress. However, all three specimens had a ∆Vpp corresponding to two different rebar prestress levels, and the mapping relationship between the ∆Vpp and working stress could not be established. Therefore, the corresponding relationship between working stress and the ∆Vpp variation under each stress level was discussed in sections.
The whole unloading stage bounded by the turning point can be divided into two sections: the high stress section and low stress section. Since the importance of the two sections was the same, it was necessary to evaluate the fit effect as a whole. The Taylor expansion of Equation (13) was carried out, the higher order term after the third order was ignored, and Equation (14) was obtained. The first, second, and third orders of the corresponding relationship between the ∆Vpp and rebar working stress were discussed separately, as shown in Equation (15). The turning points of the corresponding curves of each specimen in Figure 6 were 119.37 MPa, 157.19 MPa, and 119.37 MPa, respectively. Taking the turning point as the dividing line, the three specimens were fitted to obtain the corresponding linear, quadratic, and cubic fit curves. Therefore, the goodness of fit (R 2 ) was used to evaluate the fit effect. The R 2 of each specimen was calculated based on two segmented data.
The R 2 is shown in Figure 7, demonstrating that as the order of fit increased, the R 2 approached one. The R 2 of cubic polynomial fit was higher than that of quadratic polynomial fit and linear fit, and its R 2 reached 0.98 on average. The cubic polynomial R 2 of the specimen D20-P90-T2 was as high as 0.99781, which was close to 1. In addition, when the order increased from three to four, there was little room for improvement in the R 2 . Considered comprehensively, the cubic polynomial was selected for piecewise fit to explore the correlation between working stress and the ∆Vpp. To verify the feasibility of using cubic polynomial fit to determine the correlation between ∆Vpp and working stress, the ∆Vpp data of each specimen were fitted by cubic polynomial, and the R 2 was shown as follows.
Considered comprehensively, the cubic polynomial was selected for piecewise fit to explore the correlation between working stress and the ΔVpp. To verify the feasibility of using cubic polynomial fit to determine the correlation between ΔVpp and working stress, the ΔVpp data of each specimen were fitted by cubic polynomial, and the R 2 was shown as follows. As shown in Figure 8, the R 2 of D18-P50-T2 was at least 0.96928. The R 2 of each specimen was more significant than 0.96, indicating a high degree of compliance with the cubic polynomial fit of the line between σ-ΔVpp. Therefore, the working stress of the rebar could be determined from the σ-ΔVpp curve. As shown in Figure 8, the R 2 of D18-P50-T2 was at least 0.96928. The R 2 of each specimen was more significant than 0.96, indicating a high degree of compliance with the cubic polynomial fit of the line between σ-∆Vpp. Therefore, the working stress of the rebar could be determined from the σ-∆Vpp curve.
Considered comprehensively, the cubic polynomial was selected for piecewise fit to explore the correlation between working stress and the ΔVpp. To verify the feasibility of using cubic polynomial fit to determine the correlation between ΔVpp and working stress, the ΔVpp data of each specimen were fitted by cubic polynomial, and the R 2 was shown as follows. As shown in Figure 8, the R 2 of D18-P50-T2 was at least 0.96928. The R 2 of each specimen was more significant than 0.96, indicating a high degree of compliance with the cubic polynomial fit of the line between σ-ΔVpp. Therefore, the working stress of the rebar could be determined from the σ-ΔVpp curve.
Relationship between Working Stress and d∆Vpp
As shown in Figure 5, the gradient of the σ-∆Vpp curve (d∆Vpp) decreased continuously during the unloading stage. The curves of ∆Vpp and working stress for different diameters had similarities. When the working stress decreased gradually, one ∆Vpp corresponded to two different stress levels of the rebar. Therefore, in the data analysis, d∆Vpp could be chosen as the fit variable to characterize the variation of the magnetic properties of prestressed rebar with working stress, which was recorded as Method 2. D16-P90-T2, D18-P90-T2, and D20-P90-T2 were used as examples.
As shown in Figure 9, the working stress of rebar could be uniquely determined by the d∆Vpp. In the unloading stage, the trend between the d∆Vpp and the working stress was basically the same. With the decrease of working stress, the d∆Vpp decreased gradually and was linearly correlated. Therefore, to clarify the relationship between the two variables, a linear fit was made between the d∆Vpp and working stress of the three specimens. The goodness of fit (R 2 ) was used to indicate the linear fit of the specimens. The R 2 corresponding to D16-P90-T2, D18-P90-T2, and D20-P90-T2 was 0.97112, 0.97041, and 0.91294, respectively. Therefore, it was preliminarily shown that there was a good linear relationship between the working stress and the d∆Vpp curve. The R 2 of all specimens was calculated, and the results are shown in Figure 10.
responded to two different stress levels of the rebar. Therefore, in the data analysis, dΔVpp could be chosen as the fit variable to characterize the variation of the magnetic properties of prestressed rebar with working stress, which was recorded as Method 2. D16-P90-T2, D18-P90-T2, and D20-P90-T2 were used as examples.
As shown in Figure 9, the working stress of rebar could be uniquely determined by the dΔVpp. In the unloading stage, the trend between the dΔVpp and the working stress was basically the same. With the decrease of working stress, the dΔVpp decreased gradually and was linearly correlated. Therefore, to clarify the relationship between the two variables, a linear fit was made between the dΔVpp and working stress of the three specimens. The goodness of fit (R 2 ) was used to indicate the linear fit of the specimens. The R 2 corresponding to D16-P90-T2, D18-P90-T2, and D20-P90-T2 was 0.97112, 0.97041, and 0.91294, respectively. Therefore, it was preliminarily shown that there was a good linear relationship between the working stress and the dΔVpp curve. The R 2 of all specimens was calculated, and the results are shown in Figure 10. could be chosen as the fit variable to characterize the variation of the magnetic properties of prestressed rebar with working stress, which was recorded as Method 2. D16-P90-T2, D18-P90-T2, and D20-P90-T2 were used as examples. As shown in Figure 9, the working stress of rebar could be uniquely determined by the dΔVpp. In the unloading stage, the trend between the dΔVpp and the working stress was basically the same. With the decrease of working stress, the dΔVpp decreased gradually and was linearly correlated. Therefore, to clarify the relationship between the two variables, a linear fit was made between the dΔVpp and working stress of the three specimens. The goodness of fit (R 2 ) was used to indicate the linear fit of the specimens. The R 2 corresponding to D16-P90-T2, D18-P90-T2, and D20-P90-T2 was 0.97112, 0.97041, and 0.91294, respectively. Therefore, it was preliminarily shown that there was a good linear relationship between the working stress and the dΔVpp curve. The R 2 of all specimens was calculated, and the results are shown in Figure 10. It can be seen from Figure 10 that the R 2 of each specimen was more significant than 0.9, indicating an excellent linear fit between d∆Vpp-σ. Therefore, the working stress of rebar could be determined by the linear relationship of d∆Vpp-σ. Among them, the minimum R 2 was 0.91293 for D20-P90-T2, and the maximum R 2 was 0.99208 for D18-P50-T1. The R 2 for each of the three diameters was discussed by taking the average values of each specimen. The average values of R 2 for Group 1 and Group 2 were similar: 0.96699 and 0.97510, respectively. The average value of the R 2 of Group 3 was slightly lower, 0.94390. This was because the relative effective working area of the rebar decreased with increasing diameter due to the skin effect at a high alternating frequency.
Working Stress Monitoring Error Analysis
To propose a more reliable evaluation method for the working stress of vertical prestressed rebar, the errors of Method 1 and Method 2 proposed were compared. The calculation steps can be shown in Figure 11. This was because the relative effective working area of the rebar decreased with increasing diameter due to the skin effect at a high alternating frequency.
Working Stress Monitoring Error Analysis
To propose a more reliable evaluation method for the working stress of vertical prestressed rebar, the errors of Method 1 and Method 2 proposed were compared. The calculation steps can be shown in Figure 11. For Method 1, the curve fit degree was good; all groups' R 2 were greater than 0.96. This showed that working stress had an excellent functioning relationship with the ΔVpp. The fit relationship was generalized to Equation (16). The measured ΔVpp was substituted into the fit equation. The results were compared with the actual measured working stress. The relative error values of each specimen were calculated as shown in Figure 12. For Method 1, the curve fit degree was good; all groups' R 2 were greater than 0.96. This showed that working stress had an excellent functioning relationship with the ∆Vpp. The fit relationship was generalized to Equation (16). The measured ∆Vpp was substituted into the fit equation. The results were compared with the actual measured working stress. The relative error values of each specimen were calculated as shown in Figure 12. From the error analysis of the fitted and measured values under the unloading stage, it was found that the relative error values did not exceed 20% under any working conditions. The relative error values were concentrated below 10% in the high stress section. The measured ΔVpp was substituted into the corresponding fit equation under different working conditions. The percentage of relative error at the turning point of D20-P90-T1 was the highest, 18.21%, and the maximum relative error between the fitted and measured value was 21.73 MPa. The high relative errors were concentrated near the turning point. Therefore, increasing the measurement points near the measured turning points during the calibration in the laboratory could significantly reduce the relative error. The relative error values of all specimens were normalized, and the average relative error values with robustness were used for comparative analysis. The maximum average relative error values for Group 1, Group 2, and Group 3 at different stress levels were 3.68%, 4.16%, and 2.79%, respectively. The average relative error values for all specimens were less than 5%, close to the results of the REME method for testing strand stresses [28].
For Method 2, the R 2 were greater than 0.90. This showed that working stress has a From the error analysis of the fitted and measured values under the unloading stage, it was found that the relative error values did not exceed 20% under any working conditions. The relative error values were concentrated below 10% in the high stress section. The measured ∆Vpp was substituted into the corresponding fit equation under different working conditions. The percentage of relative error at the turning point of D20-P90-T1 was the highest, 18.21%, and the maximum relative error between the fitted and measured value was 21.73 MPa. The high relative errors were concentrated near the turning point. Therefore, increasing the measurement points near the measured turning points during the calibration in the laboratory could significantly reduce the relative error. The relative error values of all specimens were normalized, and the average relative error values with robustness were used for comparative analysis. The maximum average relative error values for Group 1, Group 2, and Group 3 at different stress levels were 3.68%, 4.16%, and 2.79%, respectively. The average relative error values for all specimens were less than 5%, close to the results of the REME method for testing strand stresses [28].
For Method 2, the R 2 were greater than 0.90. This showed that working stress has a good linear correlation with the d∆Vpp. The measured induced voltage peak-to-peak values were substituted into Method 2. The results were compared with the actual working stress. To ensure the consistency of the d∆Vpp loading step, only the prestress levels with a design stress above 20% of the yield strength ratio were analyzed. The results are shown in Figure 13.
The measured ΔVpp was substituted into the corresponding fit equation under different working conditions. The percentage of relative error at the turning point of D20-P90-T1 was the highest, 18.21%, and the maximum relative error between the fitted and measured value was 21.73 MPa. The high relative errors were concentrated near the turning point. Therefore, increasing the measurement points near the measured turning points during the calibration in the laboratory could significantly reduce the relative error. The relative error values of all specimens were normalized, and the average relative error values with robustness were used for comparative analysis. The maximum average relative error values for Group 1, Group 2, and Group 3 at different stress levels were 3.68%, 4.16%, and 2.79%, respectively. The average relative error values for all specimens were less than 5%, close to the results of the REME method for testing strand stresses [28].
For Method 2, the R 2 were greater than 0.90. This showed that working stress has a good linear correlation with the dΔVpp. The measured induced voltage peak-to-peak values were substituted into Method 2. The results were compared with the actual working stress. To ensure the consistency of the dΔVpp loading step, only the prestress levels with a design stress above 20% of the yield strength ratio were analyzed. The results are shown in Figure 13. More than 75% of the test points had relative error values below 20%, and the maximum relative error value was 23.85%. The errors of all specimens were normalized and the average relative error value with robustness was used for comparative analysis. The results are shown in Figure 12. In the error analysis, it was found that the maximum average relative error values of each group were 9.77%, 8.20%, and 14.53%, respectively. Therefore, under any working conditions, the average relative error values were less than 15%, better than the 25% average relative error value of the ultrasonic guided wave method [42]. This result showed that using Method 2 to monitor vertical prestressed rebar's working stress loss had good reliability. However, the error was greater than that of the traditional magnetoelastic method [22].
In summary, Method 1 could avoid high error by increasing the measurement points near the turning point. Therefore, the Method 1 test error value can be considered as low and could meet engineering needs. Method 2 avoided the uncertainty of the turning point in the laboratory calibration process, but its error was greater than the traditional magnetoelastic method. Therefore, the cubic polynomial segmental fit (Method 1) was selected to establish the mapping relationship between working stress and the ∆Vpp. Then, the working stress monitoring method of prestressed rebar based on magnetic resonance was proposed.
Conclusions
In this paper, the relationship between the sensor induced voltage and the rebar stress was derived based on the electromagnetic induction law, magnetoelastic effect, and magnetic resonance theory. Working stress monitoring experiments with different design stress levels were carried out for rebars with diameters of 16 cm, 18 cm, and 20 cm. The induced voltage peak-to-peak values under working stress variations were collected with a magnetic resonance sensor. The main conclusions were as follows: (1) The curves of the working stress and the induced voltage peak-to-peak values at different design stress levels showed nonlinear correlation. Due to the hysteresis effect, the induced voltage peak-to-peak values measured in the loading stage differed from those in the unloading stage. Two characteristic indicators, the ∆Vpp and d∆Vpp, were proposed for evaluating the working stress. The correlation between the two characteristic indicators and the working stress was analyzed. On this basis, the mapping relationships from the characteristic indicators to the working stress were obtained by nonlinear fitting and linear fitting, respectively. (2) For the d∆Vpp overall linear fit method, the R 2 was greater than 0.90. The average relative error values in different design conditions were less than 15%. This method ignored the influence of different turning points caused by external factors, but the measurement accuracy and stability needed further improvement. For the ∆Vpp segmented polynomial fit method, the cubic polynomial fit was better than the quadratic polynomial and linear fit. The R 2 of the cubic polynomial fit was greater than 0.96, and the relative error values in the high stress section were all concentrated below 10%. The high errors were concentrated near the turning points, and the errors could be reduced by increasing the measurement points near the turning points. The average relative error values in different design conditions were less than 5%. (3) According to the actual demand, the method of ∆Vpp segmented polynomial fit was selected to monitor the working stress of the rebar. The magnetic resonance sensor has the advantages of small power supply, small size, light weight, and high accuracy, which is suitable for the internal monitoring of working stress of rebar. This paper verified the applicability of the induced voltage peak-to-peak value to characterize the rebar working stress.
This paper provided a new method for the working stress monitoring of vertical prestressed rebars. | 11,230.8 | 2023-05-30T00:00:00.000 | [
"Engineering",
"Materials Science"
] |
Multi-Sensor Data Fusion for Accurate Traffic Speed and Travel Time Reconstruction
This paper studies the joint reconstruction of traffic speeds and travel times by fusing sparse sensor data. Raw speed data from inductive loop detectors and floating cars as well as travel time measurements are combined using different fusion techniques. A novel fusion approach is developed which extends existing speed reconstruction methods to integrate low-resolution travel time data. Several state-of-the-art methods and the novel approach are evaluated on their performance in reconstructing traffic speeds and travel times using various combinations of sensor data. Algorithms and sensor setups are evaluated with real loop detector, floating car and Bluetooth data collected during severe congestion on German freeway A9. Two main aspects are examined: (i) which algorithm provides the most accurate result depending on the used data and (ii) which type of sensor and which combination of sensors yields higher estimation accuracies. Results show that, overall, the novel approach applied to a combination of floating-car data and loop data provides the best speed and travel time accuracy. Furthermore, a fusion of sources improves the reconstruction quality in many, but not all cases. In particular, Bluetooth data only provide a benefit for reconstruction purposes if integrated distinctively.
Introduction
For various applications in traffic engineering, it is fundamental to know about the traffic conditions on a road stretch with high certainty and sufficient spatio-temporal accuracy.A complete representation of traffic conditions is especially crucial for understanding traffic flow, for the effectivity analysis of control measures and for training data-driven prediction models.In contrast to real-time or predictive state estimation, these applications are usually applied retrospectively.
The retrospective analysis often focuses on average vehicle speeds per time and space interval on a road since this provides benefits such as enabling the deduction of travel times for road users, providing jam tail warnings [1] aiming at the reduction of rear-end collisions at jam tails, etc.However, using current sensor technology, average vehicle speeds are not measured for all times and places on a road stretch.Rather, various types of sensors are available that provide traffic-related data at different times for different places.Raw sensor data must therefore be processed in order to determine an accurate reconstruction of traffic conditions.
Nowadays, several sensor technologies are in place that gather data, each coming with advantages and disadvantages when applied.Induction loops, that are buried in the road surface, provide very exact and reliable speed information but are mainly limited to few road stretches since the installation and maintenance costs are high.Floating-Car Data (FCD), also called probe data, are gathered from vehicles or smartphones that determine their position via Global Navigation Satellite Systems (GNSS) and report this position on a regular basis to a central server.Time and space differences allow for reconstructing the probe's speed profile on a road.FCD are available wherever traffic is flowing, but represent only a sub-sample of the whole fleet.With WiFi/Bluetooth (BT) sensor technology, the unique MAC address of a device that passes two neighboring stations is registered, allowing the derivation of the travel time and therefore the average speed of devices that pass two neighboring stations [2,3,4,5,6].BT installation is not expensive but -like FCD -the receivers do not collect information from all vehicles and additionally, since they are conceivably placed several kilometers apart from each other, the average speed can be less granular.
Measuring traffic conditions with various sensors offers a great opportunity to increase the accuracy of traffic state estimates.However, the mentioned differences and characteristics of each technology challenge the fusion of the sources.The aim of an advanced fusion method is to make use of all information hidden in the data and compute a combined result that outperforms estimates based on a single source.Additionally, a combination of satisfactorily precise sensor combinations which are available at lower costs might be a reasonable compromise for decision makers, so knowing these combinations would be beneficial to them.
Given various sensor technologies, and various algorithms to process collected data, it is difficult to decide, which technology one should adopt and which algorithm one should deploy.This paper seeks to support decision makers, practitioners and researchers in selecting the combination of sensor data and a reconstruction approach that provides the greatest benefit for their specific problem.Since a real-world application requires algorithms to cope with sparse and missing data, this paper studies approaches with high robustness that can be applied directly.Based on real data collected on a German freeway, various algorithms and combinations of sensor technology are evaluated.Results comprise the accuracy of reconstructed space-time speeds as well as the accuracy of deduced travel times.
The paper is structured as follows.Section 2 gives a literature review on the comparison of different traffic data detection systems and on information fusion approaches.Section 3 describes the study site and data that are used to evaluate subsequent approaches.In section 4, existing applicable fusion methods are briefly summarized.Subsection 4.2 describes the adaption of the Phase-Based Smoothing Method (PSM) to consider BT data in a distinct way.Section 5 presents the applied quality metrics and the obtained results applying the methods to varying sensor setups.The conclusion in 6 wraps up the results and provides potential further research directions.
State of the Art
Comparisons of different traffic detection technologies have been widely performed in the past.In [7], a comprehensive summary of available sensors and fusion techniques is given.The authors of [8] compared Bluetooth measurements and loop detector data in the Greater Toronto Area on a stretch of several kilometers.In [9], the authors describe an offline comparison between loop detectors and floating cars, determining which is able to detect a traffic incident earlier.
In [10], the authors statistically analyze the differences between loop detectors and floating car data in the area of Lille, France.
Additionally, different fusion techniques have been investigated.El Faouzi and Klein [11] give a survey of current data fusion techniques for intelligent transportation systems.In [12], they present three widely applied data fusion techniques and describe their relevance to Intelligent Transportation Systems (ITS): Bayesian inference, Dempster-Shafer evidential reasoning, and Kalman filtering.In [13], an evidence-theory-based data fusion approach for traffic incident detection is described.Data from inductive detectors, camera observation and floating car data are fused on a rather short stretch of a few hundred meters on an urban highway.The authors of [14] applied data fusion techniques for traffic planning and control in a setting with satellite images, acoustic and GPS data.In [15], the authors describe a real-time capable framework for the fusion of loop detector and GPS data.This framework is able to distinguish lanebased traffic states.The authors of [16] study the fusion of loop data and toll collection data using a Dempster-Shafer approach in order to get an improved travel time estimate.In [17], an approach to network-wide traffic state estimation combining loop detector and floating car data is presented.The authors of [1] developed a model to fuse FCD and loop detector data to forecast congestion fronts on a freeway.A comparison of two model-based approaches on filtering methods is conducted in [18].The results are confirmed using synthetic data from a simulation.Liu et al. [19] describe an extended Kalman filter method for freeway traffic state estimation fusing two data sources: wireless communication records and microwave sensor detections.Another Kalman filter based approach is given in [20].In [21], the authors discuss a data fusion approach for cellphone probes and fixed sensors, and give a sensitivity analysis on impact factors.The article [22] describes a data fusion for travel time estimation from toll collection stations and stationary vehicle detectors in Taiwan.Rostami et al. [23] propose a fusion of loop data and FCD at intersections to estimate queue lengths and outflows.In [24] and [25], also a fusion of loop data and FCD is described with the goal to approximate the Macroscopic Fundamental Diagram of urban networks.Bachmann et al. [26,27] compared seven fusion methods for traffic speeds and travel time estimations.One key finding is that a simple convex combination of loop detectors and BT measurements is one of the best fusion strategies.However, data stems from micro-simulations which tend to idealize real data.The authors of [28] fuse various sensors, loops, FCD and camera data using the Adaptive Smoothing Method (ASM) to improve the speed of jam detection and respective control measures.An evaluation is performed using simulated data.
The mentioned studies are mostly limited to the usage of two different sensors, which limits the applicability in many scenarios.Furthermore, they mostly consider only one quality metric that is investigated, e.g. the spatio-temporal speed distribution or travel time.Some of the mentioned studies focus on the estimation of traffic conditions in dense networks, which is a different challenge than the one emphasized in this paper.Furthermore, data are often derived from micro-simulations, which allow for extensive studies but result in data that are usually more homogeneous and less noisy than real data.If studies utilize empirical data, they often focus on a rather short road stretch which gives an insight into only that specific freeway section.
The approach described in this paper is based on empirical data collected via three common sensor technologies: loop detectors, FCD and low-frequency travel time data from BT devices on a long stretch of a German freeway.The number of data points is large, which allows a detailed study of all combinations of data as well as several algorithms processing the data.Furthermore, this work applies two metrics which provides insights into the accuracy of both reconstructed traffic speeds and reconstructed travel times.The algorithms compared in this study, are state-of-the-art methods such as the ASM, the PSM, simple averaging methods and an extension of the PSM.This extension is a minor, but effective change to the PSM, which allows for the integration of low-frequency travel time data in order to achieve higher reconstruction accuracies.
Notation & Data
Speed measurements for all sensors are considered on a road stretch with length X and a time period T .The data of all detection technologies are represented as spatio-temporally discrete speed values in a uniform grid with step size ∆X = 100m and ∆T = 60s.Thus, the domain can be represented as a matrix with n X rows and n T columns, where an entry (also called cell in the following) is referred to as (i, j), where i = 1, . . ., n T and j = 1, . . ., n X .In each cell, the speed value is constant per data source and is denoted as v i,j .Given a set S of sensor technologies on the considered road stretch, V s , s ∈ S with S = {F CD, LOOP, BT } denote the speed matrices of FCD, loop detectors and BT sensors, respectively.
FCD comprise trajectories of vehicles.A trajectory of one vehicle contains all information that a vehicle, equipped with a GNSS, collects about its space-time speed.An equipped vehicle samples its current position x at time t with a certain frequency, and thus generates tuples of (t, x), t ∈ [0, T ], x ∈ [0, X] along the road stretch.Since no further speed information is given, for simplicity, the vehicle's speed between two sampled positions is assumed to be constant.With sampling frequencies, that are in the same order of magnitude as the time discretization of the domain, this basic assumption is sufficient.In order to turn the piece-wise linearly interpolated vehicle position into grid speeds, for each grid cell which is passed by the vehicle, i.e. the vehicle traveled ∆x i,j : ∆x i,j ≥ 0 m and ∆t i,j > 0 s in that cell, a cell-wise speed is computed as v i,j = ∆x i,j /∆t i,j .All cell-wise speeds of all traces are computed, and subsequently, the speeds of all traces are aggregated.If there are multiple speeds for the same cell, the harmonic mean of all assigned speed values is considered.The respective output matrix comprising all speed data from all equipped vehicles is denominated as Speeds measured by loop detectors are given at discrete positions along the road stretch, and with a temporal resolution of one minute.For each loop detector, the measured speeds are assigned to corresponding cells in the grid.The given name is V LOOP ∈ R n X ×n T .
Low-resolution travel times provided by BT are interpolated based on the Bluetooth Interpolation Algorithm [29].This method considers travel times through predefined cells and weights all crossing paths through any cell according to the share of the path inside the cell in order to obtain an averaged speed distribution The studies presented in the subsequent section are applied to data collected on May 29, 2019 on German autobahn A9 (Fig. 1) in the northbound direction during severe traffic congestion.The markers depict the positions of the loop detectors and Bluetooth receivers, respectively.FCD is collected from a fleet of cars which are equipped with a GNSS device.With sampling times between 5 s and 20 s, depending on the software version, the vehicle collects positions and timestamps.Packets of positions and timestamps are reported to a central server.In order to ensure privacy, the transmission ID is shuffled from time to time, and some packets are retained such that tracing a vehicle over its entire journey is not possible.
All in all, time-discrete data of 27 loop detectors, 11,722 BT samples and 1,578 FCD traces are available.Fig. 2 displays the raw data.
Fusion Methods
This section presents the fusion methods that are studied in this paper.Three considered state-of-the-art fusion methods are summarized and an extension to the PSM is presented.All methods investigated in the subsequent evaluation require to take as input only gridded speed data.That is necessary, as FCD and BT contain little information about flow or density.Furthermore, there must not exist requirements regarding minimum data coverage, e.g. a penetration rate of FCD or a minimum distance between neighboring detectors.That is necessary to ensure real-world applicability, where a sensor may fail, or where no equipped vehicles may pass a road segment for a longer period of time.Finally, the output of the algorithm must be a continuous speed estimate
ASM Approach
The ASM is a well-known approach used for traffic state reconstruction [30,31,32,33] and also for on-line traffic speed estimation [34].Briefly summarized, raw data of a sparse input source are smoothed in two traffic-characteristic directions: v cong denominating the wave speed in congested traffic conditions, and v f ree denominating the wave speed in free-flow conditions.In a discrete time-space domain, the resulting complete speed matrices V cong (t, x) and V f ree (t, x) The weight w(t, x) is adaptive and favors low speeds: with V thr a threshold where weight w(t, x) equals to 0.5 and ∆V a parameter to control the steepness of the weight function.In a theoretical analysis as well as evaluation with real data, van Lint et.al. pointed out that smoothing speeds yields a significant error considering travel time accuracy [35].Instead, they propose smoothing the inverted cell-wise speeds in order to reduce the error.Since travel time accuracy is one of the two key quality metrics in this evaluation, this procedure is adopted in this study, replacing the original formulation of the ASM.
Accordingly, for each data source, the discrete space-time matrices V ASM S ∈ R n X ×n T are computed.For a fusion, raw data are combined cell-wise and the combined raw data are processed with the ASM.In case of at least two data sources providing a speed for the same cell, the harmonic mean is taken.
PSM Approach
The PSM is an approach that is based on concepts of the ASM.It was developed to reconstruct space-time traffic speeds with higher accuracy given only FCD [36].It utilizes findings summarized by the Three-Phase traffic theory [37,38] in order to distinguish between localized and moving congestion.The method outperformed the ASM in a recent study [36] and is therefore included in the comparison as a state-of-the-art method.We refer to the original paper for a detailed method derivation and evaluation.
Briefly summarized, in the first step of the PSM, raw data are smoothed in the direction of typical speed propagation of each traffic phase.v cong is assumed to be the propagation speed of moving congestion with low vehicle speeds (also called Wide Moving Jams (WMJs) in the Three-Phase traffic theory).Congestion that is caused by a bottleneck, e.g. a construction site or an on-ramp, is often localized and its downstream front is attached to the bottleneck location.In order to account for the locality, data are smoothed only in temporal direction for the so-called synchronized traffic flow phase.Based on the speeds and the amount of available data, each cell (t, x) is classified into one of the three phases: Free flow, synchronized flow or WMJ using probability theory.
In the second step, phase-specific speed estimates are computed.Raw speed data that are assigned to a specific phase are smoothed using either a free-flow kernel parameterized with v f ree or a congested kernel parameterized with v cong .The phase-specific speed estimates are aggregated into a final speed estimate using a weighted average.
The input of the PSM are gridded speeds.Additionally, for each cell, a weight matrix w P SM ∈ R n X ×n T can be given as input to the method.Applying the PSM to the raw data of the input sources as well as their cell-wise combinations (see section 4.1), the respective output matrices V P SM S are computed.The weight w P SM is set to one for cells with valid data, and zero for cells without data.
Extended PSM Approach Considering Low-Frequency Probe Data
In order to apply the mentioned approaches, BT data are turned into cell-wise speeds by computing their mean speeds and assigning passed grid cells [29] (see Fig. 2).However, since the BT detectors are usually places several kilometers apart, taking the mean speed of a vehicle is a significant simplification of its real speed.For instance, if there was a mixture of congested and free traffic between two detector locations, a mean speed will smooth all details.For travel time estimations, this approach gives accurate results.In the case, that the space-time speed data is desired, the grid-wise cell speeds lack accuracy.Combining such smoothed speeds with other data sources which deliver more accurate information, will even worsen the resulting output, despite using more data.
Therefore, the idea, presented in this extension, is to introduce a dynamic weight that is assigned to gridded BT speed data, which express the trustworthiness of the computed grid speeds.The trustworthiness is influenced by the detector spacing and the measured travel time: Assume a vehicle needs time ∆t to travel distance ∆x (see Fig. 3).It has a maximum speed of v max and a minimum speed of v min .Further assume that the vehicle is not standing, such that v min > 0.Then, for an observer who only measured ∆t and ∆x, it is not known where the vehicle was positioned, and at what speed it was driving, while passing the measured distance in measured time.From the observer's perspective, however, given the assumed minimum and maximum speed, the vehicle's position can be restricted to a certain space-time area.This area is depicted as a parallelogram in Fig. 3, along with three examples of potential vehicle trajectories.Each potential trajectory can be described as a function of the vehicle's position x(t), and its corresponding velocity v c (t).As illustrated, a medium travel time allows for strong deviations of v c (t) over time, whereas low travel times restrict v c (t) to higher speeds.Long travel times can only be realized with vehicle speeds close to v min .
A reconstruction method such as the PSM is sensitive to wrongly assigned speeds in cells.Therefore, given the chance that the vehicle had a completely different speed profile than the speed profile computed using a simple linear interpolation, the accuracy of the reconstruction suffers.In order to consider the probability of deviation in the reconstruction method, the following approach is implemented: The variety of potential trajectories is modeled as the space-time area A BT of the parallelogram formed by the time and space difference, and the assumed minimum and maximum vehicle speeds v min and v max .The magnitude of the area is supposed to affect the weight of a trace: If the area is large, indicating a great variety of potential trajectories, the weight shall be low.If the area is small, the number of potential trajectories is low and the weight shall be high.An exponential function is utilized to model the decay of the weight w A with increasing A w with γ ∈ R a parameter to adjust the sensitivity.The weight w(A) ∈ [0, 1] of all traces passing (t, x) assuming a linear interpolation is averaged and assigned to w BT .The novel fusion method is denominated as 'PSM-W' referring to a dedicated input source weighting of BT data.When combining the raw data of loops, FCD and BT, in this approach the weighted average of all speed cells is taken as input.Raw loop data and FCD are assigned a constant weight of one, and said w BT as weight for BT data.
Section Average
The 'section-average' approach averages collected data in predefined sections.Due to its simplicity, it is still applied in practice and, thus, considered as a relevant approach in this comparison.For each data source, time-space sections are defined and all data that are related to such a section are collected and averaged.Specifically, for loop detectors, section borders are located in the center of two adjacent detector positions.A cell is assigned the speed measurement that is collected by the spatially closest detector at the same moment in time.If, due to an outage of a detector, a measurement is missing, the next closest measurement in time is taken.The resulting speed matrix is denominated as V SEC LOOP .Start and end times of BT samples are collected at the locations of the BT detectors.For each section and each time step ∆t, all BT traces that cross such a section are identified.The total distance covered by these traces in this section for ∆t divided by the respective total time of all traces in this section is the resulting average speed at time t for all cells that belong to the section.The resulting speed estimate is denominated as V SEC BT .The same approach is done for FCD.Compared to stationary detectors, there are no predefined sections.For simplification, the same sections as for detector data are used.In order to assign values to sections without data, a temporal linear interpolation is performed.The resulting matrix is called V SEC F CD .Fusions of mutual pairs and all three matrices are simple cell-wise averages of the speeds.
Methodology
The aim of an accurate reconstruction method is to generate a complete speed estimate in time and space that is suited to various subsequent applications.Conventionally, the quality of a reconstruction is assessed using speed data only.The drawback is that a potential bias in estimated speeds, e.g. a systematic over-estimation, is not penalized.As a result, estimated travel times over larger segments are erroneous.Therefore, we see it necessary to assess both the accuracy of cell-wise speed estimates and the accuracy of virtual travel times.In the following, the combination of both aspects is considered as the reconstruction quality or accuracy.In order to assess the reconstruction accuracy, the following considerations are taken into account: (1) As visible in the raw data plots, the measurements of each data source are sparse in time and space.
(2) Loop detectors provide accurate speed measurements but are limited to certain locations.
(3) FCD provide relatively accurate speed estimates for varying times and spaces but do not represent macroscopic speeds.
(4) BT-based travel time measurements are abundant, though the cell-based speeds are inaccurate due to large distances between neighboring stations.
For these reasons, in order to assess the space-time speed, those data sources with high spatiotemporal accuracy should be used -for the evaluation of travel time data, a source with accurate travel time measurements is required.Therefore, a combination of FCD and loop detector data assesses the cell-wise speed estimates, and BT data are used to assess the travel time accuracy.A commonly used approach in model training and evaluation is to divide available data into a training and a test data set.Fig. 4 depicts the methodology applied in this evaluation.First, each data source is randomly divided into a training and test set with a ratio of 50:50.Specifically, all speed measurements that are gathered by one detector position are either assigned to training data or test data.FCD and BT are assigned per trace.Training data are fused in order to generate an estimate V E , and test data of FCD, loop detectors and BT are used to assess the reconstruction quality.
The quality assessment with a combination of FCD and loop data is done using the Inverse Mean Average Error (IMAE), eq. ( 4).It is a symmetric metric that is sensitive to deviations of lower speeds: with v test representing all tuples v i,j that correspond to a cell-wise speed contained in the test set v test .The set is defined as the union of all cell-wise speeds in the test sets of FCD and loop data.
Quality assessment of travel times with BT is based on the comparison of virtual trajectories with the measured traces using BT detectors.For each measured trace, a virtual trajectory is computed that starts at the same time and location (t start , x start ) of the real trace.The virtual vehicle drives with the continuous representation of speed V E (t, x(t)) until reaching x end : Its virtual travel time is defined as: Given n BT as the number of BT travel time samples in the test set, T T i as the measured and V T T i , i = 1, ..., n BT as the virtual travel times, the Mean Absolute Percentage Error (MAPE) is applied as a quality metric.A relative metric reduces the effect of varying segment distances between neighboring BT receivers.
The parameter set for the ASM is taken in accordance with [31].The PSM is parameterized according to [36].Based on some experiments, γ is set to 500, 000 m • s.A formal sensitivity analysis and optimization is left for future work.v min is set to 5 km/h and v max is set to 130 km/h.The random split between test and training set is done at each run.In total, speed estimation for all scenarios and algorithms as well as quality assessment was done 50 times and average results are presented.
Results
This study intends to give insights into several aspects that come up considering a multi-sensor data fusion.In order to structure the outcomes, the results are examined with respect to two questions: 1. Given a certain sensor set-up on a road and several algorithms that can be applied to process raw data, which algorithm returns the most accurate results?
2. Given the freedom to choose between the three sources of sensor data, which data source or which combination yields best results?
Algorithm Assessment
Fig. 5 depicts the mean IMAE and MAPE of all scenarios and algorithms.Several observations can be made: 1.The available sensor data have a significant impact on the resulting errors for each algorithm.
2. The IMAE has a higher variance than the MAPE.
3. Some algorithms perform best with respect to the IMAE in a scenario but are outperformed with respect to the MAPE (e.g. with FCD only, 'PSM' has a lower IMAE but 'ASM' a lower MAPE).This shows that both quality metrics measure different properties of an algorithm.
4. The 'SEC-AVG' is the algorithm which results in the lowest accuracy, for IMAE as well as MAPE in most scenarios.Given only 'LOOP+BT', this algorithm has a slight advantage over the 'ASM' and 'PSM'.Still, the 'PSM-W' performs better.
5. The 'PSM-W' performs significantly better in IMAE and MAPE in all scenarios that involve BT data.
6. On average, the 'PSM-W' provides the best quality results.In a 'LOOP'-only scenario, the 'ASM' performs better.6 visualizes the estimation results of all algorithms as well as the IMAE with respect to all available data.It can be observed that the estimate computed with the section-average approach (a) results in large errors downstream of the heavy congestion at kilometer 522.Furthermore, the approach failed to reconstruct the moving jams that emerge after 3:30pm.The reconstructions given with ASM (b) and PSM (c) reveal a higher spatio-temporal accuracy.Though, even these approaches spatially overestimate the heavy congestion and are not very accurate at reconstructing the moving jams either.The main reason is that all BT data, with their low space-time accuracy in mid-range speeds (compare section 4.3) are smoothed, which blurs the fine structure of the congestion.
Applying the 'PSM-W' (d) with the adapted weighting of BT according to eq. ( 3) (see Fig. 7) overcomes this issue.Traces with medium travel times and those collected on long segments tend to have a lower weight.Thus, both the speed profile of the heavy congestion and that of the moving jams are reconstructed more precisely.The PDFs of 'SEC-AVG', 'ASM' and 'PSM' are similar to each other, and exhibit a wider distribution than the PDF corresponding to 'PSM-W'.This explains the lower resulting MAPE of the 'PSM-W'.
Sensor Setup Assessment
Suppose that one wishes to install an array of traffic sensors on a stretch of road for the purpose of providing accurate traffic speed information.In that case, it is relevant to know about the quality that a single sensor technology or a combination of sensor technologies may achieve.Fig. 9 shows, for each sensor combination, the lowest achieved IMAE and MAPE across all algorithms.Several observations can be made: 2. The usage of more technologies does not necessarily improve the reconstruction quality.
For example, 'LOOP+FCD+BT' is not the most accurate combination.
3. With respect to IMAE, BT provides the lowest accuracy.
4. With respect to MAPE, loops provide the lowest accuracy.
5. Using FCD or combinations with FCD increases both quality metrics significantly.
6.The integration of BT data improves the quality in some cases (MAPE: 'FCD+BT', 'LOOP+BT'), but worsens it in others (IMAE: 'FCD+BT') Apparently, loop and FCD is the best choice.However, if for instance FCD are not available, a combination of loop and BT data is able to provide more accurate results.Thus, these findings support in the decision process of setting up sensors on a road, or amending stationary data with FCD.
Discussion
The present study examines two major aspects of a multi-sensor data fusion: the reconstruction accuracy using different combinations of sensor data, and the accuracy applying different stateof-the-art algorithms (as well as a novel approach) to different sensor combinations.Additionally, the reconstruction accuracy is measured using two metrics.A welcome result of such a study would be a clear recommendation on which algorithm or data to use in general in order to obtain the most accurate estimates.However, as the comparison showed, the choice of metric has an influence on the most accurate approach and sensor combination.For example, adding BT data barely improved, and sometimes even worsened, the quality of the space-time speed reconstruction.On the other hand, the travel time accuracy of Figure 9: Lowest IMAE and MAPE using the most accurate reconstruction algorithm with respect to the available data source virtual trajectories improved by adding BT.The same is true for the choice of algorithm.If only loop data are given, the ASM performs best in IMAE and MAPE.Given other data, specially BT data, the weighted PSM-W performs best.Compared to the original PSM, its accuracy is the same or better, thus, it successfully extends this approach without compromises.Thus, as a result, depending on the desired speed and travel time accuracy, this study helps to pick the optimal sensor setup or algorithm, depending on the given situation.
Some factors which may have an impact on the results are set as fixed in this study, though they may vary in other applications.First, the penetration rate and sampling interval of FCD and the spacing of stationary detectors may vary.Secondly, the situation used for assessment in this paper is a mixture of two traffic patterns using the classification of the Three-Phase theory: mega-jam and General Pattern [37].These patterns cause large travel time losses, and thus, are especially important to reconstruct accurately.For further work, the study may be extended to further congestion patterns occurring on different days and roads.
Conclusion
This paper studies a multi-sensor data fusion for traffic speed and travel time reconstruction.Two aspects are analyzed: (1) Which is the most accurate algorithm depending on different combinations of data sources, and (2) which is the best performance one can achieve with a flexible sensor setup.Therefore, three state-of-the-art methods such as the ASM, the PSM and a simple averaging method, as well as a novel approach, are used to reconstruct the traffic speed and travel times given sparse data.
The novel approach extends the PSM.It introduces a variable weighting of BT measurements, depending on detector spacing and measured travel time, which expresses the trustworthiness of a measurement.The weighting allows for a dynamic integration of BT data with other data sources.
The mentioned questions are studied using empirical loop data, BT data and FCD collected during severe congestion on a German freeway.Data are divided into a reconstruction and a test set.Various combinations of algorithms and data are used to reconstruct the space-time traffic speed and the travel times.The error metrics IMAE and MAPE are used to assess the resulting reconstruction accuracies.
Key findings are that the novel approach outperforms the other algorithms in most of the cases.Furthermore, a combination of FCD and loop detector data provides the best overall results.The integration of Bluetooth data does not necessarily improve the reconstruction quality, depending on the error measure chosen.However, if no FCD are available, a combination of loop data and BT data is a better choice than only one source of data.
Next steps may include a mathematical optimization of the applied parameters and further studies on sensor spacings.Furthermore, the study could be extended to other locations and congestion patterns.
Figure 2 :
Figure 2: Raw speed data measurements provided by (a) loop detectors, (b) equipped vehicles and (c) Bluetooth receivers
)
Medium travel time (ii) Short travel time (iii) Long travel time
Figure 3 :
Figure 3: Different travel time measurements and the space of potentially realized trajectories that result in each travel time
Figure 4 :
Figure 4: Flow of information of test and training set of sensor data for fusion and quality assessment
Figure 5 :
Figure 5: Mean (a) IMAE and (b) MAPE of all runs with respect to the available sensor technology and the applied algorithm
Figure 6 :
Figure 6: Reconstructed speeds applying each algorithm (a) SEC-AVG, (b) ASM, (c) PSM, (d) PSM-W to the training data (on the left) and resulting IMAEs comparing the reconstructed speeds to all available data (right)
Figure 7 :
Figure 7: Resulting weight applying the speed-adaptive conversion of travel time samples
Figure 8 :
Figure 8: Approximated probability density function of relative errors comparing the travel times of virtual trajectories based on each algorithm with the measured travel times collected via BT devices | 8,114.4 | 2021-05-08T00:00:00.000 | [
"Engineering",
"Computer Science",
"Environmental Science"
] |
Hadronic $b^\prime$ search at the LHC with top and W taggers
We study the sensitivity of a down type quark $b^{\prime}$ via process $pp\rightarrow b^{\prime}\bar{b^{\prime}} \rightarrow tW^-\bar{t}W^+$ using jet substructure methods at the LHC with the collision energy $\sqrt{s}=14$ TeV. We consider the case that the $b^\prime$ is heavy (say from 800 GeV to 1500 GeV) and concentrate on the feasibility of the full hadronic mode. Both top tagger (the HEP top tagger) and W tagger (the CMS W-tagging) are used to reconstruct all objects in the final states. In order to suppress huge SM background events and take into account various cases with different number of boosted objects, we propose a comprehensive reconstruction procedure so as to extract the most crucial observables of the signal events. When $b^\prime$ mass is 1 TeV, it is found that with a 200 fb$^{-1}$ dataset, the LHC may be able to detect the $b^\prime$ with a significance up to $10$ or better. With a 3000 $fb^{-1}$ dataset, the LHC may be able to probe the $b^\prime$ with a mass around up to 2 TeV, only by using the hadronic mode.
Introduction
The LHC collaborations have discovered a Higgs boson [1,2], it is quite natural to ask what will be the next discovery that could be expected for future LHC runs. Extra quarks are one of the possible signals for the new physics, which are supposed to offer solutions to the fundamental issues of the standard model on electroweak symmetry breaking and mass generation of fundamental particles [3]. The heavy bottom like quarks have been predicted in Top-Coloron model [4] and top flavor seesaw [5], non-minimal supersymmetric extentions [6] and extra dimension models with warped space [7], etc.
The extra quarks are good targets for future LHC runs due to their strong interaction with the particles of the SM, especially with gluons. The LHC can be called as a gluon-gluon machine due to the large gluon fluxes in highly accelerated protons. When kinematically accessible, these extra quarks can be copiously produced at the LHC. There are quite a few phenomenological studies for the feasibility of heavy quarks at the LHC, which can be found in literatures [8,9,10,11,12]. Meanwhile, signature of extra quarks are one of focus for experimental searches [13,14,15,16,17].
In this paper, we focus on the search of vector-like b . 1 Vector-like fermions do not contribute to "oblique parameters" in the leading order, and thus these parameters do not constrain their masses. However, the mixing angles between the vector-like fermions and the SM three generations fermions are required to be small because there is no GIM mechanism to suppress the FCNC related to these vector-like fermions. Currently, the most stringent limit on b comes from CMS search [17]. Focusing on the strong pair-production mechanism, CMS has set lower limits between 582 and 732 GeV on the vector-like b quark mass for various decay branching ratios at 95% confidence level [17]. If the b exclusively decays into a top quark and a W boson, considering the same sign lepton final state, the b with mass below 732 GeV has been excluded at the 95% confidence level.
It is well-known that the LHC is a top quark factory and the discovery and precision measurements of pp → tt in all the decay modes have a great significance to test the prediction of the SM. Among all the decay modes, the signal of the semi-leptonic mode is relatively easier to pick out, which enjoys a relative larger branching fraction and smaller SM backgrounds. The dileptonic mode has the smallest branching fraction but enjoys an even cleaner backgrounds [19,20]. The fully hadronic mode is relatively difficult due to the large QCD and W + jets backgrounds and large uncertainties in determining the QCD activities. Nevertheless, measuring the fully hadronic mode is an important indispensable test of the SM prediction. The success of the measurement of fully hadronic mode at the Tevatron [21,22] and the LHC [23] demonstrates that these detectors of hadronic machines are capable to detect the final state with a large multiplicity of jets and new physics with full hadronic final states [24,25]. Recently, phenomenological studies using the fully hadronic mode to probe the ttH signal [26,27], charged Higgs tH ± signal [28] and top partner signal [29] have been done.
The early analysis on the search sensitivity of b can be found in [8], where a simple W-jet mass method was used. By using the semileptonic and dileptonic modes, the authors found that 1 TeV heavy quark can be reachable with 100 fb −1 dataset. Another interesting work can be found in [9], where mainly using leptonic modes, Bob Holdom observed that it is difficult to use one cone to capture both boosted W boson and Top quark from b decay. For the semileptonic mode studied in [10,11], it is observed that once all physics objects (say two top quarks, two W bosons, two b quarks) can be reconstructed it is possible to extract the most crucial variables (like the mass bump of b ) to suppress the SM background to a controllable level. A thorough study for top-partner can be found in [12], where leptonic and b jet modes have been comprehensively analyzed. But the full hadronic mode has been left undone.
To our understanding, the study of hadronic mode of t and b has been untouched due to two major difficulties: 1) the full hadronic mode of the signal has high multiplicity of jets, and the combinatorics to find the characteristic parameters, like the masses of b and t are challenging; 2) Without characteristic variables for signal, it is difficult to distinguish signal from the SM multiple jet final states, say tt + jets. In the study for charged Higgs boson [28], two of our authors have noticed that the top tagger indeed can help to capture signal while maintaining suppression to the SM background even in full hadronic mode. It is observed that when the featured kinematic variables of signal are reconstructed, by using the multivariable analysis techniques, like the boost decision tree [30,31,32] and neural network analysis, it is possible to pick out sufficient signal events when luminosity is large enough (say 100 fb −1 ). Taking into account the recent quick development in tagging the boost objects [33,34], it is well-motivated to explore the hadronic mode by adopting the recently developed hadronic top quark taggers and W boson taggers.
When an extra quark is heavy, massive objects in its decay final states like top quarks, W/Z/Higgs bosons, can be highly boosted. Using the jet substructure techniques [33,34], it offers a promising method to pick out possible signals while keep good suppression to the SM multiple jet final states. Based on Monte Carlo methods, these jet substructure techniques have been demonstrated to work quite well in searching for top partners and bottom partners [35,36,37,38,39,40]. Recently, theoretical understanding on jet physics from QCD side has brought new insights to the jet substructure and related phenomenological analysis methods, such as jet functions [41], grooming [42], quark/gluon separation [43,44] etc. For a comprehensive review on the jet substructure based on first principle QCD calculation and monte carlo tools, we refer to Ref. [34].
In this work we use the hadronic top quark taggers and W boson taggers to explore the sensitivity of the LHC to b . We consider the process for pp → b b at LHC by assuming that b decays to top quark and W boson 100% and study the heavy quark b in the mass range 0.8 TeV < m b < 1.5 TeV. We propose a reconstruction procedure and demonstrate how to reconstruct all physics objects in the signal events. We further use multivariable analysis methods to optimize cuts and explore the sensitivity of the LHC to b . This paper is organized as follows. In Sec. II, we briefly review the boosted massive object taggers which will be used in this work. In Sec. III, we present our phenomenological analysis. Finally, we make a discussion and give our conclusions in Sec. IV.
Brief introduction to top taggers and W taggers
At the LHC, there are large samples of W and Z bosons, Higgs, and top quarks with a transverse momentum P t that considerably exceeds their rest mass. In this kinematic regime, conventional reconstruction algorithms that rely on a one-to-one jet-to-parton assignment are often inappropriate, in particular for hadronic decays of such boosted objects. The technique of jet substructure has been developed to tag the boosted electroweak massive particles with hadronic decay [33,34,45]. Roughly speaking, these tagging algorithms work in two steps: firstly cluster jets with a much larger radius parameter to capture the energy of the complete hadronic decay in a single jet; secondly use delicate discriminating variables to anatomize the internal structure of these fat jets in order to separate boosted objects from the large QCD background. Below we summarize several most common used algorithms for boosted top and boosted W on the market.
Top-taggers
Top quarks play an important role in understanding electroweak symmetry breaking and searching for new physics. Unlike the case at Tevatron where most of top quarks are produced near the threshold, at the LHC many boosted top quarks can be produced. So, the jet substructure technique used to identify the boosted top from its hadronic decay has been developed in recent years. For a recent review on top taggers, we refer to Ref. [46]. Here, we give a brief review on John Hopkins top-tagger [47] and the HEPTopTagger (Heidelberg-Eugene-Paris) [36].
A1. Johns Hopkins top-tagger
After the success of BDRS algorithm [45] in Higgs search, Johns Hopkins group extended the BDRS algorithm to top study and proposed a top tagging method for the highly boosted top in hadronic decay [47]. We will dub it as "JHTopTagger" for simplicity and use it in later analysis. As well-known, a boosted top from its hadronic decay looks like a fat jet with three hard cores. Similar to the BDRS jet substructure method for boosted Higgs, the JHTopTagger firstly uses a large cone to cluster the event in order to capture all the decay products and relevant radiations of a boosted top and then de-clusters the top jet to find three subjets inside the massive mother jet.
To resolve a fat jet into the relevant hard substructure from top decay, the following recursive procedure are applied in JHTopTagger [47]: 1. Four momenta of all particles from top decay are clustered into a massive jet with a large cone size R ( CA algorithm are used in original paper), 2. Undo the last combination to get two objects j 1 and j 2 . If the P t ratio of the softer jet j 2 over the original jet j is too small, i.e., P t j 2 /P t j < δ p , throw the softer j 2 and go on to decluster on the harder one.
3. The declustering step is repeated until two separated hard objects are found. If any criterion below are satisfied, the declustering is failed: 1) both objects are softer than δ p (2) two objects are too close, ∆η + ∆φ < δ r (3) the original jet is considered irreducible.
5. It is required that the total mass of these subjets (only 3 or 4 hard subjets are considered) should be near m t and the mass of two subjets among those resolved subjets should be in the m W window. Furthermore, W helicity angle θ t should be consistent with a top decay due to the left handedness of the SM. Here, the helicity angle θ t is defined in the rest frame of the reconstructed W and is equal to the angle between the reconstructed top's fly-in direction and the fly-out direction of one of the two jets of W decay products. Typically, the softer subjet in the lab frame are chosen to set the angle.
The parameters involved in the method can be optimized event by event [47]. In our study, for the LHC context, these parameters are fixed as below:
A2. HEPTopTagger
Similar to the Johns Hopkins tagger, the HEPTopTagger [36] (Heidelberg-Eugene-Paris) is developed to capture moderately boosted top and is firstly used to improve ttH searches. It begins with a large R = 1.5 to cluster a fat CA jet. Such a large R allows us to access top quarks down to a lower P t ∼ 200 GeV at the price of a large combinatorics of subjets and serious pile-up problem. The HEPTopTagger uncluster the fat jet using an iterative mass-drop criterion. At the meantime, it employs a filtering [45] procedure to pick up three hard subjets as candidates of top daughter jets and then test them with top kinematics. The detailed delicate steps in HEPTopTagger to capture boosted tops are given: 1. The last cluster of the fat jet j is undone to get j 1 and j 2 . And then the mass drop criterion min m j i < δ m · m j determines if we keep j 1 and j 2 . A subjet with a large jet mass m j i > 30 GeV are further decomposed; otherwise, the subjet is put to the list of relevant substructure.
2. The algorithm further uses the filtering procedure to construct one three-subjet combination with a jet mass closest to m t as the top candidates.
3. If the three invariant masses (m 12 , m 13 , m 23 ) for the P t ordering subjets j 1 , j 2 , j 3 satisfy one of the following three criteria, accept them as a top candidate: 4. For consistency, require the combined P t of the three subjets to be above 200 GeV.
Here, the mass drop parameter δ m and the mass windows parameters R min and R max are taken as δ m = 0.8, R min = 85% × m W /m t and R max = 115% × m W /m t . The soft cutoff R soft = 0.35 is supposed to remove QCD and W+jets background events. The HEPTopTagger has an identification efficiency of roughly 40% for top quarks with P t > 400 GeV [36].
We have compared the performance of these two top taggers and noticed that the HEPTopTagger can have a relative better performance, which can be attributed to the following two reasons: 1) the HEPTopTagger can capture not only highly boosted top but also intermediate boosted top; 2) due to more variables are used, the tagger can maintain a remarkable rejection to the SM background events even for the highly boosted top. Therefore, in the following study, we will adopt the HEPTopTagger to tag boosted top quarks in the signal events.
W-taggers
There are large samples of highly boosted electroweak massive particles, such as W bosons at the LHC. The hadronic decay products of these massive particles will be collimated to form fat jets. These W-jets are different from QCD jets in two main aspects. Firstly, a W jet contains two hard subjets in similar energy and mass, originated from the two quarks in the W decay, while a QCD jet usually has only one hard subjet and asymmetric energy-flow distribution. On the other hand, a QCD jet is initiated from a color triplet or octet, which is color-connected to the beam or the other side of the event. Whereas, the two subjets of a W-jet are from a color singlet and they tend to correlate to each other in color. Along these lines, many sophisticated W-tagging tools has been developed to pick out the highly boosted W bosons from backgrounds [33,48,49,50].
B1. CMS W tagger
The LHC experiment has employed the W tagging algorithms to search for new physics [48,49]. Here, we briefly introduce the W tagging algorithm used by CMS collaboration (CMSWTagger) [49], which mainly use pruning [51] and mass drop [45] methods. The algorithm can be applied to a massive jet and is given as follows.
1. The pruning method: the clustering history for a fat and massive jet is checked at every step. For a merging step say (i + j → p), two conditions are examined: If this (i + j → p) step does not satisfy these two conditions, i and j will not be merged and instead the softer of the two clusters is removed.
2. The mass drop method: the total mass of the above pruned jets are required to be in the W mass window 70GeV < m jet < 100GeV. Undoing the last clustering iteration of the pruned jet to get two subjets. The ratio of masses of the hardest subjet (m 1 ) and the total pruned jet mass is defined as the mass drop µ = m 1 m jet . To discriminate against QCD jets, the mass drop is required to satisfy µ < 0.4.
B2. Multivariate analysis W tagger
Unlike the case in top tagger, there are only few orthogonal variables in the two body decay of a highly boosted W. In Ref [50], a jet substructure algorithm with multivariate analysis was proposed for distinguishing highly boosted hadronically decaying W from QCD jets. The algorithm, dubbed it as "TMVAWTagger", selects 25 most useful variables and combines them using the Boosted Decision Trees method. These variables include the masses and P t 's after jet grooming, planar flows, P t R-cores, etc. The detailed steps of the TMVAWTagger are presented as below: 1. Begin with fat jets with large R = 1.2 and then use the filtering/mass drop [45] to identify W jet candidates.
2. Apply a filtering step to get the leading three filtered subjets. The jet mass of combination of these jets is required to be within the mass window (60,100) GeV.
3. After the mass window cut, the original unfiltered fat jets are treated by using the multivariate analysis to maximize the efficiency. The 25 variables used in the analysis are: (2.5) Here, c Pt 's are P t R-cores [50], from 0.2 to 1.1 by 0.1 and sens m,Pt filt,trim,prun represent 6 grooming [45,51,52] sensitivities. P f and P f (0.4) are the planar flow parameters for the original jet and for the highest P t subjet from reculstering with R = 0.4, respectively. ∆R sub is the distance between the two leading subjets and n sub is the total number of subjets after the filtering process.
By using the multivariate analysis, the TMVAWTagger can be quite robust to reject background. Nonetheless, to simplify the current study, we use the CMSWTagger and choose a smaller cone to capture the W bosons from the decay of b .
Numerical Results and Analysis
At the LHC, b pair is mainly produced by the gluon fusion process. The cross section of pp → b b has been studied at reference [53] up to NLO + NLL. For the collision energy √ s = 14 TeV, when m b is around 1 (2) TeV, the cross section can be 69 (0.3) fb. When we assume that b decays 100% to top and W boson, its decay width is less than 10%, so the narrow width approximation is still held.
Features of signal
In order to determine the right parameters to tag both top quarks and W bosons, we analyze the distributions of cone sizes of top quarks and W bosons in the final states at the parton level. We call the W bosons directly from the b decay as the isolated W bosons and label them as W iso . In contrast, we call the W bosons from the top quark decays as non-isolated W bosons and label them as W non .
The correlations between the transverse momenta and the largest angle separation between two jets of two types of W bosons are shown in Fig. 1. In order to estimate the value of cone parameter R to cluster two jets from W boson hadronic decay into one fat jets, we define R iso W as R iso W = max(R(P (W ), P (j 1 )), R(P (W ), P (j 2 ))), where P (j 1 ) and P (j 2 ) label the momenta of two daughter jets from the W boson decay and P (W ) labels the momentum of the W boson. From the plots, it is obvious that these two types of W bosons can be distinguished from their transverse momenta and angle separations. The most probable value of angle separation between two jets from the isolated W bosons is around 0.3 and is smaller than that from the non-isolated W bosons, which is around 0.6. The most probable transverse momenta of isolated W boson is around 500 GeV. It is larger than that of the non-isolated W bosons, which is around 300 GeV. These kinematic features can be utilized to determine the correct combinations of jets.
We also evaluate the largest angle separation of three partons from the top quark decay, which is defined as R max t = max(R(P (t), P (j 1 )), R(P (t), P (j 2 )), R(P (t), P (j 3 ))). The most probable value is around 0.8, which tells us that in order to capture the boosted top quarks, we'd better use a cone size parameter around 1.1 or so. By comparing the middle and right plots in the lower row given in Fig. 1, we can conclude that, at most of time, the R(t) is determined by the angle separation of non-isolated W boson, which can also be read out from the left plot in the upper row from the curve R max t − R non W . We also examine the number of jets and one observable defined as η 2 (j) with the change of the cone size parameters in the anti-kt algorithm, as demonstrated by Fig. 2. It is obvious that when the size of cone parameters for jet algorithm is changed, the number of jets can be changed, so as some kinematic observable, like η 2 (j). There are also some observables, like the centrality, which are found to be insensitive to the change of cone parameter.
We also examine the jet mass distribution with the change of cone parameter R in the anti-Kt jet algorithm, as shown in Fig. 3. We would like to mark a few salient features from Fig. 3.
• When R = 0.4, it is found that more than 80% of the first leading jet can has a jet mass in the W-mass window (the window is defined as |m(j) − m PDG W | < 20), while more than 50% of the second leading jet can have a jet mass in the W-mass window. Most of these massive jets are from the isolated W bosons, which is consistent with our analysis at the parton level shown in Fig. 1.
• When the cone parameter R is changed to 0.7, more than 40% of first leading massive jet has a jet mass in the top quark mass window (the window is defined as |m(j) − m PDG t | < 30) and 30% of the first leading massive jet has a mass in the W-mass window. It is remarkable that more than 80% of the second and third leading massive jets are in the W-mass window. This indicates that the optimized cone parameters for W-jets should be around R = 0.7.
• When the cone parameter R is changed to 1.0, more than 50% of the first leading massive jet has a jet mass in the top quark mass window. There are around 25% of the second leading massive jet in the top quark mass window and 60% in the W-mass window. More than 85% of third leading massive jet is in the W-mass window. It is remarkable that there are around 40% the fourth massive jet in the W-mass window.
• When the cone parameter R is changed to 1.3, more massive jets can be in the top quark mass window. Compared with the plot for R = 1.0, we can read out that the optimized cone parameter R for a fat jet as a top quark should be around 1.0 < R < 1.4 or so. Nevertheless, the optimized cone parameter should also take into account the behavior of background events. Another noticeable point is that the mass of the fifth jet indicates the mass dependence on the R.
Although some massive jets are outside the W-mass window or the top quark mass window, it is expected that the jet tagging techniques should help us to find their identities.
It is obvious that different R's can reveal parts of the full information of signal, a better way to separate signal and background is to utilize all available information with different R's when the computing time is allowed. When the computing resources are limited, we can use some tight preselection rules to choose the most relevant events in our analysis.
Obviously, when the mass of b increases from 1 TeV to 2 TeV, both W bosons and top quark become more energetic and their decay products can be more collimated. We observe that smaller cone size parameters can capture a considerable fraction of W bosons and top quarks, respectively, which is understandable from rule of thumb R = 2 m/P t . It is remarkable that the origin of jet masses of top quarks and W bosons is different from that of QCD jet. The masses of those fat jets from top quark and W boson are from EW symmetry breaking, while the mass of QCD jet is from the collinear and infrared which can lead to wrong combination of pseudo-jets into a massive QCD jet.
Jet Mass (GeV
In our Monte Carlo study, the signal events are generated by Madgraph/MadEvent [54] and background events by Alpgen [55]. We have used the MLM matching [56] to avoid the double counting issue. These events are fed to DECAY to generate full hadronic decay final states and pass to PYTHIA [57] to simulate showering, fragmentation/hadronization, initial state radiation, final state radiation, and multi-interaction as well. After that, fastjet [58] and SpartyJet [59] are used to perform jet clustering and massive object tagging analysis.
We would like to make a comment on the modeling of the SM background events. It is highly nontrivial to model the SM background events with 10 jets. For example, we noticed that the QCD jet sample is quite difficult to be generated by the MC tools on the market. Instead, by choosing the jet parameter P t min > 100 GeV in the Alpgen, we generate exclusive datasets of 2j, 3j, 4j, 5j events, and an inclusive 6j data sample. In our later analysis, we demand n j > 7 and the P t of the leading two jets momenta is larger than 200 GeV, so those extra jets can only be produced from the initial state radiation and finial state radiation. In this sense, for QCD jets data sample, our treatment can be regarded as leading order approximation. It is also true for case with the background events W/Z+ jets and diboson jets, where at most, Alpgen can allow us to generate W/Z + 6 jets at matrix element level. Nonetheless, we noticed that these two types of background can be efficiently suppressed by b taggings and the kinematics cuts introduced below. While for the tt dataset, we have used Alpgen to generate exclusive datasets tt + 0j, tt + 1j,tt + 2j, tt + 3j, and an inclusive dataset for tt + 4j, and we merge these exclusive and inclusive datasets into an inclusive data for tt type background. For tt type background events, at most, we can marginally generate final states with 10 parton by the matrix elements. Keeping this fact in mind, the treatment to the SM background demonstrated in this work can only serve as a leading order approximation.
A proposed reconstruction procedure
To extract useful information of signals, we propose to cluster jets with three different sizes and the following reconstruction procedure to find all objects of an event: 1) For the small size jets, we use the anti-K t algorithm with jet parameter R = 0.4. We only consider high jet multiplicity events with n j ≥ 9 and H t > 1.5m b . When there are massive jets in the event, we demand the number of massive jets n m (defined as m(j i ) > 60) and the number of non-massive jets should satisfy 2 n m + n j ≥ 10.
2) For the mediate size jets, we use the CA algorithm with jet parameter R = 0.6. These mediate jets are supposed to find massive objects, especially the massive W bosons. Some of highly boosted top jets can be also found.
3) For the largest size jets, we use the CA algorithm with jet parameter R = 1.3, we find massive objects, especially the boosted top quarks. We label the number of tagged top quarks as n t .
4)
We identify non-isolated W bosons by using the massive jet found at step 2 and 3. We examine whether each of identified W bosons at step 2 is in the cone of the identified top quarks. If a tagged W boson is in the cone of a top jet, we label it as a non-isolated W boson. If not, it will be labelled as un-used and will be used to further determine the missing objects. The number of un-used tagged W bosons is denoted as n W .
5)
We identify isolated small jets with R = 0.4 which is neither in the cone of W bosons nor in the cone of top quarks. And we use them to reconstruct all missing objects, like top quark(s), W boson(s) and b s. To avoid the severe issue of wrong combinatorics, we throw away events when less than two objects are identified, i.e. n t + n W < 2.
There are several comments in order: 1) We use the minimum χ 2 approach to find the missing objects. For example, if in one event, we have tagged two top quarks with n t = 2 and n W = 0, then the rest of work is to reconstruct two W bosons by using the rest of isolated small jets. The χ 2 is defined as . If in one event, we have tagged two W bosons with n t = 0 and n W = 2, then the χ 2 is constructed as where we have taken into account the possibility that any one of or both W bosons could come from top quark decays.
2) Once two top quarks and two W bosons have been reconstructed, we choose the value of m rec = m min which can minimize the χ 2 (m) = as the reconstructed b mass, where the mass of b i is the combination of a pair of top and W boson, where both two possible combinatorics have been taken into account.
From the results presented in Table 1, we observe that if we require that n t = 2 and n W = 2, there are only 3 − 4% of signal can be taken into account. While with n t + n W ≥ 2 and the proposed reconstruction procedure, more than 50% of signals can be reconstructed successfully, while less than 1% of the dominant background tt + nj can pass through this reconstruction. These events can be correctly triggered at LHC collaborations due to both large H t and large number of jets with the standard anti-K t jet algorithm with the cone parameter R = 0.4. To further reduce reconstruction time, we choose n t + n W ≥ 2 and n t ≥ 1 as our reconstruction conditions. It is found that by choosing this selection rule we can achieve similar results.
In Table 1, fractions of tagged objects in the process pp → b b → tW −t W + with different R are provided. This Table provides important hints as how to capture our signal. There are a few comments in order. 1) The optimization in different cone sizes for R W and R t can affect the signal in 10% percentage level. Therefore, for different masses of b , it might be useful to optimize R W and R t . 2) It is crucial to capture top quark and W boson jets in our reconstruction procedure. 3) When R W becomes too large (say larger than 0.8) , the fraction of signal events in the reconstruction procedure becomes fewer due to the failure of W-tagger.
Signal and background discrimination b b [fb] tt + jets [fb] tt + W + jets [fb]
σ × branching fraction × btagging 6.0 1.67 × 10 5 55.6 1.5 3.7 0.02 Table 2: The cut efficiencies for signal and main background processes are shown here, where the signal is for the case m b = 1TeV . The cross section of tt is taken as 945 pb from [53], we assume all heavy particle decay in the hadronic mode. The optimized cut efficiencies for both MLP and BDT methods are provided for comparison. We cluster jets by using the standard anti-Kt algorithm with the cone parameter R = 0.4.
In order to suppress the tremendous QCD background events and make hadronic mode doable, at the preselection level for further analysis, we demand that the scalar sum of transverse momentum of all final states must be larger than 3 2 m b and the centrality of each event must be larger than 0.55. Furthermore, we require that at least two hadronic heavy objects (i.e. n t + n W ≥ 2 ) must be identified and two b jets must be tagged. In this work, we assume that b tagging efficiency as 0.6 with a rejection factor 300. We further demand that there must be more than 7 jets with P t (j) > 20 GeV and the transverse momentum of leading two jets should be larger than 200 GeV in each event when jets are clustered with jet parameter R = 0.4. With these conditions, we observe that the background of QCD multiple jets are highly suppressed by the conditions of leading two jets P t (j 1 ) > 300 GeV and P t (j 2 ) > 200 GeV, H t , b taggings and jet numbers. Similarly, the background of tt + W + jets is also suppressed significantly by H t and jet numbers. After these conditions for preselection, we find that the dominant background is pp → tt + jets.
We have considered the contributions of diboson (WW, ZZ, etc.) backgrounds, tt+Z+ jets, and have found that these types of reducible background events can be safely neglected after imposing preselection rules. Diboson background are also generated by Alpgen with the number of jets upto 3. Such type of background can also be heavily suppressed by the requirement of boosted objects and reconstruction criteria. Background events from tt + Z+ jets with the number of jets upto 3 are very similar to tt + W + jets, which can at most reach to 1 percent of the signal after all cuts, therefore we neglect it here.
For the irreducible background tt + W W + jets with the number of jets upto 2 by using Madgraph5, we noticed that the cross section (3 fb for hadronic mode) of this type of background is close that of our signal when m b = 1 TeV, but the H t cut and the requirements in leading jets, the kinematics of reconstructed W bosons (two W bosons in our signal have very large P t and are highly boosted), and the mass bump of b (the background events occur near the threshold region) can help to remove such type of background down to a percent level of the signal after all cuts. Therefore, we neglect such type of background in Table 2. For the same reasons, we also neglect tttt background with the number of jets upto 4 by using Alpgen, of which the cross section is 2 fb for fully hadronic mode.
In Table 2, we illustrate how signal and background change with our preselection conditions. From it, it is observed that before reconstruction the dominant background is pp → tt+jets. As demonstrated in left plot of Fig. 4, even after the reconstruction, it is still quite challenging to find the signal, the total background is around two order of magnitude larger than our signal. In order to achieve a better S/B and a better significance, obviously a dedicate signal background discrimination analysis is needed.
Multivariate analysis
Considering that there are 10 physics particles in our final state at parton level, the dimension of phase space of signal is 30 or so without taking into account the phase space of background events. As done in works [10,11,28], in this work we have adopted two Multivariate Analysis methods: the neural network (multilayer perceptron) and the boosted decision tree.
Below we roughly describe the crucial observables which can be used to distinguish signal and background. We can define the kinematic observables into two categories: observables without reconstruction and observables with reconstruction. The observables without reconstruction include observables which can be directly extracted from jets in the final state. For example, the transverse momentum and invariant mass of leading two jets can be obtained once we specify the jet clustering algorithms. Event shape observables, like the H t ,ŝ, centrality, and sphericity, can also be computed. As demonstrated in Fig. 5, where the transverse momentum and invariant mass of leading two jets, the event shape variables, H t ,ŝ, and centrality are shown. The second type of observables are those which can only be obtained after reconstruction. For example, the reconstructed masses, transverse momenta, and ηs of W bosons, top quarks and b can only be obtained after we can identify all physics objects in term of our reconstruction procedure. In Fig. 6, we show the most useful and important observables which can help to discriminate signals and backgrounds, like the transverse momenta of reconstructed W bosons and top quarks, the transverse momentum of reconstructed b . Figure 6: The observables for intrinsic theoretical parameters and phase space of signals are displayed, which can be obtained by using our proposed reconstruction procedure.
For signal events, all these two types of observables are intrinsically correlated to the mass parameter of b . In contrast, for the background events there is no such a correlation. By utlizing these observables and this correlation, we use the package TMVA to perform the training process and then apply the determined weights for each events which have not seen by the training process. We have applied both MLP neural network method and the boosted decision tree method [30,31,32]. The discriminant distributions for these two MVA methods are provided in Fig. 7, which clearly demonstrate the discriminant analysis indeed works. We have also used the cut based method and observed that the MVA methods can optimize the signal and background discrimination better and improve the significance by a factor 100% or so, similar to the observation in our previous work [28] where the heavy charged Higgs boson search was studied. After using the MVA cuts, as demonstrated in Fig. 4, we can see the mass bump of reconstructed b clearly standing out from the SM background.
Sensitivity of the LHC to b
We use the analysis presented above to other values of m b from 800 GeV to 1500 GeV, where top quarks from b decay can be either intermediately or highly boosted, and we arrive at the sensitivity given in Table 3. We observe that when the b is heavier its production rate becomes smaller, which leads to a smaller significance. In Table ( Table 4: The significance and sensitivity of LHC for b production are shown, where we assume the total integrated luminosity as 200 fb −1 . We use S √ B = 2.5 to define the exclusion upper bound on the cross section.
In Fig. 8, we present the sensitivity of the LHC to the hadronic b mode with integrated luminosity 200 f b −1 and 3000 fb −1 , respectively. From this plot, we can estimate that with 3000 fb −1 dataset just using the hadronic b mode, we can either find or rule out a b up to 1.8-2.0 TeV or so. Compared with the semileptonic modes analyzed in [8], it is expected that the hadronic mode demands more luminosity due to the large SM background events, similar to the case of the hadronic mode of tt.
Discussions and Conclusions
In this paper, we have studied the full hadronic mode for the process pp → b b → tW −t W + at the LHC 14 TeV collision. The main task is to reconstruct the b from the large combinatorics and to suppress the huge QCD and tt+ jets background events, where we have found that b taggings are essential to suppress background events with large jet multiplicity from QCD. By using the top-tagger and W-tagger and some comprehensible cuts, we propose a full reconstruction procedure and demonstrate that if we could reconstruct the most important parameters of the signal, like the mass of b and transverse momentum of W bosons, etc., the hadronic mode of b could be feasible for the future LHC runs.
The current work can be directly extended for the higher energy collisions (say 100 TeV collisions). Obviously, for the signal with a fixed mass (say m b = 10 TeV), the signal will be enhanced due to the increase of collision energy and the corresponding large enhancement in the gluon fluxes. Nonetheless, more background processes may become dominant, for example, the multiple W boson final states, tt + W , tt + W W , tttt, and tW . Some of these backgrounds could have significantly large enhancement in cross sections, say tttt and tth. Moreover, the collimated W bosons from EW showers [60,61] in energetic b jets might fake the top quark taggers to some degree, which might be crucial for high energy collisions. Another challenging issue for 100 TeV collisions study is to model the multijet background events from the SM. We leave a detailed analysis for high energy collisions in our future works.
To project the sensitivity for b at higher energy collisions, it might be useful to take into account leptonic modes. If so, a top tagger with leptonic modes should be useful [37]. When combining both leptonic and hadronic modes, we expect that higher exclusion bounds for b can be achieved or a better significance can be obtained if a b is there.
We have not included the pileup effects to the top and W taggers here, which is necessary for a more realistic analysis at either LHC future runs or future high energy collisions. As demonstrated in the reference [62], the pileup effects might decrease the significance to a certain degree. Another interesting thing for high energy collisions is that when a top quark is very highly boosted (say P t > 5 TeV), the current top tagger should be improved as demonstrated in [63] by taking into account additional information from tracker system, or it might be improved from hardwares, say by increasing the granularity of detectors from 0.1 × 0.1 to 0.01 × 0.01. Obviously, studying boosted physics objects and their taggings at high energy can help us in the detector designs for future high energy collisions. | 10,215.8 | 2014-05-11T00:00:00.000 | [
"Physics"
] |
Conference-ISSS-8-A One-Dimensional Model for Photoemission Calculations from Plane-Wave Band Structure Codes
A computational method is devised for calculating angle-resolved photoelectron spectra using a plane-wave basis and repeated-slab geometry. The method is tested with a one-dimensional model with a rectangular potential well. The model parameters are adjusted to reproduce electronic structure of graphene at the Γ point of the Brillouin zone, as obtained from density functional theory. Photoemission final states with proper boundary conditions are constructed from linear combinations of supercell eigenstates such as to match the free wave at the center of the vacuum region. These states, calculated with a moderate plane-wave cut-off, agree very well with the exact wave function. The computed photoemission intensity differs strongly from the popular (single) plane-wave approximation and shows a pronounced energy dependence. [DOI: 10.1380/ejssnt.2018.49]
I. INTRODUCTION
Angle-resolved photoelectron spectroscopy (ARPES) is the most direct method for probing the band structure of crystalline solids [1].It can also be used to measure wave functions of molecules through the so-called orbital tomography method [2].While the theory of photoemission is well-established [3], computation of ARPES spectra remains a challenge for many systems.In practice, the final state plane wave (PW) approximation [2,4] is often used despite its known shortcomings [5].Photoemission final state calculations beyond the PW approximation have been done with multiple scattering and band structure methods.For metals, good results are obtained with multiple scattering theory, where the proper photoemission boundary conditions can be easily implemented, either in the layered KKR approach [3,6] or in a fully real-space scheme [7].However, the multiple scattering method is not sufficiently accurate for molecules and other covalently bonded open structures including light elements.ARPES can also be calculated by matching bulk bands to the free electron waves in vacuum via some surface potential model [8].This approach yields also good results for metal surfaces [9,10] but it seems difficult to generalize it to complex surfaces and low-dimensional systems.On the other hand, the supercell (or "repeatedslab") method with a PW basis set, can describe accurately the electronic structure of very diverse systems, including molecules, complex surfaces and adsorbates.The supercell approach has been applied to ARPES only very recently by Kobayashi et al. [11] who computed the spinpolarization of low energy ARPES from a Bi(111) surface.
Here we outline a method for obtaining final state wave functions with the proper photoemission boundary condi-tions.Our method is similar to that of Ref. [11], but there are some differences which we shall discuss below.The final states waves are expanded over a set of supercell eigenstates with different perpendicular momentum and with energy approximately equal to the chosen photoelectron energy.These waves are matched with the free photoelectron wave at the center of the vacuum region, i.e. between repeated slabs.We test this scheme with a onedimensional model which mimics the electronic structure of graphene at the Γ-point of the Brillouin zone, as shown by direct comparison with band structures obtained from density functional theory (DFT).Using a moderate PW cut-off, we obtain virtually exact wave functions for the rectangular potential well.Photoemission from the highest occupied band is calculated and found to display a pronounced energy dependence.The computed ARPES spectrum differs dramatically from that obtained in the (single) PW approximation, despite the fact that the photoemission final state bands resemble free electron bands.
II. THEORY
In the independent particle approximation, the ARPES intensity for a transition from initial state wave ψ i to final state wave ψ f is proportional to the square of the transition matrix element where A is the vector potential of the light and P is the electron momentum operator.ARPES boundary conditions are such that for points r far from the surface, the final state wave ψ f becomes a PW, ϕ p (r) = exp(ip • r), with energy ϵ p = p 2 /2m, where p is the measured photoelectron momentum.Such a final state with proper boundary conditions will be denoted ψ p .We compute both ψ i and ψ p in a supercell approach with PW basis set.Since the supercell has periodic boundary conditions in all three dimensions, which is wrong for the perpendicular direction, the supercell eigenstates must be matched to the photoelectron PW in the vacuum region.For crystal surfaces the parallel component of the crystal momentum, k || , is conserved in the photoemission process.The perpendicular component k z is not conserved, so we develop the final state over a number of Bloch waves with different k z .In this paper we introduce a matching technique for the one-dimensional case, where the wave functions are only functions of z, and we put k = k z .The general method in three dimensions will be presented in a forthcoming publication.Inside the supercell of length c, the photoelectron wave ψ p (z) is expanded over a set of Bloch eigenfunctions ψ nk of energy ϵ nk , where the prime indicates that the sum is restricted to a few states with ϵ nk ≈ ϵ p .The coefficients α nk are found by matching the wave amplitude and the first derivative of ψ p , to the free wave ϕ p (z) = exp(ipz) at the cell boundary z 0 is chosen at the center of the vacuum region between repeated slabs.In one dimension there are only two matching equations ( 3), and so we include only two band states (nk = 1, 2) in the sum (2).The supercell periodicity introduces small gaps in the band structure, as it is well known from the Kronig-Penney model [12] and confirmed in our calculations below.Moreover, in numerical practice, the Brillouin zone is sampled, and thus the energy spectrum ϵ nk is discrete.As a consequence, energy conservation between inner and outer waves can in general only be satisfied approximately, i.e. the states included in the sum (2), have energies ϵ nk slightly different from ϵ p .Here we select the two band states with energies just below and just above ϵ p .The precision with which the condition ϵ nk = ϵ p can be met, depends on the number of k-points and the width of the band gaps, which scale inversely with the supercell size c.We use a PW basis, so the eigenfunctions ψ nk are written as where G is a reciprocal lattice vector and C nk G are the PW amplitudes.Inserting (4) into (3) yields the following 2×2 linear system for the coefficients α 1 , α 2 of the two selected band states. ( ) The wave function ψ p in Eq. ( 2) with coefficients α 1,2 so obtained, is a continuum wave with proper photoemission boundary conditions.In the application below, we use a simple rectangular potential well and choose parameters appropriate for normal emission from graphene.The present method is similar to the one recently proposed by Kobayashi et al. [11] but there are some clear differences.While Kobayashi et al. determine the Bloch wave coefficients by numerically minimizing the difference between the combined Bloch wave and the plane wave in a finite range of the vacuum region, we perform a direct matching of wave functions on a single plane in vacuum.With our method, the exact wave function can in principle be recovered as we show in Fig. 3 for a simple model potential.In the method of Ref. [11], when the matching region is chosen too small, the result will be inaccurate.If it is chosen very large, the supercell becomes very large and thus the numerical calculation becomes much more heavy.This problem is absent in our method.The matching can be done at any plane in the vacuum region and it does not increase the supercell size.Both methods should have advantages and shortcomings and so it is interesting to pursue both approaches in the future.
A. Density functional theory calculation of graphene
In order to find realistic parameters for graphene, we have performed a DFT calculation in the repeated slab geometry using the plane wave code VASP [13].The supercell lattice parameter c is set to 20 Å, which is large enough to avoid interactions between periodic images and to get free electron-like states at high energy.The origin of the energy scale is chosen as the vacuum level, determined at the center of the supercell between graphene layers.Figure 1 (E > 0) follows closely the free electron result with √ E dependence.This shows that the vacuum is large enough and the supercell continuum states are sufficiently complete.
B. One-dimensional model with rectangular potential well
We test our method with a 1D model and a rectangular potential well.The width (2.1 Å) and depth (−52 eV) of the potential well are chosen such as to roughly fit the k z -bands of the DFT graphene calculation at the Γpoint.The model is solved by numerical diagonalization of the hamiltonian, with a PW basis and periodic boundary conditions with a period of c = 20 Å as in the DFT calculation.The PW cut-off was set to 1200 eV and the one-dimensional 1st Brillouin zone was sampled with 34 k-points.As seen in Fig. 2, both the continuum bands and the bound state at −7 eV fit the DFT bands very well.In the DFT band structure, there are a few additional continuum bands with vanishing k z dispersion (thin lines in Fig. 2 a).As these states have zero group velocity along z, they do not contribute to the photocurrent and can be ignored for the present problem.
Figure 3 shows the wave functions obtained with the present matching method (red lines) for (a) the bound state ψ i at E i = −7.2eV and (b,c) the final continuum state ψ f at E f = 14.0 eV = E i + ℏω(He I).The wave ψ f is compared with the free wave (thin black line) and the exact solution (dashed blue line) of the (non-periodic) single well problem solved in the usual way by matching the plane wave eigenstates of exact kinetic energy in each region.The numerical wave function is almost identical with the exact wave.This shows that the present match- FIG. 3. Bound state (a, ψi at Ei = −7.2eV) and continuum state (b,c ψ f at E f = 14.0 eV) wave functions (red lines) obtained by numerical solution of the one-dimensional periodic potential model with PW basis set.ψ f is compared with the exact wave function of the non-periodic potential well (dashed blue lines) and to the free wave (thin black lines).The vertical dashed lines indicate the borders of the potential well.
ing method yields accurate photoemission wave functions with a moderate PW cut-off (∼ 1000 eV) comparable to ground state calculations.However, the number of k zpoints must be taken much larger than in ground state calculations (where a single k z is sufficient for well separated slabs) in order to obtain photoelectron waves of all possible perpendicular momenta.We also see from Fig. 3, that inside the potential well, the exact final state differs strongly from the free wave (thin black line), which highlights the shortcoming of the PW approximation.Volume 16 (2018) Ono, et al.
C. Photoemission intensity calculation
From the wave functions obtained with the matching method, we have calculated the photoemission intensity using Eq. ( 1) with A=e z .The intensity is plotted in Fig. 4 (red lines) as a function of final state energy.The curve shows some numerical noise below 20 eV, indicating that for some photoelectron energies, our simple scheme of selecting two band states in Eq. ( 2) is not very accurate.We are currently working on an improved method with a larger set of trial Bloch waves.For comparison, Fig. 4 also shows the photoemission intensity obtained in the (single) PW approximation (blue lines).At any given photon energy, the calculated intensities differ dramatically.In the important ultraviolet region below 40 eV, the energy dependence of the PW approximation is opposite to that of the matching method.This clearly shows that the PW approximation cannot be trusted for ARPES intensity calculations [5], especially at low energy.Interestingly, however, on a larger energy scale (Fig. 4, inset) the energy dependence looks similar, except for a shift of about 60 eV.This can be understood from the fact that the kinetic energy inside the potential well is 52 eV larger than outside.As the initial state is essentially localized inside the potential well, only the inner region matters for the photoemission calculation.Thus the correct intensity can roughly be reproduced using the PW approximation with a final state energy increased by about 50 eV.At present we do not know whether this is a particular features of the rectangular well potential, or whether such energy scaling also holds for other potential shapes.
IV. CONCLUSIONS
We have outlined a method for ARPES calculations from PW band structure codes and have successfully tested it with a simple one-dimensional model.The model parameters have been chosen to fit the k z band dispersion of graphene at the Γ-point obtained from a DFT calculation in the repeated slab mode.The DFT density of states above the vacuum level roughly follows the electron curve which shows that the PW basis is sufficiently complete.In the 1D model, photoemission final states are obtained by matching the proper combination of Bloch waves with the outer free wave.These numerical waves agree very well with exact solutions of the rectangular well potential.The photoemission intensity has a strong energy dependence and differs dramatically from the (single) PW approximation for any given energy.The final state band structure of the 1D model reproduces quite well the DFT bands at the chosen k || point (Γ), indicating that the present model calculation is realistic, and that the matching method can be extended to wave functions obtained from DFT supercell calculations in real 3D systems.
FIG. 1 .
FIG.1.Density of states (DOS) of graphene obtained from density functional theory (red solid line) compared with free electron DOS (dashed blue line).
FIG. 2 .
FIG. 2. Comparison of band structures.(a) kz band dispersion at the Γ-point of graphene from DFT. Thin lines indicate dispersionless bands.EF is the Fermi-level.(b) Bands obtained in the 1D model.Ei and E f indicate the levels used in Fig. 3. (c) Free electron bands.
FIG. 4 .
FIG. 4. Photoemission intensity from bound state at Ei = −7.2eV as a function of final state kinetic energy.Present wave function matching method (red) versus PW approximation (blue). | 3,311 | 2018-03-31T00:00:00.000 | [
"Physics"
] |
Continuously revised assurance cases with stakeholders’ cross-validation: a DEOS experience
Recently, assurance cases have received much attention in the field of software-based computer systems and IT services. However, software changes very often, and there are no strong regulations for software. These facts are two main challenges to be addressed in the development of software assurance cases. We propose a method of developing assurance cases by means of continuous revision at every stage of the system life cycle, including in operation and service recovery in failure cases. Instead of a regulator, dependability arguments are validated by multiple stakeholders competing with each other. This paper reported our experience with the proposed method in the case of Aspen education service. The case study demonstrates that continuous revisions enable stakeholders to share dependability problems across software life cycle stages, which will lead to the long-term improvement of service dependability.
INTRODUCTION
Assurance cases are documentation-based engineering with structured arguments on safety and dependability.Originally, assurance cases were developed in the field of safety engineering for public transportation and industrial plants, and they have been adopted broadly as a documentation standard (Bloomfield & Bishop, 2010).Many regulators, especially in EU countries, are likely to validate assurance cases before the developed systems are deployed.
Recently, due to increased attention to safety and dependability in software, many developers have become interested in the application of assurance cases for software.However, software often changes over time and even needs to change after deployment.The emerging style of DevOps development suggests that it would be difficult to separate developments from service operations.This also makes it difficult for a regulator to assess assurance cases, thereby resulting in the absence of strong regulators for software in general.
To overcome these difficulties, the DEOS process (Tokoro, 2015) was developed with the life cycle maintenance of assurance cases.The idea is straightforward: assurance cases are revised in a synchronized way as software updates.An arising question is as follows: who validates such revised assurance cases, even in the post-development phase?The answer is still unclear in the DEOS process.In this paper, we assume that stakeholders who are competing with each other are motivated to validate cases because they will suffer directly from others' faulty claims in assurance cases.However, many questions remain.Can non-expert stakeholders learn about assurance cases and then join dependability arguments?Is the validation strong enough?
To confirm these questions, we organized a case study experiment, the Aspen project, in which multiple stakeholders (e.g., developers, operators, and users) are involved in the software life cycle from development to service operation.Throughout the life cycle, all stakeholders will have participated in arguing for or against the dependability using assurance cases written in Goal-Structuring Notation (GSN) (Kelly & Weaver, 2004), a standard notation of assurance cases.
Unfortunately, service failures occurred during the experiment period, although all the stakeholders made extensive arguments in favor of GSN notations.The occurrence of service failure does not imply the weakness of stakeholders' cross-validation, because system failure happened in a case of regulator validations.Rather, the analysis of the failure case gives us a useful insight: the structured dependability arguments in GSNs make it easier to find and share dependability problems across organizations.Since transferring dependability problems is a missing part of software life cycle iteration, continuously revised assurance cases can be a new approach to the long-term dependability of ever-changing software.
This paper focuses on the report of the Aspen case study.The rest of the paper proceeds as follows: 'What Are Assurance Cases?' introduces assurance cases and reviews-related work; 'Argumentation Architecture' presents our basic ideas for developing assurance cases for software; 'Experimental Setup: Aspen Project' describes the Aspen project; 'Aspen Cases' examines the assurance cases that were developed in the Aspen project; 'Lessons Learned and Discussions' discusses lessons learned; and 'Conclusion' concludes the paper.
WHAT ARE ASSURANCE CASES?
Assurance cases are document-based engineering with structured arguments related to safety and dependability (Avizienis et al., 2004).In this paper, we use the term dependability in a broader sense related to safety.The documents of assurance cases are structured to transfer the dependability confidence of products and services to others, such as regulators and third-party organizations.To make the confidence explicit, assurance cases are usually argued in the form of claim-argument-evidence (CAE).Figure 1 illustrates the conceptual structure of assurance cases with the CAE arguments.
For example, consider the claim that a system is adequately dependable for operating in a given context.The argument explains the available evidence, showing how it reasonably supports the claim.The top-most claim is decomposed into a series of sub-claims until these can be solved with evidence.Since the arguments make the rationale for the claim explicit, they are rigorous, justified, defensible, and transparent.
Due to the high transparency of dependability arguments, assurance cases generally serve as an efficient risk-communication tool between organizations.However, the most practically used scenario is transferring the developer's confidence to a regulator or a
Arguments
Evidence supporting their claims third-party company to assess the conformance of dependability regulations (Graydon et al., 2012).Through this assessment mechanism, the regulator forces the developer's product to meet its regulations, and then the user trusts the developer's product due to the regulator's authority.In contrast, the self-assessment of conformance or the absence of dependability regulations makes assurance cases self-righteous and less confident.
Related work
Our work builds on many excellent existing ideas for the development of assurance cases in software, including life cycle developments (Graydon, Knight & Strunk, 2007), argument patterns (Weaver, McDermid & Kelly, 2002;Hawkins et al., 2011), and reviewing arguments (Kelly, 2007;Yuan & Kelly, 2012).In particular, Graydon, Knight & Strunk (2007) proposed a closed approach to integrating assurance into the development process by co-developing the software system and its assurance case.Hawkins et al. extensively studied the assurance aspect of the software process (Hawkins et al., 2013) and software evolution (Hawkins et al., 2014).A clear, new idea presented in this paper is the use of accountability (by dependability arguments with stakeholder identity), which allows multiple competing stakeholders to share dependability problems across the life cycle stages.
In general, assurance information needs to be kept confidential in safety-critical systems (Bloomfield, 2013).However, many experimental research reports have been published for researchers as in an unmanned aircraft (Denney, Habli & Pai, 2012), automobiles (ISO 26262) (Ruiz, Melzi & Kelly, 2015), autonomous vehicle and aircraft safety critical software (Hawkins et al., 2011), generic infusion pumps (Kim et al., 2011), pacemakers (Jee, Lee & Sokolsky, 2010), and health IT services (Despotou et al., 2012).In these reported areas, there exists strong regulators who validate the safety of products and services, and the development of reported assurance cases is initially motivated for their regulators.In comparison, our experience report is unique in terms of neither regulators nor safety standards.How assurance cases to be developed for improved software without regulators is an interesting open question for software practitioners (Tokoro, 2015).
ARGUMENTATION ARCHITECTURE
This section describes our ideas on how to use assurance cases in software-based IT systems with no strong regulator.
Sharing dependability arguments
Our initial motivation comes from the risk of miscommunication between stakeholders, such as developers and operators, who separately act in distinct phases of the life cycle.In other words, limitations discussed during software development are quite useful for operators attempting to deliver the correct services, but they are unseen at the time of operation.On the contrary, discussions at the time of operation can provide useful feedback for further development.Sharing such discussions, which are focused on dependability, is demanded extensively to improve the long-term dependability of the products and services.
Our aim in the use of assurance cases is to share dependability arguments among stakeholders throughout the life cycle.As introduced in 'What Are Assurance Cases?', the arguments are well structured and more likely to inspire confidence in stakeholders due to the supporting evidence.This would suggest that assurance cases serve as a good foundation for sharing focused knowledge and risk communications.
The argumentation architecture needs to change slightly when we attempt to apply it between (a) one stakeholder and another and (b) many stakeholders to many others.First, the top claim must represent a common goal and assumptions that are shared among all stakeholders.We decompose the common claim into sub-claims so that each stakeholder can separately lead his or her active part of the dependability arguments.
The top claim is decomposed by stages in the life cycle of products and services.Then, we decompose each stage claim by stakeholders if multiple acting stakeholders exist in the same stage.Each stakeholder has to provide available evidence that supports dependability claims that are part of the common goal.
Staging in the lifecycle varies from project to project, but we refer to the following stages in this paper.Note that the abovementioned stage decomposition is based on the open system dependability (Tokoro, 2015) that we proposed in the JST/DEOS project.It is distinct in its evolution stage, when all stakeholders argue for the continuous improvement of services beyond the lifetime of a single system operation.
Accountability, rebuttals, and revision
Currently, most software-based IT services run under no regulation.As described in 'What Are Assurance Cases?', the absence of strong regulators may reduce the practicality of assurance cases.This is a challenge to be avoided in practice.The first idea to confront this problem is the use of the concept of accountability (Haeberlen, Kouznetsov & Druschel, 2007); accountability is widely used to build trust and reputation among competing individuals and organizations by exposing failures.In the context of assurance cases, we can integrate the concept of accountability by recording the stakeholder's identity in every element of assurance cases.That is, the stakeholder's identity can be used to trace who makes a faulty claim or who gives faulty evidence when a problem occurs.In general, this results in strong incentives to avoid faulty claims and evidence.
Claim
In addition to stakeholder accountability, we include a form of rebuttal in the dependability arguments.In the context of assurance cases, a rebuttal is a challenge to a claim or an objection to the evidence, usually noted in the review process.Rebuttals do not remain during the assessment process because they need to be solved prior to certification.In the case of the absence of a regulator, a rebuttal is not strong enough to enforce modification.Unsolved rebuttals are considered conflicts.If the conflicts remain between stakeholders, the claim containing the rebuttal also is regarded in terms of the stakeholder agreements.Note that the rebuttals are recorded with the stakeholder's identity for accountability.
Based on the recorded rebuttals, we use cross-validation between stakeholders instead of third-party reviewers, since stakeholders in part compete with each other (e.g., a developer wants reduced costs for development, but this makes improperly developed systems a potential risk).A faulty claim often becomes a potential risk for other stakeholders.Naturally, non-rebuttal claims are regarded as approved by all stakeholders with some sharable responsibility when a problem occurs.This also leads to other incentives to make rebuttals to others' claims.Figure 2 illustrates our proposed argumentation architecture with life cycle decomposition and stakeholder identities.
More importantly, recall that our aim is to facilitate sharing dependability problems between stakeholders, not to facilitate competition among them.The developers and the operators can change software or service operations if they agree on the given rebuttals.In addition, they also are allowed to revise the related assurance cases if their practice is changed.This results in an iterative process that enables us to better capture the ever-changing nature of software and maintain the dependability of changing software.
Note that we assume that all revised versions of assurance cases can be maintained by a proper version control system.AssureNote, which used in this experiment, has been developed for this purpose.
EXPERIMENTAL SETUP: ASPEN PROJECT
The Aspen project is our organized experiment as a part of the JST/DEOS project (Tokoro, 2015) to investigate the life cycle maintenance of assurance cases without any regulators.The Aspen project includes not only the development of assurance cases across different organizations but also Aspen's software development and service operation with DEOS industrial partners.This section describes the experimental design in the Aspen project.
System and service overview
Aspen is an online education system that provides exercises on programming to students via the Web. Figure 3 provides the overview of the Aspen service.The Aspen system are not so unique and consists of multiple servers, including Apache Web servers, MySQL servers, and Zabbix monitor servers, which run on Linux operating systems.All of the software that constitutes the Aspen system are written in scripting languages such as Python and JavaScript.Due to the Agile feature of these languages, the Aspen system is updated often, even after its deployment.
Aspen is a typical Web-based system, not a safety-critical system, which is the system on which assurance cases mainly have been developed so far.However, Aspen involves several dependability attributes (Avizienis et al., 2004) that are commonly required in software-based IT services: • Availability: the service always will be available to the users (i.e., students).
• Reliability: no hardware or software failures occur during provision of the service.
• Integrity: programming assignments supplied by the owner do not disappear.
• Privacy: personal information is not disclosed to unauthorized parties.
Documentation and tool supports
In the Aspen project, we use Goal Structuring Notation (Kelly & Weaver, 2004) to share assurance cases among stakeholders.GSN is a standard argumentation notation of assurance cases in safety-critical industries.GSN consists of four principal elements, goal (depicted as a rectangle), strategy (parallelogram), evidence (oval), and context (rounded rectangle), as shown in Fig. 4. The goal element is used to state a claim that a system certainly has some desirable properties, such as safety and dependability.The evidence element is some piece of material to support that the linked claim is true.The goal without linked evidence is called undeveloped.
As in the CAE notation, a goal is decomposed into sub-goals until a point is reached where claims can be supported by direct reference to available evidence.The strategy element is used to state a reason for claim decomposition.The context element is used to state an assumption (the system scope and the assumed properties).There is no special support for stating a rebuttal.We regard the context element linked to the evidence as the rebuttal element.
In the experiment, we used AssureNote (Shida et al., 2013), a Web-based authoring tool that allows multiple users to share a GSN document via the Web. Figure 5 is a screenshot of AssureNote.In AssureNote, all GSN elements are automatically recorded with the user identity under the version control of GSN elements.
Stakeholders
Another main aim of the Aspen project is to examine the effect of assurance cases in the absence of a strong regulator.As described in 'Argumentation Architecture', we need to set up some competing relationship between stakeholders.
All stakeholders were selected from different institutes.First, we contracted two different firms separately: one that took charge in software development and the other in service operation.Second, we asked an instructor who had adopted the Aspen system in her classroom to join the experiment as a stakeholder.The author plays a coordinator role, not a regulator role throughout the whole stage.The stakeholders involved in the Aspen project are listed below.
• Owner: The author • Developer: A programmer working for a software development firm • Operator: A system engineer with more than 10 years' experience with Web-based service operations • User: An instructor who use the Aspen in her classroom.
In this paper, we identify stakeholders by role names-Owner, Developer, Operator, and User-for readability.However, on the assurance cases, stakeholders are identified by a personal name for the sake of accountability.
Development procedure
In the experiment, we attempt to develop assurance cases in parallel with the development and service operation of the Aspen system.All assurance cases and other communications between stakeholders are written and spoken in Japanese.
In the planning stage, the owner defines the top claim, which includes dependability goals and assumptions, for which the Aspen system is assumed to deliver correct services for the users.Following the planning stage, we undertake the Aspen system with the following procedures: • The developer claims that the developed system meets the owner's dependability goals with supporting evidence.
• The operator, the user, and the owner review the developer's claims and agree or disagree.
• The operator, based on the developed system, claims that the system operation meets the owner's dependability goals with supporting evidence.
• The developer, the user, and the owner review the operator's claims and come to agreements on the conflicted claims.
• Any stakeholder can revise the assurance cases if they contain any insufficiencies or flaws.
As shown above, we focus on dependability-related issues and avoid general issues with software implementations and operating procedures.When we handle the disagreement, we ask all stakeholders to meet together at the same place to agree on the conflicts.
ASPEN CASES
The Aspen cases were developed with the method that we proposed in the 'Argumentation Architecture' and 'Experimental Setup: Aspen Project' sections.This section reports how the arguments are organized with a fragment of GSNs and excerpted from the developed assurance cases.
Overview
First, we overview the statistics of the Aspen cases.As we described in 'Stakeholders1', the Aspen cases are written in GSN.We first gave the top goal, which was decomposed into the Development stage, the Service stage, and the Evolution stage with common assumptions.The GSNs were revised 40 times throughout the Aspen project.Here we use #n to represent the nth revision.The GSN document grew from four elements (at #1) to 134 elements (at #40).We identify the major revisions as follows: Figure 6 shows the growth of the Aspen cases in the number of GSN elements: goals, contexts, evidences, and rebuttals.The increase in contexts suggests that the reduced ambiguity of the goals and the increase of evidence reduce the reduced uncertainty in their dependability claims.
Development agreement
The developer started the argument with the claim ''Aspen is dependable'' and decomposed it into sub-claims by dependability attributes (cf.Aspen is available, integral, safe, etc.).The forms of evidence that the developer provided were mostly other external experience reports (collected from the Internet).Some goals included a lack of evidence.Note that a lack of evidence does not directly imply a lack of dependability, but it does indicate uncertainty about dependability.
Figure 7 illustrates the fragment with the developer's claim that the software is integral in data storage.One could consider that Evidence E22.1 was not reasonable evidence to support Claim G22.Likewise, the operator pointed out a risk of hardware failure in the disk storage.However, there was not enough time to change the storage system.Instead, the operator agreed to fault tolerance at the time of operation.In the end, the operator made nine rebuttals to the developer's claim prior to the operations.
Service agreement
In the operation stage, we focus only on fault mitigation and failure recovery.The operator led the arguments of this part using the fault-avoidance pattern, which consists of the following two parts: • The symptom of a failure (an error) is detectable (by monitoring).
• The detected symptom is mitigated before the service stops.
The completeness of fault-avoidance analysis is important but not pursued in the experiment, in part because we want to evaluate the iterative updates of assurance cases during the operations.
Figure 8 is a fragment of assurance cases arguing about the server's availability.Note that some embedded parameters are used for operation scripts (Kuramitsu, 2013).One could consider the given evidence questionable, but the user and the owner trusted the operator's claim without any doubt due to their limited knowledge.They did not make any rebuttals against the operator, except for some help-desk support in case of service failures.
Failure recovery
We encountered several service failures while running the Aspen system.Since unexpected failures imply faulty arguments, the operator or the developer needs to revise the assurance cases.
Here, we highlight a service failure that occurred in the middle of the classroom.This failure appeared only when students used Aspen in the classroom.The system monitor indicated that the server's operating system was unexpectedly down.At first, the operator suspected that there were unknown bugs in the Aspen system.Unfortunately, the developer found some bugs that seemed related to the service failure.If there were no assurance cases, they used an incorrect method to recover the service failure.
In reviewing assurance cases, the claim ''the servers can scale out'' was overconfident.The operator never tested the server in any network traffic settings.However, no one pointed out that this claim seemed faulty.After the server problem occurred, the operator recognized that the scale-out setting was incapable of handling simultaneous access by 40 students in the classroom.The instructor strongly requested that the operator should increase the servers as the operator had claimed in the assurance cases.
Another serious dependability problem was found later in the context of the top goal, which described common assumptions about the Aspen system.Originally, the Aspen system was assumed to allow 100 students to submit their assignments from home computers.Based on this assumption, the maximum simultaneous access was estimated to be at most five connections.The number of students in the classroom was fewer than 100 students, but the density of access traffic differed from the estimated patterns.In other words, the top-goal assumption was a sort of bug, which resulting in rechecking all given evidence.
System evolution
The Aspen project ran for two years.In the second year, the Aspen system evolved with the following major updates: • The adoption of Moodle, an open-source solution to reduce in-house development • A system movement to Amazon Web Services (a standard cloud computing platform).
These system updates were not random but derived from several dependability goals and potential risks that were argued in the revised assurance cases.More importantly, all stakeholders, including those who were newly involved in the Aspen projects, could share the justification of these system updates in terms of dependability improvements.Compared to unstructured e-mail communications, the GSN-formed arguments made it easier to trace dependability problems that actually happened or were expected in the first year.
LESSONS LEARNED AND DISCUSSIONS
This section describes lessons we learned throughout the Aspen case in the form of answering research questions.
(Question 1). Do non-experts join dependability arguments with GSNs?
Yes.For all of the participants, the concept of assurance cases was totally new, and they were suspicious of the assurance cases' benefits.We gave them about a 1-hour technical lecture on the notation of GSN (not the concept of assurance cases itself.)This short lecture and a Web-based GSN viewer were all we prepared for participants to read GSNs for dependability arguments.Note that organizing dependability arguments is a known difficulty according to Bloomfield & Bishop (2010).We prepared several simple argument patterns, which are described in 'Experimental Setup: Aspen Project'.Due to the argument patterns, arguments grew in a well-structured way.
(Question 2). What was the hardest part in the development of continuously revised assurance cases?
Collecting acceptable evidence for their dependability claims was difficult and costly.In part because the assurance cases were new for both the developers and the operators, they did not prepare any forms of evidence in their process.For example, the developers performed many software tests as usual, but these test results were far from those requested in the non-functional arguments.Neither the developers nor the operators wanted to spend extra resources for evidence, while competing stakeholders always requested much more evidence.Perhaps dependability guidelines are necessary to reach agreement on proper forms and levels of evidence.
(Question 3). Did stakeholders really validate others' claims?
Yes, they were willing to review and tried to validate them.Rebuttal serves an enforced communication vehicle between stakeholders.One reason for their many responses was that we introduced some penalty (e.g., sharing responsibilities in failure cases) for no-rebuttal claims.This penalty seemed unrealistic but forced all stakeholders to find faulty claims.
The activity of cross-validation can be measured by the number of revisions and the growth of GSN elements: • 10 revisions for the development claims • two revisions for the operation claims.
The development claims were revised more often than the operation claims.The difference comes mainly from the stakeholders' expertise.The users were likely to trust the operator's claims and evidence.
(Lesson 5). Is the stakeholder cross-validation strong enough?
The answer is that the strength depends on stakeholders' expertise.The dependability arguments between developers and operators seemingly worked.System failures that occurred in the Aspen system were caused by bad operations, not a flaw in the developed software.On the other hand, the users lacked the knowledge of service operations, and they could not point out any weaknesses in the operators' claims documented in the assurance cases.However, the faulty claims were costly in cases of system failures because the users strongly requested the fulfillment of the operator's claims as documented.We expected that the GSN documentation became a strong incentive for operators to avoid faulty claims.In reality, the costs of collecting evidence overwhelmed such incentives.
(Question 6). Is the development of assurance cases useful in software?
The answer is positively yes.Our finding in the case analysis of failure recovery suggests that the developed assurance cases make it easier to find dependability problems throughout structured arguments in GSNs.Even if we are not able to avoid the service failure the first time, the dependability problems can be transferred clearly in the redevelopment phase.Since transferring dependability problems across the organization is a missing part in dependability engineering, the contentiously revised assurance cases can bridge the missing part.
CONCLUSION
Recently, assurance cases have received much attention in the field of software-based computer systems and IT services.However, software often changes, and there are no strong regulations for software.These facts make the use of software assurance cases more difficult.We proposed a development method for assurance cases with stakeholder cross-validation at every stage of the system life cycle, including in operation and service recovery in a case of system failure.
This paper reported our practitioner experience based on the Aspen project.As we expected, stakeholders competing with each other were well motivated to find the faulty claims of the others in the GSN documents.This improves the quality of dependability arguments.Unfortunately, the stakeholder cross-validation was not able to avoid simple system failures in advance.The case analysis of failure recovery with assurance cases suggests that dependability problems can be easily transferred in a structured way across stakeholders and organizations.Since transferring dependability problems is an important missing part of long-term dependability, continuously revised assurance cases may serve as a potential new approach to the long-term improvement of service dependability.In future work, we will investigate the dependability effect of assurance cases from a longer-term perspective.
Figure 1
Figure 1 Argument structure of assurance cases.
•
Planning stage (requirement elicitation and architecting) • Development stage (coding and testing) • Operation stage (service design and failure recovery) • Evolution stage (change accommodation).
Figure 2
Figure 2 Cross-Validation and Agreements on Conflicts.
Figure 3
Figure 3 Overview of Aspen system.
Figure 6
Figure 6 Growth of assurance cases in GSN elements.
Figure 7
Figure 7 Example of a rebuttal by the operator's review. | 6,210.4 | 2016-12-19T00:00:00.000 | [
"Computer Science"
] |
The Marker of Tubular Injury, Kidney Injury Molecule-1 (KIM-1), in Acute Kidney Injury Complicating Acute Pancreatitis: A Preliminary Study
Acute pancreatitis (AP) may be associated with severe inflammation and hypovolemia leading to organ complications including acute kidney injury (AKI). According to current guidelines, AKI diagnosis is based on dynamic increase in serum creatinine, however, creatinine increase may be influenced by nonrenal factor and appears late following kidney injury. Kidney injury molecule-1 (KIM-1) is a promising marker of renal tubular injury and it has not been studied in AP. Our aim was to assess if urinary KIM-1 may be used to diagnose AKI complicating the early stage of AP. We recruited 69 patients with mild to severe AP admitted to a secondary care hospital during the first 24 h from initial symptoms of AP. KIM-1 was measured in urine samples collected on the day of admission and two subsequent days of hospital stay. AKI was diagnosed based on creatinine increase according to Kidney Disease: Improving Global Outcomes 2012 guidelines. Urinary KIM-1 on study days 1 to 3 was not significantly higher in 10 patients who developed AKI as compared to those without AKI and did not correlate with serum creatinine or urea. On days 2 and 3, urinary KIM-1 correlated positively with urinary liver-type fatty acid-binding protein, another marker of tubular injury. On days 2 and 3, urinary KIM-1 was higher among patients with systemic inflammatory response syndrome, and several correlations between KIM-1 and inflammatory markers (procalcitonin, urokinase-type plasminogen activator receptor, C-reactive protein) were observed on days 1 to 3. With a limited number of patients, our study cannot exclude the diagnostic utility of KIM-1 in AP, however, our results do not support it. We hypothesize that the increase of KIM-1 in AKI complicating AP lasts a short time, and it may only be observed with more frequent monitoring of the marker. Moreover, urinary KIM-1 concentrations in AP are associated with inflammation severity.
Introduction
Acute pancreatitis (AP) is a common acute gastrointestinal inflammatory condition requiring hospital treatment. In 15%-20% of patients, the severity of inflammatory response may lead to organ injury and transient or persistent organ failure. Severe acute pancreatitis (SAP) is diagnosed in patients with organ failure lasting over 48 h, and is associated with substantial mortality [1,2].
AP is initiated by uncontrolled activation of pancreatic enzymes, including trypsin. The injury to pancreatic cells (autodigestion) induces inflammation. Moreover, early events in AP involve nuclear factor κB activation in pancreatic acinar cells, with resulting cytokines' production [3]. Local inflammation develops, self-limited in mild cases, and followed by systemic inflammation in severe AP. Neutrophil recruitment, cytokine storm, oxidative stress, endothelial dysfunction, and injury leading to increased vascular permeability and hemodynamic complications in severe cases are the features of systemic inflammation that may lead to organ dysfunction including lungs, cardiovascular system, and kidneys [1,2]. Acute kidney injury (AKI) is among the most common complications of SAP [4,5]. It may develop in early stages as a result of dehydration, increased vascular permeability, fluid redistribution, and acute inflammation, however, it may also be a late complication related to sepsis [4].
AKI is defined by Kidney Disease Improving Global Outcomes (KDIGO) criteria as a ≥50% increase in plasma creatinine concentration over baseline within 7 days or an increase in serum creatinine by 0.3 mg/dL within 2 days or a decreased (<0.5 mL/kg/h) urine output lasting at least 6 h [6]. In the course of AP, AKI is associated with adverse prognosis and mortality up to 40% [4,5], however, much better outcomes have been reported when AKI was an isolated complication of SAP [7]. AKI may also result in chronic kidney disease, moreover, acute-on-chronic kidney injury is associated with a high risk of end-stage renal disease [8,9]. Although currently the diagnosis of AKI is based on serum creatinine increase, creatinine is recognized as a late marker of AKI, significantly increasing after 24-36 h from kidney injury [10,11]. Serum creatinine increase is not specific to kidney injury, rather, it is a marker of decreasing kidney function. Therefore, there is a need for laboratory markers that enable early detection of renal injury.
Kidney injury molecule-1 (KIM-1) is a promising biomarker of kidney injury. Its expression in proximal renal tubular epithelial cells (mainly S3 segment) is highly elevated at the early stage of AKI [12,13] and increasing urinary KIM-1 levels are associated with more advanced renal injury [8]. KIM-1 is a transmembrane glycoprotein with molecular mass of 104 kDa, a member of the transmembrane immunoglobulin and mucin domain (TIM) family of proteins and immunoglobulin superfamily [13,14]. Normal kidney tissues express trace KIM-1, while increased KIM-1 expression has been observed in AKI resulting from ischemia, hypoxia, or toxicity [8]. Moreover, increased expression was reported in tubulointerstitial nephropathies and polycystic kidney disease [8,15]. The ectodomain of KIM-1 (90 kDa) is cleaved by matrix metalloproteinases and released into the urine, and this mechanism is also upregulated in proximal tubule injury [16]. In a meta-analysis of 11 studies including almost 3000 patients, Shao et al. [14] estimated diagnostic sensitivity and specificity of KIM-1 in AKI for 74% and 86%, respectively. However, they also reported that urine KIM-1 concentrations may be significantly influenced by comorbidities, including diabetes, hypertension, and atherosclerosis [14].
KIM-1 seems to have several advantages over other markers of kidney injury. It was shown to increase in urine shortly after injury, before renal tubular damage could be observed in histological examination [17]. Huang et al. [18] confirmed that KIM-1 was increased within 24 h after kidney injury. Han et al. [19] reported that urinary KIM-1 can differentiate ischemic AKI from prerenal azotemia and chronic kidney disease, and its urinary concentrations were not influenced by urinary tract infections.
To our best knowledge, KIM-1 has not been evaluated in AKI complicating acute pancreatitis. The aim of this preliminary study was to verify if KIM-1 may be a useful laboratory marker in the clinical setting of AKI developing in the early phase of AP.
Patients
The retrospective study included 69 patients (51 men, 18 women) with the diagnosis of AP admitted to the Department of Surgery, Complex of Health Care Centers in Wadowice, Poland (a secondary care hospital), between March 2014 and December 2015. The diagnosis of AP was based on revised 2012 Atlanta classification, that is, AP was diagnosed when at least two of the following criteria were met: abdominal pain suggestive of AP; AP signs in abdominal imaging (magnetic resonance imaging, contrast-enhanced computed tomography, or ultrasonography); serum amylase or lipase above three times the upper reference limit [20]. Patients were recruited within 24 h from hospital admission according to the study protocol. The study included patients with symptoms of AP lasting shorter than 24 h before hospital admission. Patients with chronic pancreatitis, active cancer, or chronic liver diseases (viral hepatitis, liver cirrhosis) were excluded from the study. Only the patients who provided written informed consent were included.
The study protocol included collection of demographic and clinical data described below, and collection of blood and urine samples during the first three days of hospital stay. Our primary interest in this study was whether urinary KIM-1 measured in samples collected on days 1 and 2 from admission enables the prognosis or diagnosis of AKI developing in the early phase (the first week) of AP. In a part of patients, KIM-1 was also measured in urine collected on day 3, to study dynamic changes in the urinary concentrations.
The study protocol was approved by the Bioethics Committee of the Beskidy Medical Chamber, Bielsko-Biała, Poland (approval number 2014/02/06/1 issued on 6 February 2014).
The demographic and clinical data were collected on recruitment and during the hospital stay of the patients. These included information on age and sex, comorbidities (cardiovascular disease, diabetes, renal disease, body mass index >30 kg/m 2 , i.e., obesity), AP etiology, imaging findings of pancreatic necrosis, systemic inflammatory response syndrome (SIRS) during the first three days of hospital stay, organ failure, intensive care unit (ICU) treatment, use of surgery or parenteral nutrition during the hospital stay, length of hospital stay, severity of AP defined according to 2012 Atlanta classification [2], and outcome.
The clinical and laboratory values on the first day of hospital stay were used to calculate the bedside index of severity in AP (BISAP) [21]. The data obtained during the first 48 h of hospital stay were used to calculate the Ranson's score [22]. AKI was defined using criteria of Kidney Disease Improving Global Outcomes (KDIGO) based on increase in serum creatinine (>50% over a week or 26.5 µmol/L over 48 h) [23]. SIRS has been diagnosed in line with the definition cited in 2012 Atlanta classification [2] as the presence of two or more of the following criteria: heart rate >90 beats/min; core temperature <36 • C or >38 • C; white blood count <4000 or >12000/µL; (4) respirations >20/min or PCO 2 < 32 mm Hg.
Laboratory Tests
Blood and urine samples were collected on admission (study day 1) and two following days (study days 2 and 3; there were no deaths during the first three days of observation). Routine laboratory tests were done on the day of collection, that is, complete blood counts with leukocyte differential, biochemistry (serum amylase, lactate dehydrogenase, albumin, total calcium, bilirubin, glucose, urea, creatinine, C-reactive protein-CRP) and citrated plasma D-dimer, using automated analyzers: Sysmex XN hematology analyzer (Sysmex Corporation, Cobe, Japan), Cobas E411 (Roche Diagnostics, Mannheim, Germany) and Vitros 5600 (Ortho Clinical Diagnostics, Raritan, NJ, USA) biochemistry and immunochemistry analyzers, and Coag XL (Diagon, Budapest, Hungary) coagulation analyzer. Excess serum and urine samples collected on study days 1-3 were aliquoted and stored at −80 • C, and were further used to assess serum concentrations of soluble fms-like tyrosine kinase-1 (sFlt-1), procalcitonin and urokinase-type plasminogen activator receptor (uPAR), and urine concentrations of KIM-1 and liver-type fatty acid-binding protein (L-FABP).
The concentrations of sFlt-1 and procalcitonin were measured by electrochemiluminescence on Cobas 8000 analyzer (Roche Diagnostics, Mannheim, Germany) in the Diagnostic Department of University Hospital, Krakow, Poland. Serum concentrations of uPAR were measured using Quantikine ELISA Human uPAR Immunoassay (R & D Systems, McKinley Place, MN, USA). The minimum detectable dose for uPAR was <33 pg/mL; the mean serum concentration in healthy volunteers was 2370 pg/mL (range 1195-4415 pg/mL) according to the manufacturer of the test.
Urinary KIM-1 and L-FABP concentrations were measured by enzyme immunoassays using commercially available kits. Urinary L-FABP was measured in samples that remained after KIM-1 measurements. Urinary KIM-1 was assessed with Quantikine ELISA Human TIM-1/KIM-1/HAVCR Immunoassay (R & D Systems, McKinley Place, MN, USA). Patients' samples were tested in series, in duplicates, according to the manufacturer's instructions. Minimum detectable dose for KIM-1 concentration in urine was 0.009 ng/mL; the normal range determined by the manufacturer of the kit was between 0.156 and 5.33 ng/mL. Urinary L-FABP concentrations were measured with Human L-FABP Assay (CMIC Holding Co., Tokyo, Japan). The sensitivity of the assay was 3 pg/mL. The readings were made with an automatic microplate reader, Automatic Micro ELISA Reader ELX 808 (BIO-TEK Instruments Inc., Winooski, VT, USA). The measurements were performed in the Department of Diagnostics, Chair of Clinical Biochemistry, Jagiellonian University Medical College, Krakow, Poland.
Statistical Analysis
Categorical data were reported as number of patients (n) and percentage of the appropriate group. Pearson's chi-squared test was used to compare categorical data between groups. Mean ± standard deviation (SD) or median (lower; upper quartiles) were reported for normally or non-normally distributed quantitative variables, respectively. Distributions were assessed for normality using the Shapiro-Wilk test. The differences between groups were assessed with t-test or Mann-Whitney's test. Spearman's rank coefficient was computed for simple correlations of urinary KIM-1 as the variable was non-normally distributed. The Friedman's test was used to analyze changes over time in urinary concentrations of KIM-1 and L-FABP. All statistical tests were two-tailed and the p-values of <0.05 indicated significant results. The calculations were made with the use of Statistica 12 software (StatSoft, Tulsa, OK, USA).
Results
In the studied group of 69 patients, there were 21 (30%) patients with mild AP, 44 (64%) with moderately severe, and 4 (6%) with severe AP. Ten patients (14%) developed AKI in the early phase of AP, diagnosed according to KDIGO criteria. We observed no significant differences in the etiology of AP and baseline comorbidities between patients with and without AKI (Table 1). However, the proportion of patients with moderately severe and severe AP tended to be higher among patients with AKI (90% versus 66%), which was accompanied by more prevalent ICU treatment and higher mortality ( Table 1). All patients with AKI were men, a significant difference in comparison with non-AKI patients ( Table 1).
As expected, serum creatinine and urea were significantly higher in the AKI group compared to non-AKI subjects. Moreover, significantly higher concentrations of serum uPAR and procalcitonin, and significantly higher activities of lactate dehydrogenase were observed in patients with AKI on the day of hospital admission ( Table 2). Neither KIM-1 nor L-FABP urinary concentrations differed significantly between patients with and without AKI on the day of admission (Table 2). Consequently, the studied markers on days 2 and 3 of the study did not differ between the groups ( Figure 1A and 1B). Most remarkably, no correlations were observed between KIM-1 and serum urea or creatinine during the study (Table 3). Also, L-FABP did not correlate with urea or creatinine.
Men and women did not differ in KIM-1 and L-FABP concentrations. We did not observe significant changes in urinary KIM-1 or L-FABP over the three days of the study. Table 3. Correlations between KIM-1 and the selected laboratory results on days 1, 2, and 3 of the study in the studied patients with acute pancreatitis. Men and women did not differ in KIM-1 and L-FABP concentrations. We did not observe significant changes in urinary KIM-1 or L-FABP over the three days of the study.
Variable
No significant differences in the concentrations of both urinary markers of tubular injury were observed between patients with mild and more severe AP throughout the study ( Figure 1C,D), although day 1 (p = 0.06) and day 2 (p = 0.07) concentrations of L-FABP tended to be higher in patients with moderately severe AP and SAP as compared with mild AP. Neither KIM-1 nor L-FABP correlated significantly with prognostic scores (BISAP and Ranson's), and only day 1 concentrations of KIM-1 positively correlated with the length of hospital stay (R = 0.35; p = 0.004).
Statistically significant positive correlations were noted between urinary KIM-1 and the inflammatory markers: serum CRP, uPAR, procalcitonin and blood neutrophil count on day 1 of the study, CRP and D-dimer on day 2, and procalcitonin on day 3 (Table 3). Also, KIM-1 negatively correlated with serum albumin on day 3 of the study. Moreover, higher concentrations of KIM-1 in urine were observed among patients with SIRS on day 2 and 3 of the study (Figure 2). Additionally, we observed positive correlations between KIM-1 and lactate dehydrogenase on days 2 and 3, and negative correlation with hematocrit on day 3. Table 3. Correlations between KIM-1 and the selected laboratory results on days 1, 2, and 3 of the study in the studied patients with acute pancreatitis. Statistically significant positive correlations were noted between urinary KIM-1 and the inflammatory markers: serum CRP, uPAR, procalcitonin and blood neutrophil count on day 1 of the study, CRP and D-dimer on day 2, and procalcitonin on day 3 (Table 3). Also, KIM-1 negatively correlated with serum albumin on day 3 of the study. Moreover, higher concentrations of KIM-1 in urine were observed among patients with SIRS on day 2 and 3 of the study (Figure 2). Additionally, we observed positive correlations between KIM-1 and lactate dehydrogenase on days 2 and 3, and negative correlation with hematocrit on day 3. Similar correlations were observed in the case of urinary L-FABP, although because of low number of available samples, we were only able to confirm the strongest associations. On day 1, L-FABP correlated positively with hematocrit (R = 0.41; p = 0.023), on days 2 and 3 with lactate dehydrogenase (R = 0.58, p = 0.005; and R = 0.79, p < 0.001, respectively), CRP (R = 0.61, p = 0.001 and R = 0.60, p = 0.006), and with D-dimer (R = 0.47, p = 0.015 and R = 0.72, p < 0.001). Moreover, on day 3, we observed positive correlation between L-FABP and procalcitonin (R = 0.63; p = 0.005). Both markers (KIM-1 and L-FABP) were significantly correlated on days 2 and 3 of the study (Table 3).
Discussion
Although diagnostic usefulness of urinary KIM-1 has been studied in various clinical settings (including AKI in intensive care patients, surgical patients, including cardiovascular surgery, in obstructive nephropathy, and cisplatin-induced kidney injury) [13,14,[24][25][26][27][28], there are no data addressing its diagnostic utility in prediction or diagnosis of AKI complicating AP. Our preliminary study assessed the concentrations of KIM-1 in urine of patients in the first 72 h of AP of various severities, in order to obtain data on the possibilities of using the marker for early prognosis of AKI complicating AP.
In the studied group, we were not able to show statistically significant differences in urinary KIM-1, neither between patients who developed AKI in the early stage of AP in comparison to those who did not, nor between those with moderately severe to severe AP in comparison to mild AP. Urinary KIM-1 did not correlate with markers of kidney function, namely, serum creatinine and urea, however, on days 2 and 3 of the study, it correlated with another marker of tubular injury, that is, L-FABP. To the contrary, significant positive correlations were observed between urinary KIM-1 and the markers of inflammation: serum CRP, uPAR, procalcitonin and blood neutrophil count on day 1, CRP and D-dimer on day 2, and procalcitonin on day 3, and negative correlation with serum albumin on day 3 of the study. Consequently, higher urinary KIM-1 concentrations have been observed in patients with SIRS. Moreover, we observed positive correlation between day 1 urinary KIM-1 and the length of hospital stay.
KIM-1 has been associated with inflammation in renal tubular injury. Although the role of KIM-1 in AKI has been usually viewed as anti-inflammatory (as a receptor to phosphatidylserine, it increases the uptake of apoptotic and necrotic bodies) and involved in tubular cells' repair [15], Tian et al. [26] showed that KIM-1 plays an important role in macrophage migration to injured tubular cells in AKI, and the mitogen-activated protein kinase signaling pathway may be involved in this process. van Timmeren et al. [29] reported that in various kidney diseases, KIM-1 expression in kidney bioptates was detected in areas of inflammation and fibrosis, while urinary KIM-1 increased in parallel to increased tissue expression and correlated with inflammation.
In the studied group, uPAR and procalcitonin concentrations were higher in patients with AKI. In AP, inflammation plays a significant role in pathophysiology of AKI [4]. Tang et al. [30] discuss the role of CRP in AKI, pointing to its role in pathogenesis of AKI. CRP is involved in development of AKI and the increased serum concentrations of CRP correlate with AKI severity. The in vitro study by Castellani et al. [31] has shown that CRP activates the mitogen-activated protein kinase pathway and upregulates regulated on activation, normal T cell expressed and secreted (RANTES) expression, which is expressed and secreted by T cells and plays a key role in recruiting leukocytes into inflammatory sites. Bear et al. [32] confirmed the effect in human renal distal tubular cells. Li et al. [33] reported increased activation of both nuclear factor κB/p65 and transforming growth factor-β/Smad3 signaling being the major mechanism involved in the process of CRP-promoting AKI at acute setting. Procalcitonin is also a marker of inflammation, not only in acute bacterial sepsis, but in other inflammatory disorders, and has been associated with AKI development in sepsis [34]. Moreover, elevated procalcitonin has been previously observed in AKI complicating AP, similarly to present results [35].
In our study, both urinary KIM-1 and L-FABP correlated positively with serum lactate dehydrogenase starting from day 2 of the study. Moreover, patients with AKI presented with higher LDH activities already on admission. LDH may be viewed as a marker of tissue ischemia and necrosis. In AP, hypovolemia and ischemia contribute to renal tubular injury [4,5,36]. The duration of renal ischemia has been well recognized in clinical studies to be associated with the severity and progression of AKI [37]. Increased urinary KIM-1 has been observed in a rat model of ischemia-reperfusion AKI [38]. In mice, KIM-1 increased in serum and urine during the first 3 h after kidney injury and increased serum KIM-1 has also been recently reported in patients with AKI [39]. Also, increased urinary L-FABP, a 14-kDa fatty acid-binding protein elevated and secreted into the urine as a result of reactive oxygen stress due to renal ischemia, has been shown to correlate with insufficient renal peritubular capillary blood flow and the progression of AKI [40]. Nonetheless, we were not able to show increased urinary KIM-1 or L-FABP in early-stage AP patients with AKI.
One explanation may be that the time frame of urine sampling in our patients may be inappropriate. There is evidence that urinary KIM-1 increase in response to kidney injury lasts a short time. In patients who underwent cardiopulmonary bypass surgery, the dynamics of KIM-1 increase has been analyzed by Shao et al. [14]. The diagnostic sensitivity of urinary KIM-1 was highly dependent on time following the surgery, with a maximum value of 90% between 2 and 6 h after the insult, and decreasing values thereafter (74% at 12 h after surgery) [14]. In our study, single measurements were performed on each of the three days of the study. The time from initial symptoms of AP to admission was not uniform in our patients, as was the time of serum creatinine increase. Considering the results of Shao et al., it may be possible that more measurements are needed to detect the increase in urinary KIM-1 in patients developing AKI in the course of AP. Although KIM-1 has been described over 20 years ago, and first commercially available tests have been introduced in 2002, the automated and robust methods of measurement of KIM-1 concentrations in urine are still not available, making it difficult to use the marker in clinical settings. Considering the lack of automated assays and the difficulties in assessing the optimum time frame of KIM-1 measurements, it is not feasible now to use KIM-1 to diagnose AKI in clinical practice.
Based on our previous studies and literature search, we must say that none of the biomarkers that have been studied in this setting are good enough to efficiently and early predict AKI complicating the course of AP [5,41]. Most promising results have been obtained for serum cystatin C, a functional marker of glomerular filtration [42] and for urinary NGAL, a marker of tubular injury [43]. Of note, serum cystatin C measurements have been automated and the standardization of measurements has been available since 2010 [44]. Also, urinary NGAL may be measured with automated methods, and although the results obtained by various methods are not directly comparable, the turn-around times are 2-3 h, enabling the use of this marker for fast diagnosis. Both serum cystatin C and urinary NGAL seem to rise quickly in AP complicated by AKI and be useful in early prognosis (in first 24 h) [42,43,45,46]. In clinical practice, however, serum creatinine remains the marker of choice to diagnose AKI, although clinicians are aware that its concentrations depend on muscle mass, changing with race, sex, and nutritional status, and are influenced by fluid abnormalities or liver insufficiency in critical illness. Therefore, in systemic inflammatory state associated with AP, it may be difficult to diagnose AKI early on the basis of serum creatinine changes [10,47]. Serum creatinine depends on the volume of distribution, thus, the fluid therapy in AP may significantly dilute creatinine concentrations, delaying the diagnosis of AKI [10]. The biomarkers of tubular injury may potentially enable earlier diagnosis or prognosis of AKI; moreover, they may enable more specific diagnosis, informing about the site of injury and possibly the mechanism of injury. However, more studies are needed to obtain robust data on their diagnostic accuracy before they can be introduced to clinical practice.
Our study has several limitations. As it was meant as a pilot study, its major limitation is a low number of patients included and low number of patients with AKI. We might have missed the most severe cases of AP (and AKI) as the study was performed in a secondary care center. The design was retrospective, but the authors performing KIM-1 measurements were blind to the diagnosis of AKI and the severity of AP at the time of measurements. Moreover, we measured KIM-1 in urine samples that were stored frozen for several months, however, de Vrie [48] and Schuh et al. [49] have shown stability of urinary KIM-1 upon long-term storage at -80 • C. Urinary KIM-1 concentrations were not corrected for urinary creatinine concentrations, but noncorrected urinary concentrations have been reported in most studies on the use of KIM-1 for the prognosis or diagnosis of AKI in various clinical settings [14,24,25,28,[50][51][52].
Based on the study, we cannot definitely exclude the diagnostic utility of KIM-1 in AP, however, our results do not support it. We may hypothesize that the increase of KIM-1 in AKI complicating AP lasts a short time, and it may only be observed with frequent monitoring of the marker. In summary, KIM-1 concentrations are correlated with severity of the inflammatory process in AP and do not seem to be a sensitive marker of AKI among patients in the early phase of AP. | 5,985 | 2020-05-01T00:00:00.000 | [
"Medicine",
"Biology"
] |
The Internal Audit Effectiveness Evaluated with an Organizational , Process and Relationship Perspective
Using a unique database of Italian companies, we perform structural equation modeling technique to test the association between organizational, processes and relationship measure of internal audit effectiveness and firm pressures and performances. We find that size, listing and Big4 are significantly and positively associated with the internal audit effectiveness. We contribute to literature showing that organizational (e.g. presence of a charter, chief auditing executive experience), processes (audit plan risk based, quality assurance program, guidelines), and relationship (with auditee, senior management, chief financial officer, audit committee) measures are useful to evaluate the internal audit effectiveness. We provide support for profession, agency and institutional theories. We implement the measure of internal audit effectiveness with a structural equation model to be able to consider the different components of organizational, processes and relationship separately in a single model. Extending previous literature, we show that this measure of internal audit effectiveness is effective in discovering significant determinant of internal audit effectiveness and could be used in future research.
Introduction
The research aims to test the association between organizational, processes and relationship measure of internal audit effectiveness and firm pressures and performances indicators.Analyzing literature about IA effectiveness, we find research developing several measures of IA effectiveness and theories useful to border our framework.However, for the best of our knowledge, none of the studies use IA effectiveness evaluated with an organizational, process and relationship perspective in a structural equation model.This methodology helps in analyzing organizational, process and relationship as different aspects that measure audit quality from different perspective (first order construct) and that together form a single measure of IA effectiveness (second order construct).We use the agency theory, institutional and profession theories to explain the different perspectives of organizational, process and relationship.Following profession theory, IA effectiveness is measured with organization because internal auditor acts to advocate the profession developing the function inside the organization.Following agency theory, IA effectiveness is measured with process because internal auditor as agent act for the benefit of the manager as principal that ask for effective actions in the process.Following institutional theory, IA effectiveness is measured with relationships with managers because the objectives and their achievement depend on the goals set out by the management, that act as institutional pressures.
We develop two hypotheses to measure the IA effectiveness.The first Hypothesis tests the association between listing status, size, consolidate financial statement and Big4 with IA effectiveness.The second hypothesis tests the association between firm performances (loss, return on assets, cash flow from operations and their volatility) and IA effectiveness.These independent variables, widely used in accounting and auditing research, can be very useful also as determinants of IA effectiveness, interpreted in turn as a set of variables grouped in the three classes of organizational, process and relationship.
In collaboration with the Italian association of internal auditors and a Big4, we develop a questionnaire.We tested it on firms on the target population.The 128 companies' answers allow us to test the measure of IA effectiveness in a unique database with empirical analyses.We also test the common method and non-response bias.
Results show that all our analytical variables selected to measure IA effectiveness are positive and significant at 0.01 level related to it.All are very useful to measure IA effectiveness.Moreover, we find that organizational, process and relationship, grouping the analytical variables in a valid and reliable structure, are also very useful to measure IA effectiveness, given their positive and significant relation with IA effectiveness latent variable.Given these strong results to measure IA effectiveness, we show its determinants in term of firms' pressure and performance.We show that listed companies, larger firms and firms audited by Big4 have a positive association with IA effectiveness.We confirm our expectation incentives towards control and transparency coming from listing status and Big4 and higher resources coming from firm size are important determinants of IA effectiveness.
We contribute to literature in several ways.Firstly, we extend Lenz et al. (2014) model, performing an empirical analysis on a large sample of chief audit executives in Italy.Secondly, we propose a measure of IA effectiveness using a structural equation model showing empirically that all the variables selected grouped in the three classes of organizational, process and relationship are valid and reliable measures of IA effectiveness.Thirdly, among performances and incentives indicators, we contribute to literature underling that listing, size and Big4 are significant determinants.Finally, this first empirical test of the Lenz et al. (2014) model has results that can be useful for practitioners, identifying the ten variables to measure IA effectiveness and helping in the external auditor choice.
Internal Audit Effectiveness Measures
IA, together with the audit committee, executive managers and external auditors, is widely recognized as one of the four cornerstones of corporate governance (Gramling et al., 2004).Prior studies summarize results related to IA for Europe, United States of America (USA), Asia (Allegrini et al., 2006;Hass et al. 2006;Cooper et al. 2006).Prior literature mainly analyzes the relations between IA and audit committee, executive managers and external auditors (Raghunandan et al. 2001;Abbott et al., 2010;Sarens & De Beelde, 2006;Sarens, 2009;Archambeault et al., 2008;Alzeban, 2015), and in other countries (Scarbrough et al., 1998;Goodwin and Yeo, 2001).Some studies employed a single variable to measure IA effectiveness, usually relating to the presence, size, or extent of investment in IA (Selim et al., 2003(Selim et al., , 2009;;Abdolmohammadi, 2009;Burnaby et al., 2009;Carcello et al. 2005a, b;Anderson et al., 2012;Sarens et al., 2011).Given that IA effectiveness is a multifaceted concept, Lenz et al., (2014) measure it distinguishing factors like organization, resources, processes and relationships.Jiang et al. (2014a, b) evaluate it with a factor score of competence, independence, planning and quality assurance.Regoliosi and D'Eri (2014) create a weighted index for it using IA variables related to its formality, structure, program and activity.Mihret and Yismaw (2007) measure it with staff expertise, scope of service, effective audit planning, fieldwork and controlling, and effective communication.Arena and Azzone (2009) evaluate it with the percentage of recommendations suggested by the internal auditors and actually implemented by the auditees.Cohen and Sayag (2010), based on Ziegenfuss (2000), categorize it into audit environment, input, process and output.See the literature review by Lenz and Hahn (2015) for the categorization of the variables used in prior literature.
Internal Audit Effectiveness Theories
Shamki and Alhajri (2017) investigate IA effectiveness through the lens of agency theory.The principal (the manager in the case of audit and board of directors in the case of the organization) hires the second party's efforts (internal auditor in the case of audit and the manager in case of organization) to perform tasks for the benefit of principal and on his behalf (Jensen & Meckling, 1976).When internal audit accomplishes its goals, brings a disciplined and systematic approach to well improve and evaluate risk management's effectiveness, control and governance processes.Thus, following this theory, IA effectiveness is when IA perform tasks for the benefit of the manager.Tackie et al. (2016) investigate IA effectiveness through the lens of profession theory (Abbott, 1988) and institutional theory.Based on profession theory, Winters (2009) argues that, individual internal auditors can only achieve their full potential if the profession as such is strengthened.Thus, they act with the purpose to advocate the profession.Based on institutional theory, when faced with uncertainty, DiMaggio and Powell (1983) suggest that, as a result of institutional pressures, firms will adopt similar characteristics through the desire to organize themselves in a manner that is similar to other firms in the same environment.Institutional pressures can be pressures exerted to establish internal audit departments (Al-Twaijry et al., 2003).The IIA (2010) defines IA effectiveness as "the degree to which established objectives are achieved."The objectives of an internal audit unit for every organization depend on the goals set out by the management of such an organization (Pungas, 2003).The advocation of profession and the institutional pressures, as well as IA effectiveness, are related linked to the management will.
Internal Audit Effectiveness Evaluated with an Organizational, Process and Relationship Perspective
Following Lenz et al. (2014) and linking the components of IA effectiveness to theories, we develop our framework of IA effectiveness based on organization, processes and relationships (Note 1).Agency, profession and institutional theories are related, and all can be used to explain any components of the IA effectiveness.Here, we propose a link with the three different components of our framework.
IA organization includes variables related to charter, experience and communication.Organization is an indicator of profession theory that shows how internal auditor acts to advocate the profession having a formal charter, developing experience in the same profession for years and taking in consideration other control functions.Firstly, IA effectiveness is positively related with the formally definition of the purpose, authority and responsibility of the internal audit activity in an internal audit charter (IIA, 2016: standard No 1000).Lenz et al. (2014) argue that IA that do not have a written IA charter will likely warrant an unsatisfactory rating in quality assessment, as a written charter is regarded as a minimum.Secondly, auditor's proficiency requires the internal auditors to be with high skills, knowledge and other competencies to better perform their responsibilities (IIA, 2016: standard No 1210).Auditing general experience is related to audit's years of experience, training, knowledge, skills and expertise that can be applied to any client (Wright and Wright 1997).Moreover, it has been showed that IA experience is positively related to IA effectiveness in many different setting (Shamki & Alhajri, 2017).Thirdly, in some countries, there are country-specific corporate governance mechanism to take in consideration.Where there is a statutory board, that is a specific board for financial reporting controls, it is also important to check the communication between IA and this board to consider effectiveness.
Risk-based, reviewed and guidelines-based processes are an index of better IA effectiveness.Following agency theory, IA effectiveness is when IA (agent) perform tasks during the process for the benefit of the manager (principal).These tasks should be risk-based, reviews and guidelines-based to achieve effectiveness.In fact, following the IIA standards, first of all, IA to be effective should establish a risk-based audit plan to determine the priorities of the internal audit activity, consistent with the organization's goals (IIA, 2016: standard No. 2010).Resources are scarce and time is easily wasted if IA looks at the wrong matters, so a risk-based IA generally helps the chief audit executives and IA staff to focus on what matters most (Lenz et al., 2014).The importance of risk-based IA is supported by the literature (e.g., Allegrini & D'Onza, 2003;Spira & Page, 2003;Burnaby & Hass, 2009).Secondly, IA quality assurance include the development and maintenance by the chief audit executive of a quality assurance and improvement program that covers all aspects of the internal audit activity (IIA, 2016: standard No 1300).Lin et al. (2011) showed, among other findings, that various IA activities help IA effectiveness, including the use of quality assurance techniques.Thirdly, IA to be effective should establish policies and procedures to guide the internal audit activity (IIA, 2016: standard No 2040).
Finally, following institutional theory, IA effectiveness is governed by institutional pressures that come from relationship between IA and managers at different level.IA to be effective should periodically communicate to auditee, senior management and the board of directors or its internal committee on the internal audit activity's purpose, authority, responsibility and performance relative to its plan.Reporting must also include significant risk exposures and control issues, including fraud risks, governance issues and other matters needed or requested by senior management and the board (IIA, 2016: standard No 2060), the results of engagement (IIA, 2016: standard No 2400).Relationships, when they are characterized by regular interactions, reports and an open dialogue, are expected to aid the IA's pursuit of effectiveness (Lenz et al., 2014).
We grouped these variables into three main classes (Figure 1).We model perceived IA effectiveness as formative (Note 2) because a change in the organization, process and relationship will lead to a change in perceived IA effectiveness.Organization, process and relationships as well as competences and independence are different aspects that measure audit quality from different perspective (DeAngelo, 1981).We model them as first order reflective constructs for each single interchangeable item.(Note 3)
Firms Incentives
We investigate the determinants of IA effectiveness answering at prior call of research.Shamki and Alhajri, (2017) emphasize that future studies are called to extend their study by examining the influence of factors on the IA effectiveness.After the collapse of Arthur Andersen in 2002, the auditing profession has faced increasing pressure from external parties to enhance and improve audit quality.These pressures led to a continued need to study the factors that affect audit quality (Hussein and Hanefah, 2013).
We expect that IA effectiveness is related to incentives to high quality from capital market (listing status, size), minority (consolidate or individual), and audit (Big4).Literature has investigated the listing status (Arena andAzzone, 2007, 2009;Anderson et al., 2012) and size (Carcello et al., 2005a, b;Abbott et al., 2010;Regoliosi & D'Eri, 2014;Anderson et al., 2012) as possible determinant of IA effectiveness, with different measures of IA effectiveness construct.We expect that our measure of IA effectiveness based on organization, process and relationship is positive related with capital market and minority pressure that increases the monitoring to have an effective IA function in all its three components.Market incentives come from the firms listing status as well as by the size of a firm.Moreover, we expect that external auditor reputation -competences (Big4) to be related to the work of IA.Big4 reputation increases the incentive to check the effectiveness of IA, and in the long run, Big4 help and promote the development of an effective internal control system.
H1: firms' incentives are positively associated with IA effectiveness
Firms' Performance
We expect that IA effectiveness is related to firms' total performance (loss), firm operating performance (ROA), cash flow (CFO) and variability of cash flow (SDCFO) that create availability of resources to invest in internal control.We investigate separately total from operating performance (Carcello et al., 2005b), expecting a higher relation with operating performance given the IA relation with the operating activity.Finally, the level and variability of cash (CFO, SDCFO) are other determinants of the development of the IA function (Carcello et al., 2005a, b;Abbott et al., 2010) related to the resources available in cash to invest in internal controls and to their stability to have similar investment over time.On the other hand, economic performance and cash flow can be negative related with IA effectiveness because negative performance provides higher incentives for controls.However, negative performance can also change the focus of the firms and reduce the investment in controls.Thus, we expect a positive relation with firms' performance.
H2: firms' performance is positively associated with IA effectiveness
Questionnaire and Sample
We collect private data through questionnaires.We prepared the questionnaire together with external auditors from one of the Big4 and from the Association of Italian Internal Auditors (AIIA).The external auditors and AIIA make a key contribution in ensuring language would be comprehensible for the target companies.We test the questionnaire on firms from the target population.Based on their responses and comments, the questionnaire, the study design and the measurement of some constructs are slightly adapted.We distribute the questionnaire using a web-based survey system.The distribution procedure involves sending out a survey package containing the questionnaire and a covering letter.In order to increase the response rate, we contact by phone companies that are slow to respond.
We opt to make the questionnaire confidential; i.e. although the names of respondent companies are known to us, they are not disclosed here and results are shown only in aggregate form.We are thus able to link the data collected by questionnaires with other sources, such as financial statement data from company websites for banks and from databases (Bureau van Dick, National Insurance Association database).In addition, we emphasize that the research is under the auspices of a well-known university, widely recognized as trustworthy, so that firms could be confident that sensitive information would not be disclosed.We sent the questionnaire to 616 companies members of the AIIA and we received 128 usable answers with a response rate of 21% (Table 2, Panel A).The questionnaire refers to the year 2013.
Non-Response and Common Method Bias
To evaluate our questionnaire, we compute the test for non-response bias and tests for common method bias.In Table 2, Panel B, we present the results for the non-response bias.We perform a comparison of firm characteristics (ROE and equity/total assets) between listed (non-listed) financial firms in our sample and listed (non-listed) financial firms in the sample of non-respondents.Then, we repeat this comparison between listed (non-listed) non-financial firms in our sample and listed (non-listed) non-financial firms in the sample of non-respondents.The latter includes 616 companies associated with the national institute of internal audit that has received but not answered at the questionnaire.We find no statistically significant differences between these groups in term of profitability and leverage, except for the comparison of leverage between non-financial non-listed firms in our sample and in the sample of Italian population (Table 2 Panel B).
Furthermore, we repeat this comparison between listed (non-listed) financial firms in our sample and listed (non-listed) financial firms in the Italian population and between listed (non-listed) non-financial firms in our sample and listed (non-listed) non-financial firms in the Italian population.The latter includes all firms listed on the Milan Stock Exchange and non-listed firms with minimum total assets of euro 2 million with data available for total assets, operating earnings, net income and share capital from the database of Bureau Van Dick.We find that there are no statistically significant differences between the groups.We conclude that our sample is qualitatively similar to the population, so that results can be generalized to the population of Italian firms (Table 2 Panel B).We perform three tests for common method bias: Harman's single factor test; a confirmatory factor analysis comparison of the model by loading all the questions of the survey into a single-factor; and the test of partialling out a general factor score following the approach of Elbashir et al. (2011) and Dowling (2009).First, in Harman's single factor test no single factor emerges from the exploratory factor analysis and no single general factor accounts for the majority of the variance in the items used in the model.Secondly, in the confirmatory factor analysis the item loadings are all lower when constrained to load onto a single-factor than when the items are loaded onto their respective theoretical construct.This suggests that the theoretical measurement model provides a better fit to the data than a single-factor item.Thirdly, in partialling out a general factor score test, we add the highest factor from the "unrotated" exploratory factor analysis on the main model used in our analysis.
We add it as a control variable.We assume that this factor contains the best approximation of the common method variance (Podsakoff & Organ 1986;Podsakoff et al., 2003).The findings show the original results are not affected by the general factor included in the model.Concluding, the results indicate no significant common method variance that threatens the quality of the data.Importantly, prior to data collection, we attempted to minimize the potential for common method bias by collecting the data with different scales, protecting respondents' confidentiality, asking respondents to answer honestly and conducting pilot tests to reduce item ambiguity (following Podsakoff et al., 2003).
Model
We use Partial Least Squares (PLS), a component based structural equation modeling (SEM) technique (Note 4), to test our hypothesis.We first discuss the choice of PLS for this analysis and its advantages.Secondly, we define our model, explaining the reflective and formative construct and the measurement scale used in the questionnaire.(Note 5) PLS has several advantages.First, given that audit quality is based on competence and that independence has two key elements of quality, it is important to use a method, which allows including both reflective and formative constructs, following the approach of Dowling (2009) and Elbashir et al. (2011) (Note 6).Secondly, because our data are from questionnaires, PLS is useful because being nonparametric and using iterative estimation algorithms that proceed block-by-block, it requires less stringent assumptions about the distributional characteristics of the raw data (Chin, 1998;Hulland, 1999).Thirdly, PLS makes it possible to perform path-analytic modelling between latent constructs like our constructs of IA effectiveness and coordination.(Note 7) Moreover, PLS is also suitable for analyzing complex models with second-order constructs, such as our concept of IA effectiveness (Chin and Newsted, 1999).PLS is used extensively in social sciences.A number of recent studies in accounting (e.g., Naranjo and Hartmann, 2007;Hall 2008;Hall and Smith, 2009;Chapman and Kihn 2009;Elbashir et al. 2011;Glaum et al. 2013;Du et al. 2013) and auditing (Dowling 2009;Diaz and Loraas, 2010;Eulerich et al. 2015) use PLS for similar reasons.However, there is high potential for adopting PLS more widely in the field of accounting (Lee et al. 2011).Hall et al. (2005) and Blanthorne et al. (2006) have recognized the potential benefits of using it on traditional accounting data sets.
We supply details (Table 1) on the development of the scales used in the survey (Lee et al. 2011), grouping variables into three main classes: organization, process and relationship.Starting from the full list of questions, we select 10 questions for the analysis of IA effectiveness.(Note 8) We measure organization variables, using a five-point Likert-like scale ranging from <2 (1) to >15 (5) for CAE number of years of experience, and a five-point Likert-like scale ranging from low frequency (1) to high frequency (5) for communication with the Statutory board.We than use a dummy variable for the presence of a formal charter.The use of different scales such as Likert-like and yes-no questions helps to lower common method bias.Next, we measure the construct process with three variables.We use a five-point Likert-like scale ranging from low importance (1) to high importance (5) to measure the risk-based approach and the policies and procedures (guidelines).We use a dummy variable for the presence of an internal program of quality assurance.We also measure relationships with four dummy variables that represent the presence of a report to auditee, senior management, CFO and audit committee.
Results
In this section, we present descriptive statistics, correlation matrix, validity reliability and the structural model results.
Descriptive Statistics
Table 3 shows the descriptive statistics for IA effectiveness measures, grouped into 3 main elements: IA organization, IA process, IA relationship.Among IA organization variables, 84% of companies of our sample have a charter that discloses objectives, competencies and responsibilities of the IA function.The mean number of years of CAE experience almost reaches class 4 (from 11 to 15 years).Communication to the statutory board has a mean value of 3.9 out of 5, showing it is considered fairly important.These results show that our sample of companies have an IA function with a good organization, independence and competencies.Processes performed by IA function are evaluated with variables related to quality assurance, guidelines and the audit plan, using a risk assessment approach.Quality assurance is not very much developed, and is more frequently performed internally (38%) than externally (16%, untabulated).On the other hand, most companies have policies and procedures to guide IA activities (score of 3.7 out of 5) and the audit plan is risk based with a score of 3.7 out of 5. Finally, IA relationships are evaluated with variables related to the reporting toward auditees, senior management, CFO and Audit Committee.Reporting is more frequent towards the auditee (91%), senior management (81%) and audit committee (74%) than towards CFO (64%).
A previous study shows that in a sample of three companies and two Big4 firms, (Chapman & Kihn, 2009) the content validity of perceived IA effectiveness is enhanced by IIA standards definitions and by pilot testing.In our study, the key determinants of perceived IA effectiveness are deduced based on such prior studies.
Item loading, together with the Average Variance Extracted (AVE), captures the convergent validity of each of the measures for constructs that are modeled reflectively.Firstly, we use confirmatory factor analyses to examine the loading of items.(Note 10) Results show that all reflective items have high and significant loadings (Table 5, Panel A, Confirmatory factor analysis loadings).(Note 11) Secondly, the output from PLS in relation to the measurement model verifies the initial results from the confirmatory factor analysis tests for reflective construct (Table 5, Panel A, Partial least squares loadings).The loadings of the reflective items are qualitatively similar (Hulland, 1999;Hair et al., 1998;Chenhall, 2005;Yi & Davis, 2003;Vandenbosch, 1999).Thirdly, results show that the AVE for all reflective constructs exceed 0.45 (square root of AVE presented in Table 5, Panel C in the diagonal), supporting the convergent validity of the items (Fornell & Larcker, 1981;Chin, 1998).This ensures that measurement error does not dominate the variance captured by the construct (Vandenbosch, 1996).
The cross loadings and the comparison of AVE and correlation coefficient capture the discriminant validity.
Looking at cross-loadings (Table 5, Panel B), all items load significantly and higher on their respective latent construct than on another latent construct (Chin, 1998).(Note 12) The comparison of correlation and AVE determines the extent to which a construct shares more variance with its measures than it shares with other constructs, following the Fornell-Larcker (1981) criterion.The values of the square roots of the AVE (Table 5, Panel C) are all greater than the inter-construct correlations indicating that more variance is shared within a construct than between constructs and thus, that all measures have appropriate discriminant validity (Chin, 1998;Yi and Davis, 2003).
Internal consistency reliability (ICR in Table 5, Panel C), also called composite reliability, incorporates the loading weights of the items and provides a more appropriate indication of internal consistency than Cronbach (1951)'s alpha when the item loadings are not tau-equivalent (Bacon et al., 1995;Salisbury et al., 2002).The ICR scores of the latent constructs are all greater than 0.70, indicating acceptable reliability for the measurement of the reflective items for each construct (Nunnaly & Bernstein, 1994;Vandenbosch, 1996).(Note 13) When assessing formative construct validity, the indicator weights (Table 5, Panel D) rather than loadings should be assessed (Chin, 1998;Diamantopoulos and Winklhofer, 2001;Petter et al., 2007).Classical measurement theory testing assumptions are not applicable for assessing formative indicators because there is no expected pattern of inter-relationship (Bollen and Lennox, 1991;Diamantopoulos et al., 2008).Table 5 Panel D shows that all weights are significant.For the reliability of formative construct instead of the correlation, the Variance Inflation Factor (VIF) should be computed.The VIF is below 3 for all indicators (Table 5 Panel D), indicating that multicollinearity is not a major concern (Petter et al., 2007).Panel C: Internal Consistency Reliability (ICR), and diagonally, the square root of the Average Variance Extracted (AVE) by latent constructs from their indicators (Calculated following Chin (1998a, b)) following the Fornell Larcker Criterion to evaluate discriminant validity (SmartPLS software).
Structural Model Results
The adequacy of the structural model is assessed with standardized beta-statistics, used as path coefficients and generated by the PLS, from ordinary least squares regression (OLS).Bootstrapping using 1000 samples with replacement is used to assess the significance of the path coefficients.The framework that posits a direct relation between constructs of Organization, Process and Relationship is confirmed by the sign and significance of path coefficients (0.270, 0.480, 0.598 respectively, significant at 0.001), which indicate the direction of the relationships among the latent variables.Also, all the survey questions related to the three constructs Organization, Process and Relationship are positively and significantly related to the respective constructs, confirm their relevance to measure IA effectiveness.
Finally, Table 6 shows results of our hypothesis.Results about the determinants show that the market pressure from the listing status and the size as well as the pressure from Big4 are positively related to IA effectiveness.This confirms our first hypothesis that the market investors, the reputation of the company and of the auditor are determinants of higher incentive to develop the IA work.This determinant has been found in a model that consider the different aspects of organization, process and relationships separately in a single model.This structural equation model better captures the nature of internal audit effectiveness and is able to show that pressure from the market and the reputation of auditors are important elements for all the three categories of internal audit effectiveness.
Robustness Checks
It is possible that results reflect the construction of the model, so we repeat the analysis without the second order latent variables.Results are qualitatively the same (Table 7).Therefore, results are robust to a model where the perceptions of IA effectiveness are not assumed to map to organization, process, and relationship.However, we suggest future research to implement the structural equation model with second order latent variable to better capture the role of organization, process and relationships in the measurement of internal audit effectiveness.
Conclusion
Including the Lenz et al. (2014) model of IA effectiveness evaluation in the agency, professional and institutional theories, this research tests the association between organization, process and relationships measures of IA effectiveness and firms' incentives and performance.Using data collected from 128 Italian companies and performing partial least square technique, we find that large companies, listed companies and companies audited by Big4 represent significant incentives toward IA effectiveness.Through these results, we contribute to literature in several ways.Firstly, we extend Lenz et al (2014) model performing an empirical analysis with the structural equation model on a large set of empirical data.Secondly, our ten variables expression of agency, professional and institutional theories are useful in the measurement of IA effectiveness, individually, grouped in three main classes (organization, process and relationships) and considered as a single index.Thirdly, the research suggests useful incentives (listing status, size and Big4) for the improvement of IA effectiveness.Finally, our results could be also useful for practitioners both in IA and external audit.
Limitation of this research can be related to the exclusively analysis of Italian context: our results are country-specific and could not be extended or comparable with those of other European, American, Asian, African and Oceania countries.Moreover, another limitation could be the choice of the variables of the model based on a specific stream of literature: other literature can suggest different variables.Future research can investigate other determinants, like corporate governance, ownership or other variables.
Acknowledgements
We express our thanks to the participants at the 39th European Accounting Association Congress in Maastricht, May 11-13, 2016 and the participants at the 14th European Academic Conference on Internal Audit and Corporate Governance in Rotterdam, April 06-08, 2016.We thank also the reviewers of the 2016 Auditing Section Midyear Meeting of the American Accounting Association.
Notes
Note 1.Given that the variables for resources do not significantly load on our model, we do not consider them.
Note 2. Reflective items are manifestations of changes in the underlying latent construct.As such, the direction of causality is from construct to items.Reflective items should be interchangeable, have the same antecedents and consequents and be highly correlated.In contrast, because changes in formative indicators cause changes in the construct, these indicators are generally not interchangeable, and are not required to have the same antecedents and consequents or be highly correlated (Jarvis et al., 2003;Petter et al., 2007).We use the term "item" ("indicator") when we measure a construct reflectively (formatively).For reflective constructs, a simple regression is performed with each item individually regressed on its latent variables; estimating inside the latent construct score to determine the outer loading.Loadings represent the correlation between the indicator and the latent construct.An indicator with a low loading implies that the indicator has little shared variance with the latent construct.For formative constructs, the weights are the beta coefficients between the latent construct and indicators in a multiple regression analysis.Weights correspond to the beta coefficient weights calculated as part of a multiple regression analysis and represent the relative importance of each indicator in the formation of the latent construct component score (Lee et al., 2011).
Note 3. The indicators are unlikely to be correlated because a change in one indicator should not automatically result in a change in all other indicators.On the other hand, each item is measured by different questions that measure the same aspect.
Note 4. Unlike variance-covariance-based SEM, which attempts to minimize the difference between sample covariance and those predicted by a theoretical model on the underlying assumptions of normal multivariate distribution (Chin, 1998), PLS estimates the structural model using an iterative OLS regression-like procedure, which aims to explain variance of the dependent variables by minimizing the residual variance of all dependent variables (both, latent and observed).
Note 5. Lee et al. (2011) suggest that future research using this approach should explain the justification of constructs as reflective or formative, and give details on the development of the scales, the software used, the power and the effect size.We aim to do this in this paper.The f square effect size is 0.231 (See Durlak, 2009).
Note 6.Using a covariance based SEM technique to model constructs as formative can result in unidentified models (Kline 2006) or in admissible solutions (Fornell and Bookstein 1982).PLS however is suitable for modeling constructs measured either reflectively, or formatively or in a combination of the two ways (Chin 1998).
Note 7. The PLS approach comprises a measurement model that specifies relations between manifest items (observed values for specific survey questions) and the latent constructs that they represent (i.e., unobserved values), plus a structural model that identifies relations among constructs.SEM is a merger of two powerful approaches (Lee et al. 2011), factor analysis and path analysis, and allows researchers to simultaneously assess the measurement model (traditionally accomplished with factor analysis) and the structural model (traditionally accomplished with path analysis).
Note 8.The items included in the model are those left after dropping items with low and insignificant loadings from the construct measure.
Note 9. Before the analysis, we check the factorability of items.The Bartlett test of sphericity shows that nonzero correlations exist at the significance level of 0.000 for all the variables (untabulated).The Kaiser-Meyer-Olkin measure of sampling adequacy (untabulated) is met in all cases with an MSA of >0.50 (Chapman and Kihn, 2009).
Note 10.We use confirmatory factor analyses instead of an explorative factor analysis because the framework to measure IA effectiveness is established in advance.
Note 11.The weighting scheme is "Path".Because there may be weaknesses in software, we repeat the analysis with two different types of software, and the results hold.
Note 12.The same results are found running a principal component analysis rotated.
Note 13.We repeat the analysis without the variable CAE experience and obtain all ICR higher than 0.75.This measure of perceived IA effectiveness yields qualitatively similar results to those in the main analysis of the hypothesis.Because the literature emphasizes the importance of CAE experience in measuring IA effectiveness, we opt to retain CAE experience in the analysis. Figure
Table 2 .
SampleNote.We compare the means of the variables through a t-test between the mean of listed financial firms, non-listed financial firms, listed non-financial firms, non-listed non-financial firms of the non-respondents (or Italian population) and the mean of respectively listed financial firms, non-listed financial firms, listed non-financial firms, non-listed non-financial firms of our sample.* and ** indicate respectively 0.05, 0.01 level of statistically significant difference between the mean.The Italian population includes all firms listed on the Milan Stock Exchange and non-listed firms with minimum total assets of euro 2 million with data available for total assets, operating earnings, net income and share capital from the database of Bureau Van Dick.
Table 3 .
Table 4 also shows descriptive statistics of the determinants.Descriptive statistics: IA effectiveness
Table 5 .
Validity and reliability
Table 6 .
PLS results: determinants of perceived IA effectiveness
Table 7 .
PLS robustness results: without Organization, Process and Relationship constructs | 8,201.2 | 2018-05-16T00:00:00.000 | [
"Business",
"Economics"
] |
Immunotherapeutic Potential of Oncolytic H-1 Parvovirus: Hints of Glioblastoma Microenvironment Conversion towards Immunogenicity
Glioblastoma, one of the most aggressive primary brain tumors, is characterized by highly immunosuppressive microenvironment. This contributes to glioblastoma resistance to standard treatment modalities and allows tumor growth and recurrence. Several immune-targeted approaches have been recently developed and are currently under preclinical and clinical investigation. Oncolytic viruses, including the autonomous protoparvovirus H-1 (H-1PV), show great promise as novel immunotherapeutic tools. In a first phase I/IIa clinical trial (ParvOryx01), H-1PV was safe and well tolerated when locally or systemically administered to recurrent glioblastoma patients. The virus was able to cross the blood–brain (tumor) barrier after intravenous infusion. Importantly, H-1PV treatment of glioblastoma patients was associated with immunogenic changes in the tumor microenvironment. Tumor infiltration with activated cytotoxic T cells, induction of cathepsin B and inducible nitric oxide (NO) synthase (iNOS) expression in tumor-associated microglia/macrophages (TAM), and accumulation of activated TAM in cluster of differentiation (CD) 40 ligand (CD40L)-positive glioblastoma regions was detected. These are the first-in-human observations of H-1PV capacity to switch the immunosuppressed tumor microenvironment towards immunogenicity. Based on this pilot study, we present a tentative model of H-1PV-mediated modulation of glioblastoma microenvironment and propose a combinatorial therapeutic approach taking advantage of H-1PV-induced microglia/macrophage activation for further (pre)clinical testing.
Glioblastoma is the most common and aggressive primary brain tumor. It has a dismal prognosis and is typically characterized by largely inevitable recurrence within six months to one year after initial treatment [1,2]. The current standard of care for newly diagnosed patients includes maximal surgical resection and subsequent concurrent treatment with radiation and temozolomide (TMZ), followed by adjuvant chemotherapy [3]. Due to glioblastoma invasiveness and frequent location in injury-prone brain areas controlling essential motor and cognitive functions, radical resection is only feasible in a subset of patients [1]. Furthermore, at recurrence only a minority of the patients is eligible for second surgery [4], which is so far the only approach firmly associated with improved
Immune-Targeted Therapeutic Approaches for Glioblastoma
Data from preclinical studies provided convincing evidence that immunotherapy is able to promote efficient anti-glioma immune responses [14,15]. Modulation of human cytomegalovirus (CMV)-specific DCs, application of glioma stem cell-antigens-loaded DC vaccines, cytotoxic T lymphocyte-associated protein 4 (CTLA-4) and PD-1 blockage, etc., are among the numerous extensive works (as reviewed in detail in [14,15]) that have been recently done and allowed for a clinical translation of glioblastoma immune targeting. Several immunotherapy approaches are currently under clinical evaluation, including tumor vaccination, immune checkpoint inhibition and adoptive T cell transfer.
Tumor Vaccination
In newly diagnosed glioblastoma patients, Rindopepimut-an epidermal growth factor receptor variant III (EGFR vIII)-specific peptide vaccine-reached phase III clinical testing but disappointingly, when combined with TMZ, failed to add significant OS benefit compared to TMZ alone [16]. This was ascribed to the relatively low percentage of newly diagnosed glioblastomas which express this EGFR mutant [17]. Indeed, the vast heterogeneity of tumor-specific antigen expression in glioblastoma is a major factor limiting the tumor vaccination approach. Hope in that regard has been raised by the identification of ten novel glioblastoma-associated tumor antigens [18] whose curative potential as a multi-peptide vaccine, using CD8 + T cell epitopes, has been tested in phase I/II clinical trials [14]. A phase III clinical assessment of a DC-based vaccine is currently active and results are awaited.
Immune Checkpoint Inhibition
The first Food and Drug Administration (FDA)-approved immune checkpoint inhibitor was the humanized anti-CTLA-4 antibody ipilimumab. Although an improved OS was achieved in a phase III melanoma clinical trial [19], ipilimumab showed severe immune-related adverse effects [20] and a clinical utility limited to only a small subset of glioblastoma patients [14]. Other immune checkpoint inhibitors are presently under clinical evaluation in glioblastoma patients, in particular anti-PD-1 (nivolumab, pembrolizumab) and anti-PD-L1 (MEDI4736) antibodies.
Adoptive T Cell Transfer
One clinical trial, in which autologous T cells specific for glioblastoma-expressed CMV antigens were adoptively transferred to recurrent glioblastoma patients, reported significant OS prolongation [21]. Another trial of autologous therapy with CMV-specific T cells is ongoing. Also ongoing are clinical studies using adoptive transfer of autologous T cells with chimeric antigen receptor (CAR) targeting different glioblastoma-associated antigens [14,15].
Despite the impressive research progress recently made in cancer/glioblastoma immunotherapy, it has to be noted that some of the approaches were associated with immune-related adverse effects, imposing the need for concerned risk-benefit assessment. Some studies have reported gastrointestinal, dermatological and endocrine toxicities attributable to immune checkpoint blockade [22]. Furthermore, life-threatening neurotoxicity and other severe complications, including on-target off-tumor toxicities, were documented after CAR T cell infusion [23].
Need for Novel Immunotherapeutic Strategies: Oncolytic Viruses
As apparent from above, an improved arsenal of immunotherapeutic agents is still needed. Recently, cancer immunotherapy using oncolytic viruses (OVs) has gained much attention and raised considerable hopes [24][25][26][27]. These agents possess the ability of infecting and killing malignant cells without causing harm to normal tissues. This oncoselectivity is a complex phenomenon and is largely due to the dependence of OV life cycle on various tumor cell-specific factors. OV-induced tumor cell toxicity coupled with host immune system stimulation warrant OV clinical development as targeted multimodal cancer therapeutics.
Oncolytic H-1 Parvovirus
An emerging candidate is the rodent H-1 protoparvovirus (H-1PV), the smallest among all OVs. H-1PV is endowed with natural anticancer activity and is nonpathogenic for humans. These properties, together with the lack of pre-existing immunity in the human population [28], the potential of H-1PV for application via multiple routes (intratumoral, intravenous, intranasal), and its capacity to cross the blood-brain barrier, make this virus a suitable tool for oncolytic virotherapy of several tumor entities, including those of the central nervous system [29][30][31][32]. In addition, H-1PV oncolysis-associated proinflammatory host immune responses observed in preclinical studies raise hopes that parvovirotherapy may offer a safe alternative to current immune-targeted approaches [33].
In Glioma Models
In contrast to pancreatic cancer and melanoma, for which extensive preclinical work demonstrated enhanced immunogenicity of H-1PV-infected versus non-infected tumors, considerably less is known about H-1PV-infected glioma interactions with the host immune system. In glioma-bearing immunocompetent animals, spleno-and lymphadenomegaly are observed upon infection with minute virus of mice (an autonomous protoparvovirus closely related to H-1PV), together with increased interferon-gamma (IFN-γ) production in spleen and tumor-draining lymph nodes. Proinflammatory cytokine release and upregulated CD80/83/86 expression were detected in antigen-presenting cells, including microglia [40]. In regard to H-1PV, the only preclinical evidence gathered so far comes from an orthotopic rat glioma model, in which H-1PV treatment was able to eradicate even advanced tumors [41]. This therapeutic effect was however present only if the host immune system was intact: T cell depletion impaired H-1PV-induced tumor regression. Importantly, the sole presence of T cells, in the absence of H-1PV treatment, was not sufficient to cause glioma suppression. These observations argue for a role of host T cell responses in H-1PV-promoted oncosuppression [32].
Immunotherapeutic Potential of H-1PV in Glioblastoma Patients: First Evidence of Immunogenic Tumor Microenvironment Conversion
Several OVs have been tested in glioma clinical trials and hold considerable promise as novel targeted brain tumor therapeutics. The most advanced are the clinical studies using herpes simplex virus (HSV), Newcastle disease virus (NDV), as well as adeno-, reo-, vaccinia, measles, polio-, and vesicular stomatitis virus (VSV) [42,43]. ParvOryx01 (NCT01301430) was the pilot clinical trial of an oncolytic parvovirus, H-1PV, in patients with recurrent glioblastoma [44]. This trial investigated the application of escalating parvovirus doses via either intravenous or intracerebral routes. In addition to assessing H-1PV safety, tolerability, pharmacokinetics, shedding and maximum tolerated dose, tumor tissue samples were acquired at resection and allowed the analysis of glioblastoma cells and glioblastoma microenvironment nine days after parvovirotherapy. The results of the ParvOryx01 clinical trial have been recently published [45]. Together with the promising clinical observations (reliable safety, good tolerability, well predictable pharmacokinetics, induction of neutralizing antibodies in a virus dose-dependent manner while providing a window for booster H-1PV reapplications, and extended median survival in comparison with recent meta-analyses), several intriguing findings arose from the in-situ analyses of resected parvovirus-treated tumors.
Glioblastoma Infiltration with Immune Cells
In comparison with non-parvovirus-treated (historical) controls, increased tumor infiltration with CD45 + /CD3 + /CD8 + T lymphocytes was observed in some ParvOryx01 patients. Tumor-infiltrating CD4 + and CD25 + cells were also present, but importantly, FoxP3 + Treg cells were only a minor subfraction of the tumor immune cell infiltrate [45]. Of note, tumor-infiltrating cytotoxic T cells (CTLs) were found to be PD-1-negative.
Activation Status of Glioblastoma-Infiltrating Immune Cells
The activated state of tumor-infiltrating CTLs was demonstrated by the abundant expression of granzyme B and the presence of perforin [45]. The CD4 + helper T cell activation marker CD 40 ligand (CD40L) was also expressed in parvovirus-treated glioblastomas. Surprisingly, CD40L expression was also detected in non-lymphocyte-infiltrated glioblastomas, hinting at CD40L cellular source other than CD4 + T cells.
CD40L Expression by Glioblastoma Cells
In line with the above, CD40L expression was detected in non-macrophage, EGFR-positive, i.e., most likely glioblastoma cells. In contrast, CD40 expression was not observed, either on tumor or on tumor-associated microglia/macrophage (TAM) cells. Interestingly, CD40L expression in glioblastoma cells was first reported in 2015 and found to be a positive prognostic factor, while co-expression of both CD40 and CD40L in glioblastoma cells correlated with negative prognosis [46]. It is noteworthy that in the ParvOryx01 study, CD40 + cells with a non-macrophage phenotype were observed in the tumor blood vessel lumen in patients who received H-1PV by intravenous infusion (Figure 1). With the limitation imposed by the unavailability of tumor samples from time points later than nine days after treatment, we hypothesize that CD40-expressing peripheral blood DCs or monocytes may be recruited to H-1PV-infected tumors and interact with CD40L + glioblastoma cells.
Viruses 2017, 9, 382 5 of 12 glioblastoma cells was first reported in 2015 and found to be a positive prognostic factor, while co-expression of both CD40 and CD40L in glioblastoma cells correlated with negative prognosis [46]. It is noteworthy that in the ParvOryx01 study, CD40 + cells with a non-macrophage phenotype were observed in the tumor blood vessel lumen in patients who received H-1PV by intravenous infusion (Figure 1). With the limitation imposed by the unavailability of tumor samples from time points later than nine days after treatment, we hypothesize that CD40-expressing peripheral blood DCs or monocytes may be recruited to H-1PV-infected tumors and interact with CD40L + glioblastoma cells.
Proinflammatory Cytokine Production in Glioblastoma Microenvironment
Two proinflammatory cytokines, IFN-γ and IL-2, were detected in the glioblastoma microenvironment of ParvOryx01 patients who also showed increased tumor infiltration with lymphocytes [45]. IL-12 was not found at detectable levels, at least at the single time point at which tissue material was collected. With this limitation imposed by the trial's risk-minimizing design, the kinetics of proinflammatory cytokine production in parvovirus-treated glioblastomas could not be followed, and a transient, short lasting expression may be missed. The cellular source of IFN-γ and IL-2 was not identified within the frame of the trial, but two types of cells (tumor-infiltrating CD4 + T cells and/or activated TAM, see below) appear as the most likely candidates.
Induction of Cathepsin B Expression
In agreement with preclinical data demonstrating cathepsin B induction and cytosolic translocation in H-1PV-infected human glioma cells [47], the expression of this lysosomal protease was significantly increased in ParvOryx01 patients, when compared with historical recurrent glioblastoma cases. Contrary to initial expectations, cathepsin B expression was observed not only in tumor cells, but mostly in TAM [45]. As increased cathepsin B production correlates with microglial activation [48], and induction of glioma apoptosis by microglia-derived cathepsin B has been demonstrated in vitro [49], first steps were undertaken within the frame of the ParvOryx01 study, to assess glioblastoma-associated microglia/macrophage activation state. Expression of inducible nitric oxide (NO) synthase (iNOS), a marker of classical (proinflammatory, macrophage phenotype M1) microglia/macrophage activation, was assessed in four ParvOryx01 patients, selected on the basis of strong CD68 positivity. While in one patient iNOS expression was not revealed, iNOS-positive cells were detected in the other three patients' tumors at day nine after H-1PV application. The availability of resection material from the primary tumor and a second recurrence (respectively preceding and following first recurrence subjected to H-1PV treatment) provided the unique opportunity to analyze glioblastoma microenvironment in a non-parvovirus-exposed tumor, as well as at a later time point after virotherapy. Compared with the control primary glioblastoma, the first recurrence (resected at day nine post-treatment) showed a clear induction of both cathepsin B [45]
Proinflammatory Cytokine Production in Glioblastoma Microenvironment
Two proinflammatory cytokines, IFN-γ and IL-2, were detected in the glioblastoma microenvironment of ParvOryx01 patients who also showed increased tumor infiltration with lymphocytes [45]. IL-12 was not found at detectable levels, at least at the single time point at which tissue material was collected. With this limitation imposed by the trial's risk-minimizing design, the kinetics of proinflammatory cytokine production in parvovirus-treated glioblastomas could not be followed, and a transient, short lasting expression may be missed. The cellular source of IFN-γ and IL-2 was not identified within the frame of the trial, but two types of cells (tumor-infiltrating CD4 + T cells and/or activated TAM, see below) appear as the most likely candidates.
Induction of Cathepsin B Expression
In agreement with preclinical data demonstrating cathepsin B induction and cytosolic translocation in H-1PV-infected human glioma cells [47], the expression of this lysosomal protease was significantly increased in ParvOryx01 patients, when compared with historical recurrent glioblastoma cases. Contrary to initial expectations, cathepsin B expression was observed not only in tumor cells, but mostly in TAM [45]. As increased cathepsin B production correlates with microglial activation [48], and induction of glioma apoptosis by microglia-derived cathepsin B has been demonstrated in vitro [49], first steps were undertaken within the frame of the ParvOryx01 study, to assess glioblastoma-associated microglia/macrophage activation state. Expression of inducible nitric oxide (NO) synthase (iNOS), a marker of classical (proinflammatory, macrophage phenotype M1) microglia/macrophage activation, was assessed in four ParvOryx01 patients, selected on the basis of strong CD68 positivity. While in one patient iNOS expression was not revealed, iNOS-positive cells were detected in the other three patients' tumors at day nine after H-1PV application. The availability of resection material from the primary tumor and a second recurrence (respectively preceding and following first recurrence subjected to H-1PV treatment) provided the unique opportunity to analyze glioblastoma microenvironment in a non-parvovirus-exposed tumor, as well as at a later time point after virotherapy. Compared with the control primary glioblastoma, the first recurrence (resected at day nine post-treatment) showed a clear induction of both cathepsin B [45] and iNOS expression in TAM cells, which persisted and even increased in the second recurrence at two months after virus application (Figures 2 and 3). These data should be put together with the in vitro demonstration of human macrophage activation as a result of their abortive infection with H-1PV [36], and with the constitutive NO and oxygen species production in human promonocytic cell clones surviving H-1PV-induced apoptosis [50]. It should also be stated that in a recent study of iNOS expression in grade IV glioblastoma patients, the iNOS levels detected failed to positively correlate with survival [51]. Altogether, the above data provide first hints on H-1PV ability to trigger M1 microglia/macrophage polarization in the glioblastoma microenvironment. This concept is still speculative but would be worth corroborating through further (pre)clinical studies, as it is of major relevance for future combinatorial approaches using H-1PV and other immunotherapeutic agents. and iNOS expression in TAM cells, which persisted and even increased in the second recurrence at two months after virus application (Figures 2 and 3). These data should be put together with the in vitro demonstration of human macrophage activation as a result of their abortive infection with H-1PV [36], and with the constitutive NO and oxygen species production in human promonocytic cell clones surviving H-1PV-induced apoptosis [50]. It should also be stated that in a recent study of iNOS expression in grade IV glioblastoma patients, the iNOS levels detected failed to positively correlate with survival [51]. Altogether, the above data provide first hints on H-1PV ability to trigger M1 microglia/macrophage polarization in the glioblastoma microenvironment. This concept is still speculative but would be worth corroborating through further (pre)clinical studies, as it is of major relevance for future combinatorial approaches using H-1PV and other immunotherapeutic agents.
Other Oncolytic Viruses and Tumor Microenvironment Modulation
In a recent editorial, de Vries et al. emphasized that the most successful OV-based strategy will be the one taking advantage of these viruses' capacity for modifying the tumor microenvironment and iNOS expression in TAM cells, which persisted and even increased in the second recurrence at two months after virus application (Figures 2 and 3). These data should be put together with the in vitro demonstration of human macrophage activation as a result of their abortive infection with H-1PV [36], and with the constitutive NO and oxygen species production in human promonocytic cell clones surviving H-1PV-induced apoptosis [50]. It should also be stated that in a recent study of iNOS expression in grade IV glioblastoma patients, the iNOS levels detected failed to positively correlate with survival [51]. Altogether, the above data provide first hints on H-1PV ability to trigger M1 microglia/macrophage polarization in the glioblastoma microenvironment. This concept is still speculative but would be worth corroborating through further (pre)clinical studies, as it is of major relevance for future combinatorial approaches using H-1PV and other immunotherapeutic agents.
Other Oncolytic Viruses and Tumor Microenvironment Modulation
In a recent editorial, de Vries et al. emphasized that the most successful OV-based strategy will be the one taking advantage of these viruses' capacity for modifying the tumor microenvironment
Other Oncolytic Viruses and Tumor Microenvironment Modulation
In a recent editorial, de Vries et al. emphasized that the most successful OV-based strategy will be the one taking advantage of these viruses' capacity for modifying the tumor microenvironment [52]. Indeed, several OVs were reported to exert positive effects in regard to tumor microenvironment modulation.
Preclinical Studies
Zamarin et al. observed marked infiltration of distant tumors with effector, but not Treg cells, in melanoma-bearing mice treated with Newcastle disease virus [53]. Intratumoral administration of an oncolytic adenovirus decreased tumor-infiltrating Treg cell numbers and stimulated IFN-γ-producing CD8 + T cells in a mouse glioblastoma model [54]. Recently, the immunotherapeutic potential of a recombinant polio/rhinovirus chimera was demonstrated in vitro in high-grade glioblastoma [55]. Other preclinical studies using bladder, colon, and breast cancer animal models also pointed to recombinant poxviruses' positive effects on the immunological components of the tumor microenvironment, as summarized in [52].
Clinical Studies
In a clinical setting, positive effects (dense tumor infiltration with effector T cells, decreased Treg and myeloid-derived suppressor cell numbers, and increased IFN-γ production by CD4 + and CD8 + tumor-infiltrating lymphocytes) of recombinant vaccinia and HSV, and of measles virus on the tumor microenvironment were demonstrated in melanoma and cutaneous T cell lymphoma patients [56][57][58][59].
Remarkably, responses were observed in both injected and non-injected melanoma lesions, in patients who were intratumorally treated with a granulocyte-macrophage colony-stimulating factor-encoding second-generation HSV [60]. The added value of poxvirus-mediated intratumoral expression of specific tumor-associated antigens was supported by clinical trials in patients with prostate and locally advanced pancreatic cancer [52]. However, clinical data on antitumor immune responses and tumor microenvironment modulation in OV-treated patients remain presently limited [61].
Tumor Microenvironment Modulation by H-1PV: Current Hypothesis and Perspective
Glioblastoma microenvironment is marked by profound immunosuppression [8]. This tumor-supportive microenvironment [51,62] is established by glioblastoma stem cells, tumor and TAM cells. The pilot ParvOryx01 study gathered initial evidence of tumor microenvironment immunogenic conversion in recurrent glioblastoma patients who underwent local or systemic H-1 parvovirotherapy (Table 1). Table 1. Main characteristics of glioblastoma microenvironment as described in the literature or observed in H-1 parvovirus-treated glioblastoma patients.
Glioblastoma Microenvironment (Literature Data) Glioblastoma Microenvironment (First Parvovirus Clinical Trial)
sparse inflammatory infiltrates (except the mesenchymal transcriptional class) [63] tumor infiltration with CD8 + /granzyme B + T cells [45] tumor-infiltrating lymphocyte involvement in inhibitory (e.g., via PD-1) interactions [8] PD-1-negative tumor-infiltrating T cells increased numbers of tumor-infiltrating Treg cells [64] Treg cells only scarcely detected [45] M2 tumor-supportive tumor-associated microglia/macrophage (TAM) phenotype [51] detection of markers of M1 TAM polarization (CD68, CTSB, iNOS) [45] release of immunosuppressive factors and anti-inflammatory cytokines [8] detection of proinflammatory cytokines (IFN-γ, IL-2) [45] Based on both preclinical experience and the observations from ParvOryx01 patients, we believe that H-1PV treatment may lead to glioblastoma-associated microglia/macrophage activation. This is supported by the increased expression of CD68, cathepsin B and iNOS in tumors of H-1PV-treated patients, in comparison with historical non-parvovirus-treated controls. As a direct result of their abortive parvovirus infection and/or indirectly, via proinflammatory mediators released by infected tumor cells, microglia/macrophages get activated and may exert toxic effects on neighboring glioblastoma cells through cathepsin B and NO release (Figure 4). Another likely scenario, supported by evidence from animal models [40], is that microglia/macrophage capacity for expressing immune costimulatory molecules (usually strongly compromised in glioblastoma) may also be increased upon H-1PV-triggered activation. Tumor tissue collection in this first trial, primarily designed to assess safety, did not allow performing such studies, but in future H-1PV glioblastoma trials, tumor infiltration with DCs, the CD40/CD40L axis, and costimulatory molecule expression on TAM and DCs will be worth investigating.
Viruses 2017, 9, 382 8 of 12 This is supported by the increased expression of CD68, cathepsin B and iNOS in tumors of H-1PV-treated patients, in comparison with historical non-parvovirus-treated controls. As a direct result of their abortive parvovirus infection and/or indirectly, via proinflammatory mediators released by infected tumor cells, microglia/macrophages get activated and may exert toxic effects on neighboring glioblastoma cells through cathepsin B and NO release (Figure 4). Another likely scenario, supported by evidence from animal models [40], is that microglia/macrophage capacity for expressing immune costimulatory molecules (usually strongly compromised in glioblastoma) may also be increased upon H-1PV-triggered activation. Tumor tissue collection in this first trial, primarily designed to assess safety, did not allow performing such studies, but in future H-1PV glioblastoma trials, tumor infiltration with DCs, the CD40/CD40L axis, and costimulatory molecule expression on TAM and DCs will be worth investigating.
(a) (b) In conclusion, H-1PV-an oncolytic parvovirus which showed excellent safety and tolerability upon local and systemic application in glioblastoma patients-may represent a novel tool for therapeutic TAM activation (Figure 4). Immunogenic conversion of TAM is the subject of intensive investigations, as exemplified by the recent preclinical demonstration of the antifungal agent's amphotericin B capacity for restoring the suppressed ability of glioblastoma-associated microglia/macrophages to target brain tumor-initiating cells [65]. We suggest that in future attempts at prolonging time to glioblastoma recurrence, H-1PV (alone or with other treatments targeting TAM) may be combined with other immunotherapeutic modalities, in particular CAR T cell-based strategies and immune checkpoint blockade, to achieve synergistic antiglioblastoma effects. In conclusion, H-1PV-an oncolytic parvovirus which showed excellent safety and tolerability upon local and systemic application in glioblastoma patients-may represent a novel tool for therapeutic TAM activation (Figure 4). Immunogenic conversion of TAM is the subject of intensive investigations, as exemplified by the recent preclinical demonstration of the antifungal agent's amphotericin B capacity for restoring the suppressed ability of glioblastoma-associated microglia/macrophages to target brain tumor-initiating cells [65]. We suggest that in future attempts at prolonging time to glioblastoma recurrence, H-1PV (alone or with other treatments targeting TAM) may be combined with other immunotherapeutic modalities, in particular CAR T cell-based strategies and immune checkpoint blockade, to achieve synergistic antiglioblastoma effects.
Author Contributions: A.L.A. conceived and designed the immunological analysis of tumor microenvironment; M.B. performed in situ immunofluorescent staining experiments; K.G. and A.U. conducted patients' treatment and post-treatment tumor tissue collection; A.L.A. and J.R. wrote the paper.
Conflicts of Interest: K.G. and J.R. are co-inventors in patents/patent applications relating to the cooperation between parvoviruses and the immune system. | 5,513.2 | 2017-12-01T00:00:00.000 | [
"Biology",
"Medicine"
] |
Surface structure influences contact killing of bacteria by copper
Copper kills bacteria rapidly by a mechanism that is not yet fully resolved. The antibacterial property of copper has raised interest in its use in hospitals, in place of plastic or stainless steel. On the latter surfaces, bacteria can survive for days or even weeks. Copper surfaces could thus provide a powerful accessory measure to curb nosocomial infections. We here investigated the effect of the copper surface structure on the efficiency of contact killing of Escherichia coli, an aspect which so far has received very little attention. It was shown that electroplated copper surfaces killed bacteria more rapidly than either polished copper or native rolled copper. The release of ionic copper was also more rapid from electroplated copper compared to the other materials. Scanning electron microscopy revealed that the bacteria nudged into the grooves between the copper grains of deposited copper. The findings suggest that, in terms of contact killing, more efficient copper surfaces can be engineered.
Introduction
Metallic copper surfaces have been shown to rapidly kill a range of microorganisms and viruses (for a recent review, see Grass et al. 2011). This so called 'contact killing' has raised renewed interest in the use of copper for touch surfaces. In health care settings, copper holds great promise as an added measure to curb nosocomial infections and a number of hospital trials have been conducted or are underway. First studies showed that copper surfaces can diminish the bacterial surface-loads up to 90% as compared to surfaces of other materials (Casey et al. 2010;Marais et al. 2010;Mikolay et al. 2010;Rai et al. 2012;Schmidt et al. 2013) and can significantly reduce nosocomial infections .
These findings have also raised an interest in understanding the mechanism of contact killing. Although this mechanism is still not fully understood, recent studies suggest that copper surfaces kills bacteria by a threepronged attack: damage of the bacterial membrane, DNA degradation, and extensive intracellular damage (Espirito Santo et al. 2008Weaver et al. 2010;. The sequence of these events is still under debate and may in fact be different, depending on the microorganism (Warnes et al. 2012). However, a key event in the killing process appears to be the release of copper ions from the copper surface; these ions can in turn, not only lead to the generation of highly toxic hydroxyl radicals in a Fenton-type reaction but also inactivate metalloproteins by replacing the respective metal with copper. In Escherichia coli, it was shown that FeS clusters are specific targets of copper toxicity (Macomber and Imlay 2009). That released copper ions are important in contact killing is further supported by the finding that bacteria resistant to copper are killed more slowly, and by the retardation of contact killing by corrosion inhibitors (Elguindi et al. 2009(Elguindi et al. , 2011Zhu et al. 2012).
The importance of copper ions in contact killing implies that the nature of the metallic copper surface plays an important role. We here used microstructured copper surfaces to show that increasing the copper surface leads to more rapid copper release and concomitantly, more rapid contact killing of E. coli. Such copper surfaces could thus provide superior antimicrobial surfaces for use in health care settings.
Generation of copper coupons
Rolled copper foils (99.9% copper, Circuit Foil Luxembourg, Luxembourg) were used as starting material. Electrodeposition was performed using a three-electrode cell with an Ag/AgCl reference electrode and two copper foils of 2.5 9 2.5 9 0.05 cm at a distance of 2 cm from each other, functioning as working and counter electrode. Thus, one foil was used as target material to structure the surface, whereas the other foil was used as substrate. For copper deposition, a current density of 20 mA cm À2 was applied for 300 seconds in 40 mL of an electrolyte solution composed of 2.5 mol L À1 CuSO 4 and 1.2 mol L À1 H 2 SO 4 . For the generation of polished copper surfaces, rolled copper was polished successively with 6 lm, 3 lm, and 1 lm diamond paste for 5 min each. Afterward the copper surface was extensively cleaned with ethanol and distilled water.
Copper ion release by copper surfaces
Copper ions released into the aqueous phase by coupons were measured by atomic absorption spectroscopy (AAS). To remove possible oxide layers, coupons were cleaned by successively dipping them for 5 sec each into 10% H 2 SO 4 , water, and 3% NaOH, followed by extensive washing in water. For copper release measurements, 25 lL of 0.9% NaCl were applied to coupons, covering a surface area of 16.0 AE 2.1 mm 2 . After different incubation times at 22°C in a water-saturated atmosphere, a quantity of 20 lL of liquid was removed and dissolved copper was analyzed by AAS with a Vario 6-MPE 50 instrument (Analytics Jena, Jena, Germany). Measurements were conducted in 20 min intervals over the course of 1 h and the average release rates determined by linear regression analysis.
Measurement of contact killing
The antibacterial activity of the different copper coupons was tested according to the common wet plating method (Wilks et al. 2005;Noyce et al. 2006;Weaver et al. 2008;Molteni et al. 2010). Briefly, test coupons of 2.5 9 2.5 cm were disinfected by dipping in 76% ethanol and drying in air, followed by treatment as for AAS described above. The Gram-negative test organism, E. coli K12 (ATCC 23716), was grown aerobically overnight in Luria-Bertani (LB) broth at 37°C (Ausubel et al. 1995). A culture volume of 1 mL was mixed with 10 mL of 0.9% NaCl. Culture aliquots of 25 lL, corresponding tõ 2 9 10 8 colony forming units (cfu), were deposited on the test coupons and incubated at 37°C in water-saturated air. After different contact times, 20 lL of the droplets were removed and diluted in 180 lL of media consisting of 3.6 g L À1 KH 2 PO 4 , 7.2 g L À1 Na 2 HPO 4 Á 2H 2 O, 4.3 g L À1 NaCl, 1 g L À1 meat peptone and 0.1% Tween 80. Serial dilutions were applied to LB agar plates and following incubation for 24 h at 37°C, cfu were assessed. Plating bacteria in parallel in an identical fashion on polycarbonate was used as a control in all experiments.
Electron microscopy
The surface topography of the copper coupons was analyzed by scanning electron microscopy with a FEI Quanta 400 instrument (FEI, Hillsboro, OR) operating in standard mode. To visualize E. coli in contact with the surfaces, 2 9 10 8 cells in 25 lL of 0.9% NaCl were applied to the surface and dried. Visualization was accomplished with a FEI Quanta 400 instrument operating in environmental scanning electron microscopy (ESEM) mode at 5 kV. Multiple images were acquired in all cases.
Surface structures
To investigate the influence of the surface structure of metallic copper on contact killing, copper coupons with different surface topographies were produced. Using standard industrial rolled copper foil as starting material, rough copper surfaces were generated by electrodeposition and smooth copper surfaces by polishing. The surface topography of the copper coupons was visualized by scanning electron microscopy with a FEI Quanta 400 instrument (Fig. 1). The starting material, rolled copper, exhibited parallel groves with an average depth of 1-2 lm, typical for this type of material. Polished copper on the other hand had a smooth surface structure, with comparatively minor grooves in the polishing direction. The dark patches in Figure 1B are irregularities of unknown origin which commonly occur in the copper starting material. Electroplating of copper finally resulted in a rough surface covered with copper grains, ranging in diameter from 1 to 5 lm (Fig. 1C). Although electrodeposited and rolled copper surfaces displayed surface structures of similar size, they were qualitatively different. While electrodeposited copper displayed a pebbled surface structure, that of rolled copper featured uneven, parallel grooves.
Copper release
It has previously been shown that there is a correlation between the release of ionic copper by the metal surface and the rate of contact killing. Copper ion release by the different copper surfaces was thus investigated. As shown in Figure essentially linear for 40 min, but decreased slightly thereafter for deposited and polished copper. Initial copper release rates were 0.42 nmol min À1 cm À2 for rolled copper, 0.33 nmol min À1 cm À2 for polished copper, and 0.77 nmol min À1 cm À2 for deposited copper, based on a contact area of 16.0 AE 2.1 mm 2 . These release rates raised the copper concentration in the aqueous phase to 0.16, 0.13 and 0.32 mmol/L in an hour. Surprisingly, copper release by rolled copper was only 20% higher than by polished copper, in spite of the much rougher surface aspect of this material. We have currently no explanation for this phenomenon. Copper release by deposited copper was, however, twofold higher than by the aforementioned copper surfaces. Electrodeposition leads to a fine-grained surface structure which is apparently more reactive toward an aqueous phase than either rolled or polished copper.
Contact killing
When bacterial suspensions were applied to polycarbonate control coupons, no significant killing could be observed over 180 min (Fig. 3). On coupons of rolled or polished copper, 2 9 10 8 bacteria were completely killed in 100 min. On electrodeposited copper, on the other hand, complete killing only took 60 min. The higher rate of copper release by electrodeposited copper thus correlated with its stronger antimicrobial properties, suggesting that the rate of copper release is a key factor in contact killing. In a previous study, it was similarly shown that the antibacterial activity of rough, cold sprayed copper surfaces was more pronounced than that of smooth, plasma sprayed or wire arc sprayed copper surfaces (Champagne and Helfritch 2013). Unfortunately, copper release by these different copper surfaces was not assessed and no direct comparison to standard copper surfaces was made. But is appears clear that the surface structure of copper has an influence on the efficiency of contact killing and a major factor for this may be the differing release of ionic copper.
Visualization of bacteria on copper surfaces
To obtain information about the behavior of bacterial cells on the different copper surfaces, we visualized them by scanning electron microscopy without using a staining procedure. The surface aspects in these pictures look somewhat different from those in Figure 1, due to the different imaging technique which had to be used (see Material and Methods). On rolled copper, the spread of cells on the surface was uneven, but it did not appear to follow the uneven surface structure ( Fig. 4A and B). In contrast, cells spread much more evenly on polished copper ( Fig. 4C and D). On deposited copper, cell spread was comparable to that on rolled copper, but the cells nudged into the grooves between the copper grains ( Fig. 4E and F). It has recently been shown that bacteriacopper contact is important in the contact killing process (Mathews et al. 2013). The lodging of bacteria into the grooves of deposited copper would of course enhance bacteria-metal contact, which could be an additional reason for the enhanced contact killing by deposited copper. Further work will have to address, whether enhanced copper release or more extensive surface contact is the primary reason for the increased efficiency of deposited copper in contact killing. The antimicrobial properties of copper and copper alloys make them materials of choice for the fabrication of antimicrobial surfaces in health care settings or food processing industries. The finding reported here that the antimicrobial activity of electrodeposited copper is superior to that of rolled or polished copper may be an important engineering consideration in this connection. Electrodeposition of copper is a straight-forward, inexpensive industrial process which can be applied to a variety of metals. This could be a cost-effective method to make surfaces antimicrobial. | 2,758 | 2014-04-17T00:00:00.000 | [
"Materials Science"
] |
Recovery of Scandium, Nickel and Cobalt from Hydrometallurgical Waste of Laterite
Recovery of new-energy critical metals including scandium, nickel and cobalt as well as copper and zinc from a neutralization residue produced in laterite hydrometallurgical process has been studied. Effect of leaching parameters such as acid consumption, solution pH and temperature has been investigated. It was found that scandium, nickel, cobalt and copper could be recovered at high efficiencies from the residues by selective leaching using sulphuric acid solutions under ambient conditions, while the co-leaching of impurities including iron, aluminium and silicon was low under the optimal conditions. The nickel, cobalt, copper and zinc in the leaching solution could be further concentrated into mixed sulphides and separated from impurities by sulphide precipitation.
Introduction
Laterite has become the main resource of nickel recovery in the world.About 0.12-3.0%Ni with 50-85% of Fe2O3, 4.0-18% of Al2O3, 0.2-5.0% of MgO, 0.6-1.0% of CaO, and 0.3-2.5% of MnO are contained in limonitic laterite produced at different sites [1].The Ramu NiCo Project in PNG (Papua New Guinea) contains a total identified resource of 143.2 Mt of nickeliferous laterite [2].It was designed to produce a mixed hydroxide product containing 31,150 tonnes of nickel and 3,300 tonnes of cobalt annually.The laterite-contained metals including scandium, nickel and cobalt are called as new-energy critical metals.Nickel and zinc were added in the draft 2021 U.S. critical minerals list, besides scandium and cobalt had been included on the 2018 list.In 2021, the average annual price of nickel was increased by 30% comparing with that in 2020, which was probably attributed to the increased application of nickel in electric vehicle batteries and continued strong demand for stainless steel.The price of scandium oxide was US$2.2 per gram, and the principal uses for scandium were in aluminum-scandium alloys and solid oxide fuel cells (SOFCs) [3].The laterite ore used in the Ramu project in PNG is a laterite with about 1% of nickel and about 0.1% of cobalt.The impurity contents of the laterite are high, such as about 40% of iron, about 3% of silicon and about 2% of aluminium.Most of the iron and aluminium impurities have been rejected in the HPAL (high pressure acid leaching) hydrometallurgical process [4,5].However, the concentrations of iron and aluminium in the pregnant leaching liquor are still too high to precipitate nickel and cobalt into a mixed-hydroxide product.Currently, the impurities are removed from the solution system by neutralisation and precipitation with limestone and calcium hydroxide, resulting in the formation of large amounts of neutralisation residues.About 80,000 tons of neutralisation residues were produced as hydrometallurgical wastes in RAMU project annually.The residues contain high contents of impurities including iron, aluminium and silicon as well as calcium.Although, in order to reduce the loss of nickel and cobalt by precipitation, the precipitation pH value had been strictly controlled and was below their precipitation pH value of about 7.0.It was found that some valuable metals including nickel, cobalt and copper were co-precipitated with the impurities in some degree.Similarly, it was reported that nickel and cobalt were present in the precipitate from synthetic laterite leach solutions even at a pH value as low as 4.0 [6][7][8].The loss of the valuable metals is significant, considering the large amount of such neutralisation residue in the world.However, it is difficult to recover the values from the laterite neutralisation residues, considering the value contents are much lower than the main impurity elements, such as iron.In most of the industrial plants, the laterite neutralisation residues were wastes which are disposed in hazardous landfill sites after stabilization treatments.In order to recover the valuable metals in an economical way, it is necessary to keep the material and energy consumptions in low levels, and it is desirable to have a high recovery of the value metals while a low recovery of the impurities by controlling their dissolutions.Thus, currently the metal values are not recovered in most of the laterite processing plants including the Ramu hydrometallurgical plant.In this article, the recovery of the valuable metals from the neutralisation residue has been studied.The effect of leaching parameters such as acid consumption and pH has been investigated.The scandium, nickel, cobalt and copper can be recovered at high efficiencies from the residues by selective leaching using sulphuric acid solutions under ambient conditions, and the co-leaching of iron was low under optimal conditions.A hydrometallurgical method for the recovery of scandium, nickel, cobalt and copper from the laterite-originated waste by selective leaching with sulphuric acid and subsequent sulphide precipitation was proposed.
Experimental 2.1. Materials
The laterite neutralisation residue used in this work is from the pilot production of the RAMU plant in Papua New Guinea.The chemical composition of the neutralisation residue sample used for this work is listed in Table 1. ) were mixed with 210 mL of de-ionised water in a 500 mL beaker covered with plastic film.The mixture was stirred mechanically at 300 rpm and heated on an electrical hotplate with the temperature controller set at 90℃ for 1 hour, and then a certain amount of concentrated sulphuric acid was added.The reaction mixture was heated and stirred continuously for 1 h.The leachate was filtrated using vacuum filtration with a paper filter, and the filtrate liquor was polish-filtered using a 0.45 μm PVDF membrane filter for sample analysis.The filter residue was re-mixed with 80 mL of de-ionised water, heated at 90℃, stirred for 10 minutes and filtered.The pH values of aqueous phases were determined with a ROSS Sure-flow electrode (model 8172BN) and a Hanna portable pH meter (HI 9025).The element concentrations were determined using inductively coupled plasma atomic emission spectroscopy (Optima 5300DV, Perkin Elmer).The electron microscope (EM) pictures were determined with a Mitutoyo microscope (Hyper MF-U).
Residue Characterization
The calcium content of the residue was about 17.92% (Table 1), indicating that the residue mainly contains calcium compounds.It is consisted with the fact that the residue was formed as a product of neutralisation process using limestone and calcium hydroxide, with formation of calcium sulphates.The other main constituents are iron (5.87%), aluminium (4.87%), and silicon (1.527%).The content of nickel, cobalt and copper was about 1.14%, 0.042% and 0.196%, respectively.The residue also contained low amounts of magnesium and manganese.
The electron microscope (SEM) pictures of the residue show the rod-like crystals and particulate matter.It is assumed that the crystals and particulates are composed with calcium sulphate hydrates (gypsum) and compounds of the other main elements, including iron, aluminium and silicon, respectively, since the former is readily to form by crystallisation, while the latter form amorphous aggregates of hydroxides.Some of the crystals are transparent and others are translucent or opaque, indicating the presence of impurities.The size of the crystals generally has dozens of micrometres in width and hundreds of micrometers in length.The residues generated through precipitation within a pH range of about 4.0-6.0 in the RAMU pilot production, so as to precipitate the dissolved nickel, cobalt and copper sulphates as mixed hydroxides, associated with iron and aluminium [9].Probably, a small amount of the mixed hydroxides could be co-precipitated with calcium sulphates.At the same time, a fraction of the nickel, cobalt and copper sulphates could be co-precipitated with the mixed hydroxides and calcium sulphates by the entrainment and adsorption.Hence, it is assumed that nickel, cobalt and copper are present, as both hydroxides and sulphates in the precipitate, together with iron and aluminium hydroxides and calcium sulphates.The value metals including nickel, cobalt and copper are generally contained in the amorphous aggregates of hydroxides with iron and aluminium, while a certain fraction of them is associated with the gypsum crystals.
Effect of Sulphuric Acid/Ore Ratio on pH Values of Leachates
A number of acid/ore ratios (mass/mass) were tested at different pH values of leachates for metal leaching.As shown in Figure 2, the pH value of both the first leachates and the second leachates decreased with the increase of the sulphuric acid/ore ratio.The pH values were in the range of about 2-4 when the sulphuric acid/ore ratio was in a range from 0.25: 1 to 0.07: 1 (Figure 2).It was found that the pH values of the second leachates using water for leaching were slightly higher than the corresponding pH values of the first leachates using sulphuric acid solutions, indicating that the residual acid from the first leaching was fractionally used for the second 1-1 W: 0.082 mm L: 0.246 mm 1-2 W: 0.053 mm L: 0.072 mm leaching, and most of the residual acid was transferred to the new leachate solution.The second leaching can be considered as a washing procedure and no more acid was necessary to be added.
Figure 2.
Effect of sulphuric acid/ore ratio (mass/mass) on pH values of leachates.
Effect of Leach pH on the Metal Concentration in the Solutions
As shown in Table 1, the contents of nickel, cobalt and copper in the neutralisation residue were relatively low comparing to calcium, iron, aluminium and silicon.Thus, calcium, iron, aluminium and silicon can be predominantly interferential elements and are the main impurities for the recovery of the valuable metals including nickel, cobalt and copper using the low-sulphuric acid method in this study.Although the content of calcium was about 18%, the concentrations of calcium in the solutions were relatively low and in the range from 0.0005g/L to 0.0037g/L, which is similar to the data reported in literature that the low saturated solubility of calcium suphate in solutions with low concentration of sulphuric acid [10].Hence, the separation of nickel, cobalt and copper over calcium has been achieved by the low-sulphuric acid method.It was found that after a single contact of the first leaching the concentrations of metal ions including nickel, cobalt, copper, iron, aluminium and silicon in the pregnant leaching solutions decreased with the increasing pH of the solutions (Figure 3), which is in agreement with the previous findings that the concentrations of metals including nickel, cobalt, copper, iron and aluminium decreased with the neutralization pH for precipitation from laterite leach solutions [6].As one of the main elements for recovery, nickel has the highest content in the residue and the highest concentration in the pregnant leaching solutions over those of cobalt and copper.The concentrations of nickel ions were significantly higher than most of the impurity metals including iron and silicon except aluminium in the pH range studied (2.0-3.7)(Figure 3).For example, at pH about 3.22, the nickel concentration was about 2.38g/L, while the concentrations of iron and silicon ions were only about 0.33g/L and 0.025g/L, respectively.In the pH range from about 2.8 to about 3.7, the concentrations of metal ions in the pregnant leaching solutions were in the following order: aluminium(III)> nickel(II)> magnesium(II)> copper(II)~ silicon(IV)~ manganese(II) > iron(III)> cobalt(II)> calcium(II).The molar concentration ratios of nickel(II) ions over other metal ions in the pregnant leaching solutions with the first leaching were showed in Table 2.It was found that the concentration ratios of nickel ions over iron, aluminium and silicon at lower pH, were significantly lower than those with higher pH.For example, the Ni/Fe, Ni/Al, Ni/Si ratios were 1.61, 0.15 and 1.21 at pH about 2.06, which were improved to be 6.83, 0.29 and 3.04, respectively, at pH around 3.36.Hence, the optimal selective extractions and separation of nickel over iron, aluminium and silicon can be achieved in a relatively high pH range, such as the pH from 2.82 to 3.68.However, the pH should be controlled in a relatively low pH level in order to achieve high concentration of nickel in the leaching solution.The concentrations of aluminium in the pregnant leaching solutions linearly depends on the pH from pH about 2.06 to about 3.68, indicating the aluminium hydroxides complexes in the neutralisation residue were gradually dissolved by sulphuric acid.It showed that the concentration of the iron ions was in small amount at low acidity of H2SO4 with pH above 3.0, but became significantly higher after the pH was below about 2.8 (Figure 3).For example, the concentrations of iron ions were about 0.33g/L and 2.22g/L at pH about 3.36 and 2.06, respectively.This behavior is consistent with the enhanced hydrolysis of iron(III) ions at the higher pH values and comparing well with the pH of 2.90 at 25℃ for iron(III) hydrolysis given by Baes and Mesmer [11].Thus, in order to avoid the significant dissolution of the impurities, such as ferric and aluminium hydroxides, the leachate pH should be controlled in a comparatively high level, and the reaction conditions benefit for the hydrolysis of metals ions, which has versa effect on dissolution.
Thereafter, a pH in a range of 2.8-3.0 is desirable considering the above data with relatively low dissolution of impurities, such as ferric and aluminium hydroxides, while with relatively high dissolution of nickel, cobalt and copper complexes.Furthermore, a relatively high temperature, such as 90℃ used in this study, is beneficial to improve the metal hydrolysis, considering the initial hydrolysis pH of metals ions, including iron(III) and Al(III) ions, can shift to lower pH with increasing temperature [12,13].
Effect of acid/ore ratio on recovery efficiency of leaching
The total recovery percentages of metals with two contacts of leaching are in the following order: Mn>Sc~ Co> Cu >Ni >Al~ Si> Fe> Ca (Figure 4).The complete dissolution of manganese was readily achieved with low to high amounts of sulphuric acid.The leaching percentage values of calcium were very low (all lower than 0.4%) in all the acid/ore ratio range studied, most possibly owing to the low dissolution of gypsum under our test conditions.It was found that the iron dissolution was low and the leaching percentages slightly increased from 1.54% to 3.61% in the acid/ore ratio range from 0.07:1 to 0.19:1 (Figure 4).The leaching percentages of scandium, nickel, copper and cobalt all significantly increased with the increase of acid/ore ratio.After contacting with acid leaching and water leaching, the complete dissolutions of scandium, nickel, copper and cobalt were all achieved when the acid/ore ratio was close to 0.19: 1.However, the dissolutions of impurities including aluminium and silicon reached to a relatively high level at the same time.Actually, an acid/ore ratio around 0.16: 1 was sufficient for leaching out about 94.79% of nickel, about 96.46% of copper and about 100% of cobalt from the residue while the leaching percentage of the impurities were much lower.Thus, the optimised sulphuric acid/ore ratio was selected to be about 0.16: 1, considering the relatively high recovery of the valuable metals including scandium, nickel, copper and cobalt and the relatively low leaching of impurities elements including iron, aluminium and silicon.
Recovery of the Valuable Metals from Solution by Sulphide Precipitation
The method with mixed sulphide precipitations was used to recover the valuable metals from the laterite PLS solution in this study, due to the strong combination of divalent transition metals including nickel, copper and cobalt and the rejection of aluminium, magnesium and calcium.The PLS solutions from the above leaching tests were blended and about 1.0 liter of the blended solution was used for a preliminary precipitation test with 0.61 mol/L of potassium sulphide solution.About 1.4 liter of a barren solution was obtained with an end pH point of about 4.10 after precipitation.Based on the metal concentrations in the original blended solution and barren solution, the precipitation percentages of the metals including nickel, copper and cobalt were calculated.It was showed that 99.6% of nickel, 99.2% of cobalt and 99.9% of copper can be preferentially precipitated as concentrate solids while only about 9.2% of aluminium, 5.2% of calcium, 11.4% of manganese and 10.9% of magnesium were co-precipitated.Although the iron precipitation percentage was about 47.8%, the iron amount in the concentrate solid can be low considering the iron concentration in the PLS solution was only about 0.22g/L (Table 3).The scandium ions with low concentrations in the barren solution could be recovered by solvent extraction with various organic extractants [14,15].
Conceptual Flow-sheet for Recovery of from Neutralisation Residue
Based on the above results, a conceptual flow-sheet for recovery of scandium, nickel, cobalt, copper and zinc from neutralisation residues of laterite hydrometallurgy can be proposed as: first, selective leaching of scandium, nickel, cobalt and copper from neutralisation residues into PLS with low concentration of sulphuric acid solutions, and separating from the main impurities including iron, aluminium and silicon; second, selectively precipitating of nickel, cobalt, copper and zinc from the leachates into concentrates with sulphides such as sodium sulphide and hydrogen sulphide, to make efficient separations from the impurities including scandium, manganese, magnesium and aluminium (Figure 5).
Conclusions
The recovery of scandium, nickel, cobalt, copper and zinc from a neutralisation residue of laterite hydrometallurgy of RAMU project has been studied.The results show that scandium, nickel, cobalt and copper can be recovered at high efficiencies from the residues by selective leaching using sulphuric acid solutions under ambient conditions, and the co-leaching of iron is low under the optimal conditions.In the pH range from about 2.8 to about 3.7, the concentrations of metal ions in the pregnant leaching solutions are in the following order: nickel (II)> copper (II)> iron (III)> cobalt (II)> calcium (II).The total recovery percentages of metals with two contacts of leaching are in the following order: Mn>Sc~ Co> Cu >Ni >Al~ Si> Fe> Ca.The mixed leaching solution is further purified with sulphide precipitation processes using sulphide salt.A conceptual flowsheet to recover scandium, nickel, cobalt, copper and zinc from laterite neutralisation residues has been proposed.These findings make practicable larger-scale evaluation of valuable metals recovery from nickel laterite neutralisation residue, reveal the fundamental behaviour of the impurity rejection process, and potentially provide a process enabling guide further industrial development of laterite-processing production with high quality.
Figure 1 .
Figure 1.EM picture of the residue.
Figure 3 .
Figure 3.Effect of leaching pH on the metal concentration in the solutions.
Figure 4 .
Figure 4. Effect of sulphuric acid/ore ratio on total recovery percentages.
Figure 5 .
Figure 5.A conceptual flow sheet for metal recovery from neutralisation residue
Table 1 .
Composition of the neutralisation residue.
Table 2 .
Effect of pH on molar concentration ratio of metal ions in the PLS
Table 3 .
Recovery of the valuable metals from solution by sulphide precipitation. | 4,162.2 | 2024-01-01T00:00:00.000 | [
"Environmental Science",
"Materials Science"
] |
Optimizing the Design of Small Fast Spectrum Battery-type Nuclear Reactors
This study is focused on defining and optimizing the design parameters of inherently safe " battery " type sodium-cooled metallic-fueled nuclear reactor cores that operate on a single stationary fuel loading at full power for 30 years. A total of 29 core designs were developed with varying power and flow conditions, including detailed thermal-hydraulic, structural-mechanical and neutronic analysis. Given set constraints for irradiation damage, primary cycle pressure drop and inherent safety considerations, the attainable power range and performance characteristics of the systems are defined. The optimum power level for a core with a coolant pressure drop limit of 100 kPa and an irradiation damage limit of 200 DPA (displacements per atom) is found to be 100 MWt/40 MWe. Raising the power level of an optimized core gives significantly higher attainable power densities and burnup, but severely decreases safety margins and increases the irradiation damage. A fully optimized inherently safe battery-type fast reactor core with an active height and diameter of 150 cm (2.6 m 3), a pressure drop limit of 100 kPa and an irradiation damage limit of 300 DPA can be designed to operate at 150 MWt/60 MWe for 30 years, reaching an average discharge burnup of 100 MWd/kg-actinide.
Introduction
A wide array of technology options for nuclear reactor systems exist, with the main parameters determining system characteristics being the physical size, power level, primary and secondary coolant and type of fuel.The dominant reactor technology in the world today is large high-power reactors that are cooled and moderated by water (light or heavy) using uranium oxide fuel, producing electricity using OPEN ACCESS a steam cycle.Recently, much of the focus of commercial reactor vendors and national programs has switched to the development of Small Modular (thermal) Reactors (SMR).There are currently ~10 small thermal modular reactor concepts with capacities below 300 MWe in well-advanced stages of development.The SMRs offer unique advantages such as the ability to manufacture and potentially mass-produce reactor units in factories rather than on-site.There are several additional advantages with SMR-type technology, which include: Enhanced safety features (robustness) o Easier implementation of passive safety features Suitable for isolated or small electrical grids Lower capital cost per unit o Small initial investment and short construction period reduces financial risks o Makes nuclear energy feasible for more utilities and energy suppliers Short construction time o Improved economics and reduced financial risk Improved quality control and modular construction Just-in-time capacity addition o Enable gradual capacity increase to meet electric demand growth Multi-purpose application (co-generation flexibilities) Appropriate size to replace retiring fossil plants and use portions of the existing plant and facilities A single SMR unit may not be able to compete economically with a large plant, since many of the same systems need to be in place while the SMR produces only a fraction of the power.However, with co-location of multiple SMR units and efficient standardized factory manufacturing of all major components, there is great potential that SMRs could radically reduce the cost of nuclear power.The Airbus A-380 is the largest available passenger airliner and is comparable in size, technical complexity and regulatory demands to an SMR; factories can produce it at a rate of about one unit every 8-9 days.
While thermal SMRs (where most of the fissions are induced by low energy neutrons) may have economic and safety potential, they are still subject to the technological limitations inherent in all solid-fuel thermal nuclear systems, which is the poor utilization of fuel resources.A thermal reactor (small or large) is able to extract a mere ~0.6% of the potential fission energy of the mined uranium.With highly complex and expensive reprocessing to produce mixed oxide (UO 2 -PuO 2 ) fuel from used fuel, this number can be increased up to ~0.9%.In contrast, a fast system (most of the fissions are induced by high energy neutrons) is in principle able to utilize the full energy potential of the fuel resource, minus inevitable inefficiency losses in reprocessing units.A small modular fast reactor (SMFR) system can combine the superior fuel utilization potential of a fast system with the economic potential of modular design methods.Due to their capability to breed their own fuel during operation, SMFRs can run on the initial fuel load for several decades, compared to the 18-24 month cycle of thermal systems.
The objective of this study is to combine existing and novel principles and ideas to develop an optimized pre-conceptual design of a new SMFR "battery" type reactor core that operates continuously on a single static fuel loading for 30 years.Existing nuclear battery concepts, from which many of the ideas of this study are based or inspired, include the ENHS (Encapsulated Nuclear Hear Source) [1], ARC-100 (Advanced Reactor Concepts-100) [2], AFR-100 (Advanced Fast Reactor-100) [3], SMFR (Small Modular Fast Reactor) [4], PEACER (Proliferation-resistant, Environment-friendly, Accident-tolerant, Continual and Economical Reactor) [5], Toshiba 4S (Super-Safe, Small and Simple) [6] and S-STAR (Secure, Transportable, Autonomous Reactor) [7].
Section 2 summarizes the basis for the core design study, including general design choices and the layout of the core.Section 3 defines the constraints and limits applied to design parameters and components.Section 4 explains the general design methodology and presents the codes and tools used in the study.In Section 5, the results of the parametric study for parameters such as core size, power density, burnup and reactivity swing are presented.Section 6 presents the reactivity feedback coefficients, which are used for safety analysis using the quasi-static reactivity balance method in Section 7. Conclusions and future work is summarized in Section 8.
Summary of General Design Parameters
A number of general design parameters have been set and are not subjected to parametric studies.This is partly to limit the scope of the study but also because some design parameters are estimated a priori to give optimal core performance.These design choices are summarized in Table 1 and their motivations are discussed in the following subsections.
Choice of Coolant
To achieve the conversion ratio required to keep the reactivity swing to a minimum and enable the discharged fuel to be remanufactured in to a new core without adding extra fissile material, a hard neutron spectrum is required.The choice of coolant is thus limited to low-moderation fast reactor coolant options such as a liquid metals or a gas.The option of a gaseous coolant was rejected due to the safety implications of a potential leak in the high-pressure coolant system.The choice between lead (or lead-bismuth eutectic) and sodium as the primary coolant for this application is in no way obvious.It was decided to limit this study to systems cooled by sodium, which is a more mature technology and which allows for a higher volumetric power density.Future studies, particularly those focusing on natural circulation cooled systems, will include lead or lead-bismuth eutectic as options for the primary coolant.
Fuel, Fuel Rod and Assembly Geometry
All else being equal, maximizing the actinide density maximizes the neutron economy of a fast reactor core of a given volume.Metallic fuel offers the highest actinide density of any available fuel alternative, even when alloyed with 10 wt% zirconium.Since long-life cores operate at low power density, peak fuel temperatures are low which allows for a reduction in the fuel solidus temperature and a smaller Zr-alloying component weight fraction.A reduction of the Zr-component from 10% to 2% in the fuel enables an 18% increase in the fuel density, from 15.85 to 18.74 g/cm 3 at 500 °C, while reducing the solidus temperature from ~1200 °C to ~1100 °C [8].Instead of primarily relying on the fuel-alloy zirconium-content as a diffusion barrier to avoid fuel/cladding chemical interaction (FCCI), the inner surface of the cladding steel is coated with a 30 μm thick vanadium liner [9].
To avoid the use of a liquid bond material and potentially limit axial fuel swelling, the fuel rod is designed as an annulus rather than the shape of a conventional solid cylinder.While the rod design allows for up to 10% axial swelling of the fuel, it is expected that the radial mechanical contact with the cladding steel will limit axial swelling to a only a fraction of this value.Limiting axial swelling improves the neutron economy and simplifies reactivity control of the core.Upcoming irradiation campaigns of "mechanically bonded" metallic fuel in the Indian Fast Breeder Test Reactor (FBTR) will make it possible to more clearly estimate the axial growth of this type of fuel [10].The reference fuel rod design is shown from above and from the side in Figures 1 and 2 respectively.A similar type of fuel was manufactured by Argonne National Laboratory in the early 1960s and was tested in the EBR-1 reactor [11].To minimize the stress induced in the cladding from gaseous fission products and reduce the overall length of the pin, a 40-cm DISCA-type diving bell fission gas venting device is installed at the top of each pin.This allows for venting of gaseous fission products into the coolant and a continuous depressurization of the rod.No specific design was worked out for the venting device; its preliminary length estimate is conservatively based on the data presented in Martini and Gerosa [12].Since the metallic fuel form is chemically compatible with the coolant (in contrast to the ceramic fuel for which the DISCA concept was developed) there may be substantial room for optimizing the fission-gas venting device-this will be a topic of future studies.
Core Layout
In theory, the most neutronically efficient shape of a volume containing fissile material is a sphere, since this geometric shape minimizes the surface to volume ratio and thus minimizes the loss of neutrons.Since it is not practical from an engineering perspective to design a (controlled) nuclear core as a sphere or spheroid shape, the preferred shape considering both engineering and neutron economy is that of a cylinder with equal height and diameter.A core made up of a lattice of hexagonal assemblies can be designed to approximate a circular shape by removing assemblies at the corners of the hexagonal lattice.The number of fuel assemblies in a core of this shape with symmetrical rings of burnup control and SCRAM assemblies (where the central assembly is not a fuel assembly) is given by [13]: where n is the number of hexagonal rings of fuel assemblies and N is the number of non-fuel (control, experimental etc.) assembly rings, excluding the central assembly As will be shown in Sections 5-7, the range of possible power outputs from an optimized battery-type core operating for 30 years is quite limited.It was found that in this limited range of power and corresponding range of core volumes, a single core layout could be used for all cores analyzed.To change the size of the core, the width and height of individual assemblies were altered.The optimal numbers for n (the number of fuel assembly rows) and N (the number of in-core control assembly rows) were found to be 5 and 2 respectively, giving a total of 48 fuel assemblies and 13 control assemblies.As core power and size is varied, the width across the flats of the ducts of the fuel assemblies range in the span 16-25 cm, which is within the span typical of fast reactor designs [14].Out of the 13 control assembly positions, 9 are dedicated to fine adjustment of reactivity (burnup reactivity swing, start-up and planned shut-down) and 1 + 3 are dedicated to two separate and redundant equal-reactivity SCRAM systems.Surrounding the core radially is one row of 24 reflector assemblies and beyond that one row of 36 shield assemblies.The complete layout of the 121 assemblies that make up the core is shown in Figure 3.The fuel assemblies have been subdivided in to three batches, which mark flow orificing zones.Radial enrichment zoning with higher feed-fuel fissile content in the outer radial zones (Mid fuel and Outer fuel of Figure 3) could ostensibly lead to a more optimized core by flattening the radial power profile.For very low levels of burnup, it is possible that such enrichment zoning can lead to better core performance, but this is likely not true for long-life cores with average discharge burnups exceeding the levels of current light water reactor (LWR) technology (>60 MWd/kg).
Moving power generation and neutron flux toward the periphery of the core increases the neutron leakage probability, which to some extent counteracts the performance gains from a flatter power distribution.More importantly for this application, radial enrichment zoning leads to severe problems with the coolant flow distribution over core life, which has a strong negative impact on the core design.In a core with a uniform level of enrichment that maintains a constant reactivity over core life, there is little change in the radial power distribution as burnup progresses [15].Thus a full-cycle optimal flow distribution can be designed by tailoring flow orifices in the fuel assembly coolant inlet regions.In a core with radial enrichment zoning that maintains constant reactivity, the central zones will "over-breed" fissile material and gain in relative power, while the outer radial zones will be "burners" and decrease in relative power during core life.Since the flow distribution to each assembly must be dimensioned to keep temperatures below constraints at maximum local power, all assemblies are "overcooled" for most of the core life, which in every sense is far from optimal.
For this reason, along with the simplicity of a single fuel enrichment design, all cores developed in this study have uniform enrichment.Since the flow is distributed radially, axial enrichment zoning does not have any adverse affects on coolant flow distribution and should be included as a parameter in future studies.
Summary of Core Design Constraints
The design constraints applied to these cores are summarized in Table 2 and discussed in the following subsections.
Thermal-Hydraulic Constraints
Design constraints related to primary coolant flow are fundamental to the core design, and often end up being the most important factors determining the geometric parameters of a low power-density system.The fundamental constraints associated with coolant flow are the mechanical limitations of the pump: allowable nozzle-to-nozzle pressure difference and the volumetric flow rate.For a single-stage mechanical impeller sodium pump, the pressure limitation has been reported as ~1.38 MPa (200 psi) [13].Multi-stage impeller or electromechanical pumps will have other limits, but as will be shown, the mechanical limitations of the pumps (regardless of type) are of no practical importance.The peak flow rate limitation of a single pump is not an issue since it can be avoided by simply adding more pumps.The coolant flow velocity is indirectly limited by the pressure drop constraints, but also by concerns for corrosion, cavitation and mechanical vibration of core components.This limit is not precisely defined and depends on parameters such as system temperatures and the coolant oxygen concentration.However, a generally applied limitation on the peak flow velocity of sodium weighing in all these considerations is 12 m/s.
Compared to these fundamental constraints, tighter limitations are put in place based on safety considerations.An inherently safe core must be able to terminate the fission chain reaction and remove the residual decay heat without the use of active systems.This implies that the decay heat from the core should be removed at acceptable system temperatures by natural circulation.The buoyancy pressure (P nc ) developed by a difference in coolant density is given by [16]: (2) where g is the gravitational constant (9.82 m/s 2 ), H xc is the thermal center elevation between the core and the heat sink (m), and ρ is the density (kg/m 3 ) of the coolant at the thermal centers.
Assuming that we want to establish a natural circulation flow at the chosen nominal coolant temperature range (355-510 °C), the pressure head for sodium as given by Equation (2) becomes P nc = 358 H xc .The friction pressure drop in the primary coolant loop is given by: (3) where X is a set of geometrical factors (of no importance for this discussion), f x is the friction factor and m x is the coolant mass flow rate.
Around 6% of the nominal mass flow rate is required to remove decay heat while approximately maintaining the same core coolant temperature rise right after the fission chain reaction has been terminated.Friction pressure drop scales by the square of the mass flow rate.The friction factor (f x ) increases as a function of Reynolds number-at 6% of nominal mass flow rate; it can conservatively be assumed to be 2.5 times larger than at full-flow conditions [17].Thus, the buoyancy pressure needed for natural circulation decay heat removal is ~0.9% that of full-power operating conditions.The required thermal center elevation can then be expressed as: H xc = ΔP f (100% Flow) /40,000.This relation gives a scaling factor for the height of the reactor vessel as a function of full-flow coolant pressure drop.In addition, the coolant elevation difference between the hot and cold pool is directly dependent on the pressure developed by the pumps.
In order to keep the vessel height below 10 m (and thus in some sense qualify the reactor as "small"), the minimum required thermal center elevation should be kept below 5 m, which implies a pressure drop constraint of 200 kPa.A "short-vessel" option with a 100-kPa pressure drop constraint was chosen as the preferred option in this paper.At such a low pressure drop constraint, resulting flow velocities are so low that flow velocity constraint considerations are effectively not applicable.
Irradiation Damage Limits
The limit of neutron irradiation experience for fast reactor steels is a fast fluence of 3.9 × 10 23 n/cm 2 (E > 0.1 MeV).This was achieved without excessive swelling or mechanical problems for HT9 steel in the Fast Flux Test Facility (FFTF) reactor.The corresponding number of displacements per atoms (DPA) was calculated to be ~208 [18].Conservatively, 200 DPA or simply a fast fluence below 4 × 10 23 n/cm 2 is most commonly used as the upper irradiation damage constraint in fast reactor design.More optimistically, TerraPower LLC is expecting optimized heats of HT9 steel to able to sustain up to 500-600 DPA of neutron irradiation damage [19].Constraints of 200, 300 and 500 DPA were considered in this study, in order to show the impact the value of this constraint has on the performance and design of battery type cores.
Component Temperature and Stress Limits
The solidus temperature of U-2Zr fuel is ~1100 °C.Applying a 30% margin-to-melt at standard operation gives a peak allowable fuel temperature of 770 °C.The cladding and duct steel are limited to a peak temperature of 560 °C to limit the drop in mechanical strength.The steel stress limits are taken from the American Society of Mechanical Engineers (ASME) code [20].
Core Design Methodology
The core design and optimization process has been automated to a large degree by utilizing the full capabilities of the integrated ADOPT & Serpent code packages [21,22].The ADOPT code takes a set of general input parameters and design constraints (as defined in Sections 2 and 3) and analyzes and optimizes the core geometry by performing thermal-hydraulic and structural-mechanical calculations.Since ADOPT does not perform neutron transport calculations, it is coupled to the Serpent monte-carlo neutron transport code.ADOPT produces a full-detail Serpent input file describing the "optimized" core geometry and its materials, and then iteratively runs Serpent to update initial guesses and finally converge on the core power & flux distribution (which cannot be known a priori).
The ADOPT code methodology is built on the principle of "Constrained Nuclear Design" [13] to optimize the core design.Optimized here refers to a core design that pushes core performance to the limits of the thermal-hydraulic and structural-mechanical constraints that confine the design space.This means, for example, that the primary coolant velocity will be at precisely the value allowed by the velocity and pressure drop constraints, which will give the most efficient (optimized) heat removal capability, allowing the highest power density.In this way, an optimized design can be arrived at quickly for a single defined set of operational parameters and constraints, but the set parameters and constraints cannot themselves be subjected to optimization.Open parameters in this study are the core thermal power level, the pressure drop constraint and the irradiation damage constraint, which are used as variables in order to develop a total of 29 full-detail core designs and associated performance characteristics.The ADOPT/Serpent package can automatically estimate core safety performance using the quasi-static reactivity balance approach [23], from which core temperatures following unprotected transients can be calculated.An explanation of this method and the results of this analysis are given in Section 8.
Since the objective of this study is to analyze cores with minimum reactivity swing, an additional in-house code called SWING was utilized in order to quickly identify the optimum level of enrichment for a given system.SWING takes 1-group cross-section data from a single Serpent calculation and then solves neutron balance and isotope-concentration equations in order to find the ratio of fissile/fertile isotopes in the feed-fuel material that minimizes the burnup reactivity swing.Step-by-step, the full core design process is carried out in the following way: produces Serpent input files for temperature-perturbed core geometries, materials and cross-section libraries 9. Reactivity coefficients are calculated using Serpent with the input-files produced in Step 8 10.Quasi-static reactivity feedback analysis and DPA-damage is calculated by ADOPT a.If requested, ADOPT runs the CHD code [24] for detailed transient analysis 11.The full data for the core geometry, thermal-hydraulics, structural mechanics, fuel cycle and safety performance is collected The steps 1-11 are fully automated, with the ADOPT code managing the data and running the other codes.The number of total iterations to find a final converged core design and the corresponding computational burden depends very heavily on the accuracy of the initial guesses.A simplified flow-chart of the core design process is shown in Figure 4.
Core Size and Power Density
A battery type fast reactor with a minimized burnup reactivity swing must be loaded with fuel containing a specific ratio between fissile and fertile isotopes in order to neither gain nor drop in reactivity during the burnup cycle.In reality, a conventional minimum-swing core first gains, then loses reactivity, but the change in reactivity over the cycle is minimized.Only traveling wave type or continuously refueled reactors can maintain an absolutely stable reactivity trajectory over time.The optimum enrichment level depends on core-specific parameters, but simulation results performed in this study indicate that it is not above 13% 235 U for any uranium-fueled system.Below a certain power density for a given coolant temperature rise and flow velocity, the core design reaches an asymptote where geometric parameters do not change.The asymptote is reached as the fuel rod pitch-to-diameter ratio (P/D) approaches 1, and rods cannot be packed more closely together.For a set operation time, cores with lower power densities will achieve lower burnup and use the fuel less effectively.The cycle time of derated cores could be proportionally increased, but this approach runs into other limitations.Operational cycles exceeding 30 years may not be realistic or rational, since components that wear (including pumps and other mechanical systems) will need to be replaced.Reducing the power output increases the reactor cost per installed power ($/kW) and increases the relative amount of fuel recycling needed since less burnup is achieved in every cycle.These characteristics effectively put a rational lower limit on the core power of any battery-type reactor system.
For a core of optimal shape (H/D = 1), the power level where this limit is reached is a direct function of the allowable primary coolant system pressure drop.At P/D = 1.015 (fuel vol.frac ~40.7%), the minimum core volume for which minimum burnup reactivity swing operation is possible is ~1.7 m 3 , which implies a minimum height and equivalent diameter of ~129 cm.P/D = 1.015 was chosen as a lower limit rather than P/D = 1.0 in order to enable a non-zero thickness for the spacer wire and to limit the difference in coolant outlet temperature between different coolant channel types (interior, edge and corner).The corresponding total uranium and fissile ( 235 U) mass is 12,500 kg and 1500 kg respectively.A primary cycle pressure drop of 100 kPa limits the power to ~50 MWt for the minimum core volume and fuel mass.If the pressure drop constraint is set higher, the minimum thermal power is correspondingly higher.At 200 kPa, the minimum power is ~75 MWt.The relation between pitch-to-diameter, core power and the pressure drop constraint is shown in Figure 5. Assuming a thermal conversion efficiency of ~40%, it is clear that there is no technical rationale to design forced-flow long-life battery-type systems with electrical outputs lower than 40 MWe, since such cores would simply be derated without changes in the geometry.As the pitch-to-diameter ratio (P/D) goes below ~1.1, the pressure drop increases rapidly for a given coolant flow velocity.Since the total pressure drop is set, the coolant velocity and thus the heat removal capacity and power density see corresponding drops.The increase in coolant velocity with thermal power output can be seen in Figure 6.The attainable power density for minimum-swing operation as a function of core power is shown in Figure 7. Below 200 MWt, a doubling of the power gives a ~50% increase in the power density, giving a strong economic incentive to aim for the highest power output possible.Going from 50 MWt to 550 MWt, an increase in power of 11 times, the core volume expands (keeping the core shape at H/D = 1) by 4 times, from 1.7 m 3 up to 6.75 m 3 .
Burnup and Reactivity Swing
The relation between core thermal power, average fuel burnup and the reactivity swing is shown in Figure 8.The higher power & power-density cores reach higher burnups and consequently require more breeding to stay critical throughout the cycle.Any minimum-swing system with a uniform fuel loading (uniform: single feed-fuel enrichment in all regions of the core) will have a parabolic uncontrolled reactivity swing trajectory, with k eff = 1.0 at the beginning and end of cycle, and a peak value for k eff near the middle of the cycle.The higher the average discharge burnup of the system, the larger the peak uncontrolled reactivity (referred to as the "reactivity swing") needs to be.This is because more 239 Pu must be built up in the fuel (i.e., higher breeding ratio) to counteract the increasing probability of neutron capture and moderation by fission products.Early in the cycle, the net reactivity gain from increasing 239 Pu content leads to increasing reactivity, which at some point is overtaken by the increase in fission product poisoning, leading to the parabolic reactivity trajectory.Reactivity-adjustment control systems have to be dimensioned so that their total reactivity worth matches the peak uncontrolled reactivity and additional margins.The amplified control requirements lead to more severe potential accidents as the power output and corresponding average burnup of the systems increase.
Irradiation Damage
As mentioned in Section 3.3, irradiation damage constraints for structural materials (such as fuel rod cladding and assembly duct steel) can severely limit the performance of battery-type nuclear systems.For a fixed full-power operational time (in this study, 30 years), the damage suffered by the structural steel in the core is directly proportional to fluence, burnup and power density.The results presented in Sections 5.1 and 5.2 show that optimized higher power cores operate at a higher power density and reach a higher burnup, and thus irradiation damage increases with core power for these types of systems.Counteracting this trend is the spectral softening in the higher-power cores due to a relatively higher coolant volume fraction.The increased moderation by the coolant lowers the effective one-group DPA cross-section for HT9 steel.The level of DPA was calculated using 100 energy-group flux detectors in Serpent, taking element-wise DPA cross-section data and the data for the energy level required to displace atoms from the documentation of the Argonne National Laboratory (ANL) SPECTER code [25].As seen in Figure 9, a relative drop of 25% in the fuel volume fraction (from 40% to 30% on a total basis) corresponds to a relative drop in the cycle-averaged 1-group HT9 dpa cross-section in the center of the core of ~8% (from 303 to 280 barns).The fast flux fraction (E > 0.1 MeV) in the center of the core drops from 65.7% in the 50 MWt core to 60.0% in the 550 MWt core.Reactor thermal power (MW) . 1-group HT9 dpa cross-section in the core center as a function of thermal power and fuel volume fraction in the 100-kPa core designs.
The impacts of different DPA limits on the characteristics of core performance are given in Table 3.The burnup and peak fast fluence corresponding to a certain level of DPA is essentially independent of specific core design parameters such as thermal power level or pressure drop constraint.Because of the spectral softening in larger cores, a higher level of total neutron fluence is needed to reach a given level of DPA.As shown in Section 5.1, a higher pressure drop constraint allows for a higher coolant velocity and more effective heat removal.This results in a smaller core volume and fuel mass, which for a set power and operational cycle time raises the flux, fluence and fuel burnup.This results in a lower maximum power level at which the core can operate for a set period of time without violating the DPA-damage constraints.Seemingly paradoxically, in this way for this specific type of core and operating cycle, a less effective heat removal allows for a higher operating power.The available range of thermal power for an optimized battery-type core becomes more narrow if the pressure drop limitation is set at a higher value, since the minimum power is raised and the maximum power is lowered.For a 200-kPa core with a DPA-constraint of 200, the lower and upper power bounds nearly coincide, and 75-85 MWt is the only operational power possible for a fully optimized system running for 30 years.This indicates that a pressure drop limit above 200 kPa would inevitably lead to sub-optimal core designs for the given design constraints.For 100-kPa 200-DPA cores, there is a span of output power possibilities from 50 MWt to 100 MWt, but the width of the span itself (as long as it is larger than 0) is not of significance.As explained in Section 5.1, the volumetric and specific (per kg-fuel) power density increases with power level.A truly optimized system will therefore be designed to operate at precisely the maximum allowable power as defined in Table 3.
Methods and Definitions
Core reactivity is impacted in four fundamental ways due to changes in the temperatures of the components that make up the core.These are briefly summarized below: 1. Neutron absorption probability in the fuel and other core components change with changes in temperature due to the nuclear Doppler effect.2. The core and fuel expands or contracts radially and axially due to changes in temperature, which causes the neutron leakage probability to change.3. Changes in the coolant temperature affect both the neutron spectrum and the leakage probability (changes in absorption probability is a minor effect).The resulting net effect can be either positive or negative depending primarily on the shape and size of the core and its nominal neutron leakage probability.4.An increase in the coolant temperature will increase the temperature of the drivelines that operate the core control systems.This causes them to thermally which effectively pushes neutron-absorbing material toward the core.Since the cores analyzed here are minimum-swing systems, the reactivity stored in control systems is small and this effect is neglected.
The feedbacks are calculated by running neutron transport calculations of a "reference" and various perturbed core models using the Serpent neutron transport code with 15 × 10 6 active neutron histories for each calculation.The resulting statistical uncertainty in the multiplication factor is ~20 pcm.Reactivity coefficients are then calculated in the unit of cents (1 ¢ = 0.01 $ = 0.01 β eff ) per Kelvin using Equation ( 4): (4) where k i and k ref is the perturbed and reference core state neutron multiplication factor, ΔT is the temperature difference between the two states (K) and β eff is the effective delayed neutron fraction of the reference state core.
The fuel Doppler reactivity coefficient (α D ) is calculated by changing the ENDF/B-VII.0 cross-section library temperature of the fuel isotopes by 900 K [26].The radial expansion reactivity coefficient (α r ) is simulated in a simplified manner by expanding the lower core grid plate steel corresponding to a temperature increase of 500 K.The resulting radial expansion increases the distance between assemblies, which results in a larger coolant volume in the inter-assembly gaps.This simplified modeling approach assumes a uniform expansion and disregards the effects of core "flowering" as duct load pads interact.These effects can be included by multiplying the uniform expansion coefficient by local temperature changes and geometrical factors, as explained in the documentation for the SAS4A/SASSYS-1 code [27].The coolant thermal expansion coefficient (α co ) is calculated by uniformly adjusting the density of the coolant within the active core region.
The reactivity effect of thermal expansion of annular fuel (α fc ) can accurately be modeled as an axial expansion only, since there is no liquid bond present to be displaced by radial expansion of the fuel.Modeling of the axial fuel expansion of annular metallic fuel does however present a large source of uncertainty.The annular fuel slug is manufactured to be in mechanical contact with the inner cladding liner.Assuming that the clad and fuel are stuck together and no sliding or plastic deformation occurs during a limited temperature transient, the combined thermal expansion coefficient of the fuel/cladding system can be estimated using thermo-physical data.The combined thermal expansion coefficient (ε fc ) is then given as: (5) where subscripts f and c denote fuel and cladding, ε is the thermal expansion coefficient (K −1 ), Y is the elastic modulus (Pa) and A is the cross-sectional area of the component (m 2 ).
In the work of many research groups, porous metallic fuel is assumed to be so weak at operating temperatures that this procedure is deemed unnecessary; the fuel component in the combined expansion calculation is simply ignored by setting its elastic modulus (Y f ) to 0. This assumption has been used by ANL [28] (US), Brookhaven National Laboratory (BNL) [29] (US), Massachusetts Institute of Technology (MIT) [30] (US), Korea Atomic Energy Research Institute (KAERI) [31] (Korea), Indira Gandhi Centre for Atomic Research (IGCAR) [32] (India) and many others.It appears to be an un-physical simplification for standard metallic fuel, since Y f is certainly larger than 0 Pa.More importantly, in some accident scenarios, this assumption leads to non-conservative results.The issue is even more important for annular metallic fuel, since fuel & cladding are mechanically bound before the fuel is noticeably weakened by porosity.For such a fuel design, the Y f = 0 assumption leads to drastic errors in the estimated reactivity impact of an increase in the temperature of cladding and fuel near the beginning of cycle (BOC).In order to correctly make use of Equation (5), a new correlation based on a re-evaluation of experimental data points has been developed.Using data from the figures of [33], the elastic modulus of unirradiated, fully dense U-2.4Zr fuel produced by arc melting is given as: (6) where T is the temperature of the material in Kelvin.
Equation ( 6) is strictly valid in the temperature range 25-500 °C.Since the temperature-dependence is linear over this temperature range, it is reasonable to assume a linear temperature-dependence up until a phase-change occurs.For the low-Zr U-Zr alloys, this happens at ~660 °C.The data in ref. [33] show that the value of Y f decreases with increasing Zr-content, which indicates that Equation ( 6) slightly under-estimates the value of Y f for U-2Zr fuel.More advanced correlations were recently developed from the same data source for metallic fuel alloys with Zr-contents in the span 6%-10% [34].
Equation (6) gives the value for Y f at 600 °C as 122.4 GPa.Using the correlation for HT9 steel from [35] gives Y c = 129.0GPa at 550 °C.Since A f is much larger than A c for any fuel rod design, the fuel primarily controls the combined expansion of an annular metallic fuel rod, at least near BOC.Using the geometric relations of a fuel rod, Equation ( 6) can be rewritten as [34]: (7) where CTR is the Cladding Thickness Ratio (explained in Section 2.2) and FSD is the fresh, un-swollen Fuel Smear Density (0 < FSD ≤ 1) For all the cores studied in this article, we have FSD = 0.75 and CTR = 0.05.Combined with the values of Y f and Y c defined above, Equation (7) yields: (8) Equation ( 8) is only valid for fresh fuel at the beginning of cycle (BOC).As the fuel swells inward, the value for Y f drops with increasing porosity in the fuel, while A f increases.Available correlations on the porosity impact on Y f indicate the following type of relationship [36]: (9) where P is the fractional porosity in the fuel.
At 75% smear density and assuming the annular fuel is not able to swell axially, the porosity developed at full inward radial swelling is ~1/0.75− 1 = 0.33 (33%).This leads to the following combined expansion coefficient at middle of cycle (MOC) and end of cycle (EOC): (10)
Reactivity Coefficient Calculation Results
An extensive study was carried out to calculate the reactivity coefficients of each core at three points during core life: BOC, MOC and EOC.It is well known from previous studies that reactivity coefficients change for the worse with core size and decreasing nominal neutron leakage probability [37,38], and similar trends are seen in this study.Another important factor is the change in reactivity coefficients as burnup progresses.Since the primary isotope responsible for neutron production shifts from 235 U to 239 Pu in these systems, the reactor physics of the cores change.The main difference is that the η-value (η = νσ f /σ a ) of 239 Pu increases more with increasing neutron energy than that of 235 U, which gives a more positive (or less negative) coolant density coefficient.This effect (in reverse) also causes a more negative radial expansion coefficient as burnup progresses, since the increased coolant volume fraction softens the spectrum.The main isotope contributing to the fuel Doppler effect is 238 U, and since its concentration decreases as burnup progresses, the magnitude of the feedback effect is smaller at EOC compared to BOC.There is little difference in the axial fuel expansion reactivity feedback magnitude (as measured in pcm/K) going from BOC to EOC.
The reactivity coefficients as calculated by ADOPT/Serpent of the 100-kPa cores are summarized in Figure 10.The axial fuel expansion reactivity coefficient corresponds to freely expanding fuel and should be reduced in magnitude by multiplication of an appropriate weighing factor for the combined fuel/clad-system to be applicable in safety analysis.The radial expansion reactivity coefficient corresponds to a uniform expansion, and does not take into account bowing effects.The uncontrolled reactivity (and thus the worth of the reactivity control system) peaks near MOC, which makes this point in the cycle the most important for control-rod ejection type scenarios.The values for MOC generally lie in between the values for BOC and EOC; they have been omitted from the figure for clarity.
Introduction to the Method
The quasi-static reactivity balance (QSRB) method was developed by Wade et al., at Argonne National Laboratory (ANL) in the 1980s [23].It is used to estimate the core state after a perturbation of core operating parameters based on solving a reactivity balance equation that depends on the ratios of three measurable integral reactivity parameters (A, B and C).The only information flow paths across the reactor boundary are the primary flow rate (F) that is controlled by pumps, the coolant inlet temperature (T in ), affected by the operation of the secondary coolant system, and an externally introduced reactivity insertion (ρ ext ).Given these three general ways to affect the state of a reactor core, a total of six potential scenarios can be analyzed: Since control rod injection is the means to shut the reactor down, it by itself cannot be considered an accident scenario.All other scenarios may raise the temperatures of certain components in the core, and they are thus the focus of the safety evaluation.The reactivity balance used in QSRB analysis is defined by Equation ( 11): (11) where A, B and C are integral reactivity parameters (to be defined), Δp is the core reactivity, P is the normalized power (P = 1 is full operational power), F is the normalized coolant flow rate (F = 1 is forced-flow at full pumping power), δT in is the change in the coolant inlet temperature and ρ ext is a reactivity introduced for example by the motion of control rods.
In any unprotected (unprotected: active core shutdown systems are not functioning) accident or transient scenario, power and temperatures adjusts up or down and the core will return to a zero-reactivity state at some new power level and temperature.Re-arranging Equation (11), the normalized power level can be expressed as: (12) The coolant temperature rise across the core is a function of the power/flow ratio.It is given by: (13) where ΔT co is the standard operating condition coolant temperature rise.
The coolant outlet temperature, using the preceding definitions, is given by: ( Combining Equations ( 13) and ( 14), the change in coolant outlet temperature can then be described as: (15) The average temperature of the fuel can be described at steady state conditions as: (16) where ΔT rcl is the average radial temperature increase across the cladding steel, and ΔT rf is the average radial temperature increase across the fuel annulus.
As the core adjusts to the perturbed conditions, the new fuel temperature is calculated as: The integral reactivity parameter A is directly dependent on the power level of the core and only includes reactivity parameters that are directly linked to the fuel temperature.In this study, three alternative interpretations of A for annular metallic fuel have been considered, defined as: (18) where ΔT f is the difference between the average fuel and average coolant temperatures.
(1) applies when the fuel is not mechanically bound to the clad; (2) applies when fuel and clad are bound and the system expansion (ε fc ) is given by Equation (7); and (3) applies when fuel and clad are bound and fuel expansion is not included, as recommended in [37].
It appears option ( 2) is most applicable for the systems studied in this paper, and it is the one used for safety analysis in this paper.In future studies, all three options should be considered in order to identify the most conservative modeling approach.On this topic, Wade states [39] (1988): "At the current time, the fuel axial expansion coefficient is an ambiguous one: if the fuel moves free of the clad, then α f goes with the fuel temperature along with α D ; alternately if the fuel is linked to the clad, then α f goes with the coolant temperature.Experimental results do not yet make a clear choice possible and we will consider both options in all that follows.This is not viewed as an uncertainty but rather as an open issue, which can be resolved by future experiments."To the author's knowledge, such experimental data have not been published since and this remains an open issue.The power/flow coefficient B is defined as: (19) The integral coolant inlet temperature coefficient of reactivity C is defined as: (20) Since the fuel axial expansion reactivity coefficient is a component of B and C as well, the same three alternatives as defined in Equation ( 16) is used as options also for the B and C parameters.
Loss of Flow
In the unprotected loss of flow event (ULOF), the primary system pumps are tripped and forced flow is lost without the actuation of the core SCRAM system.The coolant inlet temperature is assumed to remain constant (i.e., δT in = 0).The accident progression is: 1.Primary system pumps are tripped 2. Power-to-flow ratio increases raising the average core temperature 3. The temperature rise introduces negative reactivity which lowers core power 4. Natural circulation flow is established at low power In order to solve Equation (11) in a useful manner to analyze accident scenarios, some idealizations are necessary.In the ULOF scenario, it is the power/flow-ratio that determines the accident progression rather than the normalized power by itself.Thus the value for P coupled to the integral power reactivity parameter A is set to zero for the asymptotic state.Letting P/F remain a variable, Equation ( 11) can be solved to show the quasi-static (long term) response: (21) The change in the mixed mean core coolant outlet temperature for the ULOF scenario becomes: (22) The ULOF scenario has been refined to include a non-zero power and flow in the following way [40]: (23) In this study, it is assumed natural circulation is established at 2% flow (F = 0.02).
Primary Pump Overspeed
The unprotected pump overspeed scenario (UPPO) is the opposite of the ULOF.It could potentially be reached by a signal error in the primary pump control system.Depending on the type of pumps used, the severity of the UPPO event is limited by physical phenomena such as a cavitation and limits in the power supply to the pumps.Severe UPPO events could in fact be initiators of subsequent LOF & ULOF events as pumps may fail, which indicate a need to study the effects of these events in series.Initially, the increased coolant flow rate caused by UPPO will reduce the coolant outlet temperature and increase core power.Solving Equation (11) for the initial stage gives: (24) The heat removal system cannot reject all the power produced in the core, and subsequently the core inlet temperature will rise and power will return to P = 1.Again solving Equation (11) gives: (25) The normalized flow rate F in the UPPO-scenario analyzed in this paper is assumed to be 2.0 (200% of nominal flow rate), which is highly unlikely or even impossible but gives a conservative upper bound for the scenario.
Control Element Ejection
The unprotected transient overpower (UTOP) scenario studied involves the insertion of positive reactivity by the ejection of one of nine burnup control assemblies, the composition of which are all tailored to have the same reactivity worth.The peak added reactivity in a TOP scenario (occurring near the middle of the burnup cycle) is thus: (26) where Δk cycle is the burnup reactivity swing and 9 is the number of burnup control assemblies Initially, the reactivity will give an increase in power, with F = 1 and δT in = 0, which for Equation (11) yields: (27) The heat removal system on the secondary side cannot maintain a constant primary coolant core inlet temperature at the higher power level, so δT in will adjust to bring power back to its nominal value (P = 1).Solving Equation (11) for this scenario gives: (28)
Loss of Heat Sink
In an unprotected loss of heat sink event (ULOHS), heat rejection to the secondary system is lost, while primary coolant pumps continue to operate.As the transient is reaching its asymptotic state, the power level has reached decay heat levels.The larger the primary coolant inventory heat capacity, the longer time it takes to reach peak temperatures.The final stable asymptotic state in the ULOHS scenario is reached when the positive reactivity introduced by bringing the power toward zero, (A + B), is balanced by the negative reactivity introduced by the rise in coolant temperature (at this point T in = T out , ΔT c = 0).Solving Equation (11) for the ULOHS scenario gives: (29)
Chilled Inlet Temperature
The unprotected chilled inlet scenario (UCI) is, opposite to the ULOHS, a situation where the secondary cycle heat removal system is operating above nominal capacity, resulting in a drop in the primary coolant inlet temperature.The flow rate (F) remains constant, while the power P increases.Solving Equation (11) for this scenario yields: (30) The reduction in coolant inlet temperature δT in is limited to the solidification temperature of sodium (~125 °C), at which point the solid sodium causes flow blockages that turn the situation in to a combined loss of flow and loss of heat sink scenario.The situation analyzed in this paper is δT in = −155 °C, which means a reduction of the coolant inlet temperature to 200 °C.
QSRB Analysis Results
The peak quasi-static fuel and coolant temperatures were calculated for all cores for each of the seven possible isolated events presented; ULOF, UTOP (initial and final), ULOHS, UCI, UPPO (initial and final).Calculations were performed using all three interpretations of the axial fuel expansion reactivity effect, but for brevity only the results using the physical stress balance equation (Equation ( 7)) are presented.The resulting temperatures and the corresponding transient scenarios are summarized in Table 4.The temperature data in this table are indicative of trends at best, and higher temperatures may be reached at earlier stages of the transient, particularly in loss-of-flow events.This analysis will be supplemented by more detailed time-dependent transient analysis of the most promising core design options.
There are three main factors impacting the resulting temperatures and how they differ between the different cores: The fuel linear power density and corresponding ΔT f in standard operation The burnup, burnup reactivity swing and corresponding ρ ext Differences in α co While inherent safety, here defined as the response of the core and core component temperatures to unprotected transients [41], is directly linked to reactivity feedback coefficients, only one feedback (α c ) changes strongly enough between these cores to have an important impact on transient scenario temperatures.Operating parameters such as power density and the average discharge burnup affect core safety to a larger extent than the changes seen in α r , α D and α f between the different cores.
The coolant outlet temperature response to a loss-of-flow scenario is proportional to the ratio A/B, which increases ten times from 0.09 for the 50 MWt core to 1.00 for the 550 MWt core.However, if the linear power density and thus ΔT f is kept constant, the increase is a mere 35% (from 0.09 to 0.121).Similarly, the coolant temperature response to UTOP is proportional to ρ ext /|B|, which also increases ten times from 0.22 for the 50 MWt core to 2.38 for the 550 MWt core.If ρ ext is kept constant, the increase is 23%, from 0.22 to 0.27.The response to ULOHS and UCI is proportional to the ratio CΔT co /B, and does not change noticeably with core size.Fuel temperatures are higher for larger cores in these scenarios simply because standard operating fuel temperatures are higher due to the higher linear power density.
In any unprotected transient, the main objectives are to avoid sodium boiling and fuel melting (and, ideally, avoid damage to the cladding).Sodium boils at 883 °C (at atmospheric pressure) and the fuel melts at ~1100 °C, so introducing a QSRB-transient temperature margin of 150 °C gives a peak allowable coolant temperature of 733 °C and a peak fuel temperature of 950 °C.For cores larger than ~80 MWt, it is the events involving the reactivity vested in control elements that pose the most challenging transients, specifically near MOC when the uncontrolled reactivity is the highest.As is shown in Table 4, optimized 100-kPa cores with a thermal power above 350 MW require reactivity swings so large that the temperatures in the UTOP scenario exceed constraints.
The low reactivity vested in the fuel temperature above the coolant temperature leads to a relatively benign quasi-static response in ULOF scenarios, but the study of ULOF needs to be supplemented by time-dependent analysis that includes the pump coast-down period.Apart from in the ULOF scenario, higher temperatures in accident scenarios are reached if the transient occurs late in the burnup cycle.For all but the smallest cores, a UTOP occurring when ρ ext is at its maximum near MOC is the most severe accident scenario.
Conclusions and Future Work
This extensive parametric study has determined the factors impacting design choices for 30-year stationary singe-fuel loaded fast reactor cores, subject to the constraints discussed in this paper.The fuel rod geometry, core layout, and general plant design yielding optimal performance has been defined.Open parameters were the core thermal power level and constraints for pressure drop and irradiation damage.The core power for the preferred "short-vessel" (100 kPa pressure drop constraint) optimized design is limited to 100 MWt with the present irradiation damage database (200 DPA).The core can be uprated to 150 MWt with a realistic extension to this limit (300 DPA) and the power finally limited by safety considerations to 350 MWt with an arbitrarily high irradiation damage constraint.An arbitrary reduction in the core power density, which would yield a sub-optimal design for the given set of general core parameters and constraints, would allow a higher total operating power for all these cases.Some of the most important parameters of the three identified optimal designs are summarized in Table 5.It appears highly likely that advanced low-swelling steels (possibly optimized heats of HT9) will be able to perform well up to and above a neutron irradiation damage of 300 DPA.Because of its superior economic potential due to the significantly higher power density, the 150 MWt 300-DPA core will be the
Figure 1 .
Figure 1.To-scale model of the fuel rod with 75% fuel smear density as seen from above.
Figure 2 .
Figure 2. Fuel rod as seen from the side (not to scale).
Figure 3 .
Figure 3. Core assembly layout as seen from above.
Figure 6 .
Figure 6.Average coolant flow velocity in the peak-power assembly (m/s).
Figure 7 .
Figure 7. Power density vs. power output for optimized cores.
Figure 10 .
Figure 10.Reactivity coefficients at BOC and EOC for the 100-kPa cores.
1 .
Changes in primary system pumping (ΔF) a. Loss of flow b.Pump overspeed 2. Control rod motion or re-arrangement of core geometry (seismic events etc.) (Δρ ext ) a. Injection or negative-reactivity re-arrangement b.Ejection or positive-reactivity re-arrangement 3. Secondary cycle temperature & flow rate (ΔT in ) a. Loss of heat sink b.Chilled inlet temperature and F in the second column refer to peak coolant and fuel temperatures in °C respectively, and Cy marks what point the cycle (B = Beginning, M = Middle or E = End) the peak temperature occurs.
Table 1 .
Set design parameters.
Run Serpent with depletion to obtain the burnup reactivity swing 7. Depending on results from Step 6, the burnup reactivity swing is: a. Optimal: Continue to Step 8 b.Not optimal: Run SWING code, then return to and update Step 2a with new value 8.We now have the final core design, for which we need to calculate safety parameters.ADOPT
Table 3 .
Irradiation damage constraint impact on core performance parameters.
Table 4 .
Quasi-static temperatures for analyzed transient events in 100-kPa cores.
Table 5 .
Optimum 100-kPa core parameters sorted by the irradiation damage constraint. | 12,745.6 | 2014-07-31T00:00:00.000 | [
"Environmental Science",
"Engineering"
] |
Rapid Tools Compensation in Sheet Metal Stamping Process
The sudden growth of additive manufacturing is generating a renovated interest towards the field of rapid tooling. We propose a geometrical compensation method for rapid tools made by thermoset polyurethane. The method is based on the explicit FEM simulation coupled to a geometrical optimization algorithm for designing the stamping tools. The compensation algorithm is enhanced by considering the deviations between the stamped and designed components. The FEM model validation has been performed by comparing the results of a DOE done at different values of press force.
Introduction
In the conventional deep drawing and stamping processes, a tooling setup made of a die, a punch and a blankholder is traditionally used. Over the years, many different types of flexible sheet forming processes have been developed in the industry, in order to improve the process, and especially in order to compress the tooling production times and costs. Single point and double point incremental forming processes 1 have been invented and are continuously being developed to this purpose. As another cost saving option, metal tools can be replaced with a rubber membrane. In the Guerin process, a movable thick rubber pad is pressed against a die 2 or a punch 3. The Marform variant of the Guerin process, an active blankholder 4 is used. In flexforming with a fluid cell, a rubber diaphragm is pressurized by a fluid or by a bladder 5. In deep drawing flexforming, a movable punch is used, too 6. In multi-point stretch forming 7, stretch forming clamps are used with the sheet bent over a flexible die, made by a raster of metallic movable pins.
In the last few years, the tremendously rapid growth of additive manufacturing is changing completely the way of thinking about and designing functional parts. At the same time, a renovated attention is being given to rapid tooling technologies 8, which offer cost-efficient and innovative solutions for improving the sheet metal forming processes.
The rapid tooling method proposed in the present work is to machine polymeric boards, made by thermoset polyurethane, which in a few minutes can be machined into a forming tooling setup (punches, dies and blankholder). Very scarce scientific literature is available with this respect, to the authors' knowledge. One of the previous research works concerning all-polymeric forming tools with experimental and numerical analysis are by Park and Coulton of Georgia Tech 9, in the mid of years 2000. Sheet metal forming processes performed only with plastics tools are only used as prototyping methods, i.e. in prototyping job shops or for artistic uses by jewellers and metalsmiths 10.
The main advantage in using rapid polymeric tools is due to their low required machining energy and cost. The most expensive material used in this paper (commercial name Necuron 1300) has a comparable cost per unit volume, expressed in €/m3, to an AISI 1040 steel. However, the material removal rate in machining is more than 4 times faster, with a negligible tool wear in forming applications with thin sheet metals.
The main disadvantage of polymeric tools is that deflect elastically (or plastically, if they are not properly designed) under the forming forces. As a consequence, the final geometry of the formed part is difficult to predict, not only because of the usual springback, but also because of the deflection of the tools. For this reason, a numerical die compensation technique is required, able to suggest the correct shape for the tools, in order to keep the part within tolerances.
The most frequently used methods for die compensation are the displacement adjustment (DA), the surface controlled overbending (SCO) and the Force Descriptor Method (FDM). The displacement adjustment is very effective; the tool nodes are displaced in the opposite direction of the blank springback 11. The deviations calculation is done between the correspondent nodes of the simulated and the designed blank. This means that no remeshing is possible or, alternatively, any new mesh must be remapped with reference to the mesh of the designed part. For this reason, the DA method is frequently used for simple 2D forming cases 12, where a small number of nodes must be mapped or remeshing is not even required.
The surface controlled overbending algorithm performs the calculation directly on the tools CAD but, again, the calculation complexity makes the method inaccurate on a complex surface with high degree 13.
The Force Descriptor Method proposed by Karafillis and Boyce 14 is an iterative method based on the evaluation of the internal forces of the component, but the algorithm suffers from lack of convergence, especially in symmetric cases or limit values of springback.
The authors have proposed, at the ASME-MSEC 2015 conference, a compensation algorithm in combination with an FEM model 15, which allows to predict the deformation of the tools and to determine the required compensation in case the part falls outside the initial design tolerances. The proposed algorithm is inspired by the DA method, but improves the distance calculation by evaluating the normal distance from the tools node to the interpolated blank surfaces. Unlike the standard DA, there is no need to keep track of predetermined couples of nodes. The calculation of the normal distance solves the main disadvantage of the DA algorithm, allowing the applicability of the method also for 3D complex components. The results presented at the ASME paper were encouraging, but the method was tested with a relatively simple part. In the present work, a different test case, with greater geometrical complexity, has been used and the compensation algorithm has been significantly modified.
In the following Sections we will describe the experimental test case and the FEM model. Then, the development of the compensation algorithm will be described, in terms of mathematical formulation and algorithmic solutions. Finally, the validation and compensation results will be presented.
Description of the experimental test case
The test case ( Figure 1) is a stamped component with a double symmetry plane and some geometrical features which are predictably hard to be obtained in a stamping process with flexible tools. The constant radii (R6 in Figure 1) are very small, i.e. difficult to be obtained in this kind of processes, because the deformable tools usually tend to slightly deform by compression in corner regions. The presence of the central, diamond shaped, depression adds complexity to the overall geometry of the process. The material chosen for the test case is Al1050, annealed, with 1.5 mm wall thickness. The reference geometry of the part given in Figure 1, which will be called "designed geometry", is the starting point for determining the geometry of the deformable tools. An initial guess geometry of the deformable tools is built as an offset of the surfaces of the test case part; the iterative compensation algorithm will suggest a modification of this initial geometry. The deformable tooling setup ( Figure 2) is made of a die, a punch (blue tools) and a blankholder (orange tool). The base of punch (orange) has been generated by using the material milled to the centre part of the blank holder, in order to reduce the cost of the required resin.
The polyurethane materials chosen for testing the deformable tools are: Necuron 1300 for the punch basement and blankholder; Miketool 1440 for the die and punch. The material properties are discussed in the following Section. The estimated cost of the polyurethane die is about € 990 (including machining costs). The same die, made by Zamak 2 (which is a low cost alloy typically used for prototyping tools) would cost about € 1860. In Figure 3 a quantitative comparison of the tools price in terms of total manufacturing and material costs has been presented, in order to show the economic advantage related to the use of polyurethane tools. Figure 2a shows the direction of the stamping process. The stamping process is made of three steps: 1 Holding: the blank is placed on the blankholder and then the die moves downward for holding it; 2 Stamping: the die pushes the blank against a fixed punch and against the blankholder with a maximum force of 980 kN; the maximum available reaction force of the blankholder is 392 kN. 3 Springback: the tools are released and both the tools and the blank recover the elastic deformation. An experimental plan has been designed with variable levels of the blankholder force BHF, without replications ( Table 1). The plan is aiming at determining which level of maximum BHF could determine failure of the parts (by either wrinkling or fracture) or failure of the tools (by fracture or plasticization). It is also aimed at determining the influence of BHF on the geometrical accuracy of the obtained parts. The experimental results showed that no macroscopic wrinkling occurred at any level of BHF max .
The part at experimental condition no. 7 failed by fracture, hence the safe limit to fracture for BHF max was assessed at 24.5 kN. All stamped parts have been measured with a CMM. All measured parts present some deviations (errors) from the designed part. The profiles measured at the symmetry plane (cross section A-A in Figure 1) are shown in Figure 5. Not all profiles are shown, in order to improve the clarity of the figure, not making too crowded with lines. The error profiles are not perfectly symmetrical around the centre of the chart because the clamping conditions of the blankholder were not perfectly symmetrical (Fig. 4a), hence different drawin values have been allowed in different directions. Experiment number 6 (which has the largest admissible BHF value) presents the smallest possible error in the central region, but a relatively large error on the corners. The low error in the central part is due to increased stretching, while the larger error on the corners is due to compression of the plastic die corners. Experiment no. 4 seems to be the best compromise but it is not better than other profiles along the whole cross section. Indeed, this is the most interesting remark coming out the of the comparison of the error profiles: there is not a single BHF level able to generate an error which is consistently smaller throughout the whole cross section. The errors measured in some other regions of the part, away from the A-A cross section are even larger than the ones shown in Fig. 5. In order to reduce the amount of geometrical errors, a tool shape geometry compensation procedure is required, in combination with an FEM model of the process.
FEM model description
The FEM model has been implemented with the commercial code PAM-STAMP 2G V2015.1. In order to evaluate the deformation of the polyurethane tools, their mesh is made of four-node tetrahedral solid elements. The solid mesh of the plastic tools is created with VisualMesh 11 by using an automatic meshing module. The surface curvature criterion has been used to determine the element density (finer mesh is generated in areas of higher surface curvature). The number of elements and the number of nodes for each tool is shown in Table 2. A good discretization is important for the accuracy of the FEM simulation, but it is also very important for the application of the compensation algorithm described in the following Section. The edge length of the squared blank is 200 mm and the surface area of each initial element is 400 mm 2 with a total number of 100 initial elements. Every refinement step splits 1 quadrangular element into 4 smaller quadrangular shells, by an automatic refinement algorithm. Each element can be split up to 5 times. The tensile test data of the blank have been retrieved in the "CES EduPack" material database, since the Al 1050 is a very common material. Tensile data of the tool materials can be found in the literature too 16. Extensive quasi-static tensile and compressive tests have been performed on the polymeric tools in order to determine their elastic modulus. The resulting values for the elastic modulus and the Poisson coefficients are reported in Table 3. The blank material is modelled as elasticplastic. The coefficients of the Krupkowsky's strain hardening law used in the simulations: (1) are K=126.4 MPa, n=0.193, ε 0 = 0.00093.
The simulation starts at the end of the holding stage in which the blank is held between the die and the blankholder (Figure 6a).
The contact algorithm between the objects is automatically defined by the software taking into account a Coulomb friction coefficient of 0.2 9, in order to better simulate the interaction conditions between polyurethane and aluminium materials.
As shown in Figure 4a, the plastic tools are enclosed within metal clamping tools which connect and lock the tools to the press machine. The position of the locking tools along the diagonal of the die does not allow the application of the symmetry to the FEM model. In order to correctly simulate the effect of each clamp on the deformable tools shown in Figure 4a, proper boundary conditions have been applied only on specific nodes and surfaces.
For the die, an imposed displacement with constant velocity is applied on the upper and on some nodes corresponding to the clamping tools (Figure 4a). The BHF is applied on the lower surface, in order to simulate a uniform distribution of the pressure; finally, a fixed displacement is applied on the lower nodes of the punch base (Figure 6b). The nodes between the punch and the base have been fused in order to simulate the glued contact between the upper surface of the base (orange) and the lower surface of the punch (pink). The springback simulation is run by the FEM software with the "Advanced Implicit" algorithm, by locking three nodes on the stamped component.
Compensation algorithm
The main response variables in a stamping process with deformable tools are the deviations between the geometry of the real stamped component and the designed one. The proposed algorithm suggests the compensation to be applied on the plastic tools, in order to obtain the minimization of the deviations. The compensation algorithm iteratively runs the following two main steps: STEP I. FEM simulation: the user runs a stamping simulation with springback, and a mesh refinement stage. The blank mesh is built with shell elements which represent the middle surface of the part, i.e. half of the thickness must be added in the normal direction in order to model the actual outer or inner surface of the part. As a first guess, in this initial run, the deformable tools are built by offsetting the designed part by half of the initial sheet thickness. During refinement, the meshes of the simulated component and the designed one are both regenerated with shell elements of approximately uniform side length. The final mesh refinement stage is very useful for performing simpler and more accurate computations at the next step II.
STEP II. Compensation: the proposed automatic algorithm has been coded within C++. The routine takes the following inputs: the refined triangular shell mesh of the simulated and the designed parts, the outer contour of the simulated part, the external surface shell mesh of the tools in ascii. The tool geometry is modified according to the following 4 sub-steps: The parametric surfaces are reconstructed with the Multilevel B-spline Approximation (MBA) 18, where an algorithm models the surface with a recursive refinement of the B-spline knots depending on the level of desired accuracy (k). This fitting allows handling the designed and simulated objects not as numerical meshes with their nodes, but as mathematical surfaces. II.3 Compensation. This step II.3 is repeated for both tools: the punch and the die. Figure 7 shows a 2D graphical representation of the computed quantities.
II.2 Tools and blank contour import
The distances d and s between the generic tool (punch or die) node ⃗ , , , and the two fitted surfaces (simulated and designed) are computed through the conjugate gradient minimization algorithm 17. These distances are 3D vectors, with components in the cartesian coordinate system used for the simulation setup: , , The deviation vector between the simulated and designed surfaces is defined as (5) With the components: , , The tool nodes are moved from the original position ⃗ by the quantity . The final position of the compensated tool node is defined as: II.4 Exporting: The meshes of both compensated tools are exported, the FEM simulation is run again and the deviations, after compensation, are calculated again. The algorithm can be applied iteratively and the whole procedure is repeated until convergence, i.e. until the deviations between the simulated and designed parts are within the tolerance interval chosen by the designer.
Numerical Results
Before applying the compensation routine, the accountability of the FEM model must be verified. With respect to failure limits, experiment no. 7 is very useful, where the maximum force is applied on the blankholder. In the real tests, fracture occurred at this high level of draw-in restraint. The experiment and the simulation show the same location of the blank fracture localized at the deepest corners of the component (Figure 8) These levels of geometrical accuracy are in the typical range of FEM models with shell elements; they are acceptable for general purposes but they seem to be too large for a reliable compensation routine. However, it is interesting to observe the comparison given in Figure 9, which is limited to test case no. 2 for brevity. In this figure, the error of the FEM profile with respect to the designed part is compared to the error (already given in Figure 2) between the actual CMM measured profile and the designed part. Although the numbers are obviously different for the two profiles, (with a larger amplitude for the FEM error) the shape of the two profiles is surprisingly similar, with a clear indication of accountability of the FEM model.
In order to demonstrate the use of the proposed compensation technique, it has been applied to test cases no. 2 and no. 3.
TEST CASE no. 2. This test case is run with BHF=9.8 kN. As the first simulation run, the tools are simply built as an offset of the final designed part middle surface. The plot of the deviations between this simulated part and designed components is shown in Figure 10 The algorithm performed an automatic compensation of the tools geometry, with =1. As a result of the first compensation, the punch and die corners radii have been modified by the algorithm in order to reduce the deviations shown in Figure 10.
After the compensation, the range of the deviations between the designed and simulated components is reduced. In Figure 11, the results of the first iteration are shown. The range of the deviations, calculated in the normal direction, lays within the range [-0.22; 0.15] mm. This error range is not much different from the one in Figure 10 (obtained before compensation), but it must be noted that the 96.95% of the surface is within the range [-0.12; 0.10] mm. Furthermore, the increase of calculated effective stress on the tools is limited to only 1 MPa on the punch and 7 MPa on the die. This means the proposed algorithm is able not only to reduce the geometrical errors but also to save the impact on the expected tool life.
The time required for 1 simulation (run with 8 processors) and for 1 tool compensation (with 1 processor) is summarized in Table 4.
The procedure described in Section 4 is iterative, it can be repeated with constant or variable values of the correction coefficient .
In Figure 12 the RMS value of the deviation vector is plotted vs. the number of iterations, with constant value. The figure shows that the RMS values of the deviation vector decreases drastically after the first iteration and rapidly converges towards a stable solution. A very similar trend had been observed also in a previous work [15], and this indicates a typical behaviour of the proposed routine. The strain map, expressed in terms of distance from the FLD line, is shown in Fig. 13a. After the tool geometry compensation, the state of strain on the blank obviously changes, and the resulting FLD plot is shown in Fig. 13b, where a large risk of fracture is evident. In other words, in order to reduce the geometrical errors, the routine tends to increase the level of strain. This behaviour is typical since it has been observed also for test case no. 4 and for other tested geometries. As a result, the procedure described in Section 4 can be framed in a more general algorithm, which involves the selection of the correct level of BHF and the evaluation of the risk of fracture. This general algorithm is summarised in Fig. 14.
Conclusions
In this paper, a compensation algorithm has been proposed, based on the displacement adjustment (DA) approach. The proposed method allows to evaluate and reduce the deviations between the simulated component and the designed one.
The algorithm, based on the reduction the normal deviation vector, can be applied iteratively. It generates an increase of the strain level in the final workpiece, as a consequence of the change in the shape of the tools. For this reason, the an iterative algorithm has been proposed, which takes the risk of fracture into account. When the results of the compensation algorithm are far from the risk of fracture, the algorithm rapidly yields a satisfactory solution already after the first iteration. | 4,985.4 | 2016-01-01T00:00:00.000 | [
"Engineering",
"Materials Science"
] |
Reanalysis of $\Omega_c \rightarrow \Xi_c^+ K^-$ decay in QCD
The strong coupling constants of newly observed $\Omega_c^0$ baryons with spin $J = \frac{1}{2}$ and $J = \frac{3}{2}$ decaying into $\Xi_c^{+} K^{-}$ are estimated within light cone QCD sum rules. The calculations are performed within two different scenarios on quantum numbers of $\Omega_c$ baryons: a) all newly observed $\Omega_c$ baryons are negative parity baryons, i.e., the $\Omega_c(3000)$, $\Omega_c(3050)$, $\Omega_c(3066)$, and $\Omega_c(3090)$ have quantum numbers $J^P = \frac{1}{2}^-$ and $J^P = \frac{3}{2}^-$ states respectively; b) the states $\Omega_c(3000)$ and $\Omega_c(3050)$ have quantum numbers $J^P = \frac{1}{2}^-$ and $J^P = \frac{1}{2}^+$, while the states $\Omega_c(3066)$ and $\Omega_c(3090)$ have the quantum numbers $J^P = \frac{3}{2}^-$ and $J^P = \frac{3}{2}^+$, respectively. By using the obtained results on the coupling constants, we calculate the decay widths of the corresponding decays. The results on decay widths are compared with the experimental data of LHC Collaboration. We found out that the predictions on decay widths within these scenarios are considerably different from the experimental data, i.e., both considered scenarios are ruled out.
Hence, various possibilities about the quantum numbers of these states have been speculated in recent works.In [2], the states Ω c (3050) and Ω c (3090) are assigned as radial excitation of ground state Ω c (3000) and Ω * (3066) baryons with the J P = 1 2 + and 3 2 + , respectively.
On the other hand, in [3][4][5][6][7] these new states are assumed as the P -wave states with J P = − respectively.Moreover the new states are assumed as pentaquarks in [8].Similar quantum numbers of these new states are assigned in [9].Analysis of these states is also studied with lattice QCD, and the results indicated that most probably these states have J P = 1 + is given in [3].In [10], it is obtained that the prediction on mass supports assigning Ω c (3000) as J P = 1 Note that the strong coupling constants of Ω c → Ξ + c K − decays within the same framework are studied in [11], and in chiral quark model [12] respectively.However, the analysis performed in [11] is incomplete.First of all, the contribution of negative parity Ξ c baryons is neglected entirely.Second, in our opinion the numerical analysis presented in [11] is inconsistent.
The article is organized as follows.In section II the light cone sum rules for the coupling constants of Ω c → Ξ + c K − decays are derived.Section III is devoted to the analysis of the sum rules obtained in the previous section.In this section, we also estimate the widths of corresponding decays, and comparison with the experimental data is presented.
For the calculation of the strong coupling constants of Ω c → Ξ + c K − transitions we consider the following two correlation functions in both pictures, and where η Ξc (η Ωc ) is the interpolating current of Ξ c (Ω c ) baryon and η µ Ω * c is the interpolating current of J P = 3 2 Ω * c baryon: where a, b and c are color indices, C is the charge conjugation operator and β is arbitrary parameter.
We calculate Π (Π µ ) employing the light cone QCD sum rules (LCSR).According to the sum rules method approach, the correlation functions in Eqs. ( 1) and ( 2) can be calculated in two different ways: • In terms of hadron parameters, • In terms of quark-gluons in the deep Euclidean domain.
These two representations are then equated by using the dispersion relation, and we get the desired sum rules for corresponding strong coupling constant.The hadronic representations of the correlation functions can be obtained by saturating Eqs. ( 3) and ( 4) with corresponding baryons.
Here we would like to note that the currents η Ξc , η Ωc , and η Ω * c interact with both positive and negative parity baryons.Using this fact for the correlation functions from hadronic part we get The matrix elements in Eqs. ( 6) and ( 7) are determined as where, and g is strong coupling constant of the corresponding decay, λ B (i) are the residues of the corresponding baryons, u µ is the Rarita-Schwinger spinors.Here the sign +(−) corresponds to positive (negative) parity baryon.In further discussions, we will denote the mass and residues of ground and excited states of Ω c (Ω * c ) baryons as: 2 ) for scenario a); and for scenario b), the same notation is used as in previous case by just replacing . Moreover, the mass and residues of Ξ c baryons are denoted as m ′ 0 , λ ′ 0 and m ′ 1 , λ ′ 1 .Using the matrix elements defined in Equations ( 8) to (10) for the correlation functions given in Equations ( 1) and (2) we get (for case a): where The result for the scenario b) can be obtained from Eqs. ( 13) and ( 14) by following replace-ments: Note that to derive Eq. ( 14), we used the following formula for performing summation over spins of Rarita-Schwinger spinors and in principle one can obtain the expression for the hadronic part of the correlation function.At this stage two problems arise.One of them is dictated by the fact that the current η µ interacts not only with spin 3/2 but also 1/2 states.The matrix element of the current η µ with spin 1/2 state is defined as i.e., the terms in the RHS of Eq.( 17) ∼ γ µ and the right end (p + q) µ contain contributions from 1/2 states, which should be removed.The second problem is related to the fact that not all structures appearing in Eqs. 14 are independent.In order to cure both these problems we need ordering procedure of Dirac matrices.In present work, we use ordering of Dirac matrices as / p / qγ µ .Under this ordering, only the term ∼ g µα contains contributions solely from spin 3/2 states.For this reason, we will retain only g µα terms in the RHS of Eq.( 14).
In order to find sum rules for the strong coupling constants of Ω c → Ξ + c K − transitions we need to calculate the Π and Π µ from QCD side in the deep Euclidean region, p 2 → −∞, (p + q) 2 → −∞.The correlation from QCD side can be calculated by using the operator product expansion.Now let demonstrate steps of calculation of the correlation function from QCD side.As an example let consider one term of correlation Π µ , i.e. consider By using Wick's theorem, this term can be written as; From this formula, it follows that to obtain the correlation function(s) from QCD side, first of all we need the expressions of light and heavy quark propagators.The expressions of the light quark propagator in the presence of gluonic and electromagnetic background fields are derived in [13]: The heavy quark propagator is given as, where γ E is the Euler constant.
For calculation of the correlator function(s) we need another ingredient of light-cone sum rules, namely the matrix elements of non-local operators q(x)Γq(y) and q(x)ΓG µν q(y) between vacuum and the K-meson , i.e.K(q)|q(x)Γq(y)|0 and K(q)|q(x)ΓG µν q(y)|0 .
Here Γ is the any Dirac matrix, and G µν is the gluon field strength tensor, respectively.
These matrix elements are defined in terms of K-meson distribution amplitudes (DA's).
The DA's of K meson up to twist-4 are presented in [12].
From Eqs. ( 13) and ( 14) it follows that the different Lorentz structures can be used for construction of the relevant sum rules.Among of six couplings, we need only A 2 (A * 2 ) and A 5 (A * 5 ) and A 2 (A * 2 ) and Ã5 ( Ã * 5 ) for the cases a) and b) respectively.For determination of these coupling constants, we need to combine sum rules obtained from different Lorentz structures.From Eqs.( 13) and ( 14) (for case a) it follows that the following Lorentz structures / p / qγ 5 , / pγ 5 , / qγ 5 , γ 5 , and / p / qq µ , / pq µ , / qq µ , and q µ appear.We denote the corresponding invariant functions Π 1 , Π 2 , Π 3 , Π 4 and Π * 1 , Π * 2 , Π * 3 and Π * 4 , respectively.Explicit expressions of the invariant functions Π i and Π * i are very lengthy, and therefore we do not present them in the present study.
The sum rules for the corresponding strong coupling constants are obtained by choosing the coefficients aforementioned structures and equating to the corresponding results from hadronic and QCD sides.Performing doubly Borel transformation with respect to variable p 2 and (p + q) 2 in order to suppress the contributions of higher states and continuum we get the following four equations (for each transition).
where superscript B means Borel transformed quantities, The masses of the initial and final baryons are close to each other, hence in the next discussions, we set M 2 1 = M 2 2 = 2M 2 .In order to suppress the contributions of higher states and continuum we need subtraction procedure.It can be performed by using quark-hadron duality, i.e. starting some threshold the spectral density of continuum coincide with spectral density of perturbative contribution.The continuum subtraction can be done using formula For more details about continuum subtraction in light cone sum rules, we refer readers to work [14].
As we have already noted in case a) we need to determine two coupling constants g 2 (g * 2 ) and g 5 (g * 5 ) for each class of transitions.From Eqs (23) and ( 24) it follows that we have six unknown coupling constants but have only four equations.Two extra equations can be obtained by performing derivative over (1/M 2 ) of the any two equations.In result, we have six equations and six unknowns and the relevant coupling constants g 2 (g * 2 ) and g 5 (g * 5 ) can be determined by solving this system of equations.
The results for scenario b) can be obtained from the results for scenario a) with the help of aforementioned replacements.
From Eqs (23) and ( 24), it follows that to estimate strong coupling constants g 2 (g * 2 ) and g 5 (g * 5 ) responsible for the decay of Ω c → Ξ c K and Ω * c → Ξ c K, we need the residues of Ω c and Ξ c baryons.For calculation of these residues for Ω c , we consider the following two point correlation functions The interpolating currents η Ωc and η µΩc couples not only to ground states, but also to negative (positive) parity excited states, therefore their contributions should be taken into account.In result, for physical parts of the correlation functions we get, where the dots denote contributions of higher states and continuum.The matrix elements in these expressions are defined as As we already noted, only the structure g µν describes the contribution coming from 3/2 baryons.Therefore we retain only this structure.
For the physical parts of the correlation function, we get Here in the last term, upper(lower) sign corresponds to case a) (case b).
Denoting the coefficients of the Lorentz structures / p and I operators Π 1 , Π 2 and / pg µν , g µν as Π * 1 , Π * 2 respectively and performing Borel transformations with respect to −p 2 , for spin 1/2 case we find, The expressions for spin 3/2 case formally can be obtained from these expressions by replacing λ → λ * , m → m * and Π → Π * .The invariant functions Π i , Π * i from QCD side can be calculated straightforwardly by using the operator product expansion.Their expressions are presented in [15] (see also [7]).
Similar to the determination of the strong coupling constant, for obtaining the sum rule for residues we need the continuum subtraction.It can be performed in following way.In terms of the spectral density ρ(s) the Borel transformed Π B can be written as The continuum subtraction can be done by using the quark-hadron duality and for this aim It follows from the sum rules we have only two equations, but six (three masses and three residues) unknowns.In order to simplify the calculations, we take the masses of Ω c as input parameters.Hence, in this situation, we need only one extra equation, which can be obtained by performing derivatives over ( −1 M 2 ) on both sides of the equation.Note that the residues of Ξ c baryons are calculated in a similar way.
III. NUMERICAL ANALYSIS
In this section we present our numerical results of the sum rules for the strong coupling constants responsible for Ω c (3000) → Ξ + c K − and Ω c (3066) → Ξ + c K − decays derived in previous section.The Kaon distribution amplitudes are the key non-perturbative inputs of sum rules whose expressions are presented in [12].The values of other input parameters are: The sum rules for g −+ and g * −+ contain the continuum threshold s 0 , Borel variable M 2 and parameter β in interpolating current for spin 1/2 particles.In order to extract reliable values of these constants from QCD sum rules, we must find the working regions of s 0 , M 2 and β in such a way that the result is insensitive to the variation of these parameters.The working region of M 2 is determined from conditions that the operator product expansion (OPE) series be convergent and higher states and continuum contributions should be suppressed.
More accurately, the lower bound of M 2 is obtained by demanding the convergence of OPE and dominance of the perturbative contributions over the non-perturbative one.The upper bound of M 2 is determined from the condition that the pole contribution should be larger than the continuum and higher states contributions.We obtained that both conditions are satisfied when M 2 lies in the range The continuum threshold s 0 is not arbitrary and related with the energy of the first excited state i.e. s 0 = (m ground + δ) 2 .Analysis of various sum rules shows that δ varies between 0.3 and 0.8 GeV, and in this analysis δ = 0.4 GeV is chosen.As an example, in Figs. 1 and 2 we present the dependence of the residues of Ω c (3000) and Ω c (3050) on cos θ for the scenario a) at s = 11 GeV 2 and several fixed values of M 2 , respectively.From these figures, we obtain that when cos θ lies between −1 and −0.5 the residues exhibits good stability with respect to the variation of cos θ and the results are practically insensitive to the variation of M 2 .
And we deduce the following results for the residues λ 1 = (0.08 ± 0.03) GeV 3 , λ 2 = (0.11 ± 0.04) GeV 3 . (37) Performing similar analysis for Ω c baryons in scenario b) we get (Figs. 3 and 4) The detailed numerical calculations lead to the following results for spin 3/2 Ω c baryon residues: λ * 1 = (0.18 ± 0.02) GeV 3 , λ * 2 = (0.17 ± 0.02) GeV 3 , (39) From these results we observe that the residues of Ω c baryons in scenario a) is larger than that one for the scenario b).This leads to the larger strong coupling constants for scenario b) because it is inversely proportional to the residue.
Having obtained the values of the residues, our next problem is the determination of the corresponding coupling constants using the values of M 2 and s 0 in their respective working regions which are determined from mass sum rules .In Figs. 5, 6, 7, and 8, we studied the dependence of the strong coupling constants for Ω * c → Ξ c K 0 transitions for the scenarios a) and b) on cos θ, respectively.We obtained that when M 2 varies in its working region the strong coupling constant demonstrates weak dependence on M 2 , and the results for the spin-3/2 states also practically do not change with the variation of s 0 .Our results on the coupling constants are: For scenario a: For scenario b: The decay widths of these transitions can be calculated straightforwardly and we we get; where m i (m * i ) and m ′ 0 are the mass of initial spin 1/2 (spin 3/2) Ω c baryon and Ξ c baryons respectively and λ(x, y, z) = x 2 + y 2 + z 2 − 2xy − 2xz − 2yz.Having the relevant strong coupling constants, the decay width values for scenario a) and b) are shown in Table I.
Our results on the decay widths are also drastically different than the one presented in [11].In our opinion, the source of these discrepancies are due to the following facts: • In [11], the contributions coming from Ξ − c baryons are all neglected.
• The second reason is due to the procedure presented in [11], namely by choosing the relevant threshold s 0 , isolating the contributions of the corresponding Ω c baryons is incorrect.From analysis of various sum rules, it follows that s 0 = (m ground + δ) 2 , where 0.3 GeV ≤ δ ≤ 0.8 GeV.Since the mass difference between Ω c (3000) and Ω c (3090) is around 0.1 GeV, isolating the contribution of each baryon is impossible while their contributions should be taken into account simultaneously.For these reasons our results on decay widths are different than those one predicted in [11].From experimental data on the width of Ω c are [16]: We find out that, our predictions strongly differ from the experimental results.
By comparing our predictions with the experimental data, we conclude that both scenarios are ruled out.
IV. CONCLUSION
In conclusion, we calculated the strong coupling constants of negative parity Ω c baryon with spins 1/2 and 3/2 with Ξ c and K meson in the framework of light cone QCD sum rules.Using the obtained results on coupling constants we estimate the corresponding decay widths.We find that our predictions on the decay widths under considered scenarios are considerably different from experimental data as well as theoretical predictions and considered both scenarios are ruled out.Therefore further theoretical studies for determination of the quantum numbers of Ω c states as well as for correctly reproducing the decay widths of Ω c baryons are needed.
FIG. 1 .
FIG. 1.The dependence of residue for Ω c (3000) on cos θ at s 0 = 11 GeV 2 and at various fixed values of M 2 for scenario a).
FIG. 5 .
FIG. 5.The dependence of strong coupling constant for Ω c (3066) → Ξ c K on cos θ at s 0 = 11 GeV 2 and at three fixed values of M 2 for scenario a). | 4,470.2 | 2018-05-08T00:00:00.000 | [
"Physics"
] |
Intratubular penetration ability in the canal perimeter using HiFlow bioceramic sealer with warm obturation techniques and single cone
Background The aim of this paper was to evaluate the intratubular penetration percentage in the perimeter of the canals of the calcium silicate-based sealer HiFlow, using three warm obturation techniques, continuous wave (CW) and vertical condensation (VC) with two different types of gutta-percha (conventional (NG) and bioceramic-coated (BG), GuttaCore (GC) and single cone (SC) with BG in different root thirds. Material and Methods 180 human teeth with a single root were selected including incisors, canines and premolars were prepared and randomly divided into six groups (n=30). Teeth were filled using a bioceramic sealer TotalFill BC Sealer HiFlow (HiFlow) and two different types of gutta-percha, with CW, VC and GC techniques, the teeth in the control group were filled with SC technique and BG gutta-percha. The teeth were sectioned and evaluated as one-third portions in each case under a confocal laser microscope. The penetration ability in the canal’s perimeter was carried out with the Autocad® programme. Data was analyzed using Levene’s test (p<0,05), ANOVA test (p<0,05), Welch’s comparison test (p<0,05), Games-Howell multiple comparison test (p<0,05), Bonferroni test (p<0,05). Results The percentages relative to penetration was higher in the warm obturation techniques than the SC in all thirds evaluated. Games-Howell test (p<0,05) showed up significant differences in multiple comparisons. There was greater penetration in the perimeter of the canals in the coronal third than in the apical third in all of the techniques. Conclusions The warm obturation techniques (CW, VC and GC) generated a greater intratubular penetration percentage in the canal perimeter of the sealer than the single cone in all thirds. Key words:HiFlow, calcium silicate-based sealer, confocal laser microscope, dentinal tubules.
Introduction
The complete sealing and filling of the root canal system are essential because after chemomechanical preparation, the presence of microorganisms is detected. Sealers fill the irregularities of the root canal system and must therefore be applied. Furthermore, the sealing capacity is just as important as the antibacterial effect. The antibacterial effect of the bioceramic sealers may be achieved by direct contact action or a localized burial process; it is essential hence to distribute the sealer along the perimeter of the canal. Additionally, the use of a sealer creates a bond between the gutta-percha and the root dentine (1). Bioceramic sealers boost the dentine remineralization processes, present acceptable cytotoxicity levels and offer a desirable degree of intratubular penetration (2). They are not prone to shrinkage, and therefore so the sealing capacity increases. In the work by Trope et al. (3), they detected evidence of expansion of bioceramic sealers in the setting reaction; they are characterized by having the ability to chemically bond to the dentine, so leakage decreases (4).
In the presence of biological fluids, calcium and phosphate ions present in the EndoSequence BC Sealer® (BC Sealer) may precipitate to form apatite (5). This ability is responsible for their bioactivity and excellent sealing capability (6). They also have antibacterial properties due to their high pH (7). The composition of the TotalFill BC Sealer HiFlow® (HiFlow) premixed calcium silicate-based sealers are made up of zirconium oxide, tricalcium silicate, dicalcium silicate, calcium hydroxide and fillers (8).
The intratubular penetration of the bioceramic sealer could generate a micromechanical interlock within the root dentine. In addition, the moisture that remains in the dentinal tubules could trigger their setting reaction with the production of hydroxyapatite, thus creating the aforementioned chemical bond with the root dentine (9). The micromechanical interlock and the chemical bond improve the resistance to any separation of the filling material and probably strengthens the root to prevent fractures (10). Recently, the behaviour of the bioceramic sealers has been investigated when they have been exposed to heat application. The chemophysical properties were investigated during or shortly after heat exposure (11). While the physical properties of the new bioceramic sealer HiFlow was not adversely affected by heat, a negative modification of the properties in the older bioceramic sealers was observed (12). The bioceramic-coated gutta-percha points (BG) is a modification of the inner composition of the gutta-percha cone and the coating of the outer surface with calcium silicate nanoparticles. According to the manufacturer, these types of points of gutta-percha should be used together with a bioceramic sealer.
The aim of this paper was to evaluate the intratubular penetration percentage in the perimeter of the canals of the calcium silicate-based sealer HiFlow, using three warm obturation techniques, continuous wave (CW) and vertical condensation (VC) with two different types of gutta-percha (conventional (NG) and BG), GuttaCore (GC) and single cone (SC) with BG in different root thirds. The null hypothesis states there are no differences between the intratubular penetration percentage in the perimeter of the canals obtained for each of the obturation techniques.
Material and Methods
This piece of research was approved by the Research Ethics Committee of UCV, (Registration number: UCV/2019-2020/001.).
-Selection of samples To carry out the study, 180 human teeth with a single root were selected (including incisors, canines and premolars). The teeth were extracted for periodontal reasons. Roots with acute curvatures, immature apex, resorption, fissures, calcification, previous endodontic treatment or initial apical sizes larger than 15 were rejected. After extraction, the teeth were immersed for one hour in a 5.25% sodium hypochlorite solution after which the root surfaces were cleaned with a Gracey® 1-2 curette (Hu-Friedy, USA) and then stored in a saline solution. Root canal preparation Two preoperative X-rays were taken in two views to check the presence of a single canal. Buccolingual and mesiodistal parallel radiographs were obtained for each tooth. After opening the root canal system with a tapered cone burr (Komet, Lemgo, Germany) and constant irrigation, the canal was located with a DG16® endodontic probe (Hu-Friedy, USA). The root of the clinical crown was separated at the amelocemental junction with a handpiece diamond disc and water cooling; a size 10 or 15 K file was then introduced into the canal space, the working length (WL) was established 0.5 mm from the apical foramen by visual observation. All canals were prepared with Protaper Gold® (Dentsply Maillefer, Ballaigues, Switzerland) according to the producer's instructions. The shaping files S1 (250 rpm and 3 Ncm) and S2 (250 rpm and 1 Ncm) were used with circumferential movements and brushing at the working length, while the finishing files F1 (250 rpm and 1.5 Ncm) and F2 (250 rpm and 2.5 Ncm), were used with a pecking motion with the Gold ReciprocTM motor (VDW, Munich, Germany). After each file was used, the canal was flushed out with 5.25% NaOCl solution. The permeability of the canals was checked by inserting a size 10 file through the apical foramen after instrumentation was complete. As the final irrigation protocol, canals were irrigated for 1 minute with 5 ml of 5.25% sodium hypochlorite, 1 mi-nute with 5 ml of 17% EDTA, and 30 seconds with 5 ml of chitosan-hydroxyapatite precursor, 10 ml of saline solution was used for a final flush out and also used in the established order of different irrigants (13,14). The irrigants were activated using the EDDY® sonic tip system (VDW, München, Germany) with Air Scaler. The canals were dried with F2 paper tips. This chemomechanical sample preparation procedure was common denominator, regardless of the obturation technique used.
-Obturation of the root canals 0,1% of Rhodamine BTM (Sigma-Aldrich Corp., USA) was added to the bioceramic sealer in relation to the weight for its subsequent observation through the confocal laser microscope, thanks to the fluorescent property of the dye. The samples were then randomly divided into 6 experimental groups (n=30). The samples were sealed with the different obturation techniques set forth as follows: •Group 1: SC with TotalFill BC Points® BG and Hi-Flow.
•Group 2: GC technique with HiFlow. •Group 3: CW technique with Protaper F2® gutta-percha, NG pellets and HiFlow. The teeth were filled using the CW technique, designed by Buchanan (15). The plugger was checked with the rubber stopper positioned at less than 4 mm from the working length. The shutter unit used was E&Q Master® (Meta Biomed, Chalfont, PA, USA), at a temperature of 220ºC for the hot plugger and a temperature of 200ºC corresponding to the warm gutta-percha injection unit. •Group 4: CW technique with TotalFill BC Points® BG, BG pellets and HiFlow. •Group 5: VC technique with Protaper F2® gutta-percha, NG pellets and HiFlow. The teeth were filled using the VC technique, designed by Schilder. We use the System-B® obturation unit (Sybron Dental, Orange, CA, USA) at a temperature of 100°C in the hot plugger, removing 2-3mm portions of gutta-percha and condensing it until reaching 4mm of the working length, and a temperature of 200ºC for the warm gutta-percha injection unit. •Group 6: VC technique with TotalFill BC Points® BG, BG pellets and HiFlow®.
-Specimen preparation Once all the samples were sealed, they were stored at 37ºC and 100% humidity in a laboratory incubator for 14 days to allow complete sealer setting. The root was divided into three parts, taking a sample from each third: the coronal, middle and apical third (the apical third was taken by subtracting a length of two millimetres from the root apex). Horizontal cuts were made using a 0,3 mm diamond disc handpiece with water cooling (16), 1 mm thick slices were then obtained; the slices were polished with Soft Lex discs (3M (™) ESPE (™) St. Paul, MN, USA). After observation with the confocal laser microscope (Leica TCS SP8 Confocal Microscope) and the 5x object lens, photographs of each of the samples were taken for analysis and studied. The intratubular penetration percentage in the perimeter of the canals of the sealer were carried out with Auto-Cad® Software from the images obtained and collected in a data sheet. Firstly, each image was scaled to 500 µm in order to obtain a correct measurement of all its elements. The appropriate AutoCad tool function was applied to the perimeter of the canals to obtain the intratubular penetration percentage (Fig. 1). The perimeter of the canal with tubular penetration was divided by the total canal perimeter and multiplied by 100 (17). All measurements were recorded by one of the authors. In case of doubt on first viewing, the sample was polished and a new image was obtained. All data was recorded, and then analyzed. -Statistical analysis The statistical analysis of the data collected for the present study was carried out using SPSS 23 software using a confidence level of 95% and considering them statistically significant (p<0,05). As the sample size is sufficiently large, (n=30), we used parametric methods of comparison. Levene's test, ANOVA test (middle and apical third), Welch's comparison test (coronal third), Games-Howell multiple comparison test (coronal third), Bonferroni test (middle and apical third) were used to evaluate the percentage of sealer penetration in the canal perimeter.
Results
The study showed the average of intratubular penetration percentage in the perimeter of the canals of the sealer (Table 1). Figure 2 demonstrated the representative samples of confocal images of the different groups and thirds. The results of Levene's test (Table 2) showed that the middle (p= 0,106) and apical (p= 0,141) third was greater than 0,05. For this reason, we used the ANOVA test (Table 3) in order to study the differences between the intratubular penetration percentage of each technique. In the coronal third (p= 0,014) we used Welch's comparison test (Table 3). In all thirds (p<0,05), there was a statistical difference between at least two of the obturation techniques. In order to study these differences, we used the Games-Howell multiple comparison test (
Discussion
In the present study, we used the confocal laser microscope, since the preparation of specimens destined for the scanning electron microscope may lead to a loss of sealer and deformation of the sample (18). Rhodamine B could be suitable with the bioceramic sealers, because the narrow amount (0.1%) used did not modify the sealer's qualities (19). The sample cuts were performed in the horizontal plane as the dentine of the root canal cannot be completely observed in the longitudinal plane (17). The intratubular penetration percentage in the perimeter of the canals suggested a highly clinical significance level (20). This penetration performance provides a physical barrier to the entry or exit of micro-organisms into the canal regardless of the depth of penetration or the area penetrated. Furthermore, a bactericidal effect is created by contact action between the sealer and the bacteria through its antibacterial effect (21). These two properties (contact action and physical barrier) are favourable for the healing of the periapical lesion. The major contact surface of the sealer with the canal walls determines the sealing of the root dentine (18). Few studies have assessed this parameter. The results of our study showed a large percentage of penetration sealer in the warm obturation techniques compared to the SC technique. In general, the heat resulted in a positive effect in terms of penetration percentage. A statistical difference showed up in the different techniques although not in all cases. These varying results may be due to the different factors that affected the penetration ability of the sealer (root third, properties of the sealer, obturation technique, irrigation, instrumenta-tion…).
Wang et al. (22) evaluated percentage sealer penetration with two different sealers (iRoot and AH Plus) and using the SC and VC techniques at 2-4 and 6 mm. There were no statistical differences between groups SC and AH Plus and VC with AH Plus and between the SC and VC groups with iRoot. At 2 mm, more penetrated segments of the root canal were observed in the iRoot groups than in the AH Plus groups. At the horizontal levels of 4 and 6 mm respectively, there were no statistically significant differences in the penetrated segment of root canal between these four groups. The differences with our outcomes may be due to the use of the specific techniques not being appropriate for these sealers. ). At 1 mm, the outcomes were lower in penetration percentage than at 5 mm. At the 5-mm level, there was no significant difference in percentage of sealer penetration between the VC or SC technique between any of the sealers. The difference with our results in the percentage of penetration may be due to the different instrumentation, the non-activation of the irrigants and the lower sample. In addition, the cuts were standardized at 5 mm in the study by McMichael; in our study however, the cuts were made by dividing the root into thirds. More outliers were measured for the SC technique than for the rest of the techniques in both studies. Sealer penetration percentage was significantly higher, at the 5 mm distance (middle third) compared with the 1 mm (apical third) with the warm obturation technique. These outcomes fall in line with the findings of our study; an explanation may be that tubular density and diameter tend to decline in apical thirds. In addition, it is difficult to transport the irrigants to the apical third in order to remove the smear layer of the dentinal tubules.
One of the interactions observed in our study was the so-called mineral infiltration zone (MIZ) which is a hybrid zone where hydroxyapatite recrystallisation occurs in dentine when a calcium silicate-based sealer is applied (23). These reactions were unexpectedly discovered when dentine tubules were converted into homogeneous structures due to by hydroxyapatite recrystallisation. However, such MIZ behaviour was not observed in all samples. MIZ has not been shown to positively or negatively affect the outcome of endodontic treatment (18). However, further studies would be required to determine the influence of MIZ on root canal treatment.
In some of the samples scanned by confocal laser microscopy, the penetration of the sealer into the dentinal tubules was not homogeneous. The varying directions of the dentinal tubules may affect the results (24). Sealer penetration was found to be higher in the buccolingual direction than in the mesiodistal direction, although not in all of the samples analyzed. This may be due to increased sclerosis in the dentinal tubules located on the mesial and distal sides of the canal lumen, with greater buccolingual than mesiodistal penetration observed. It is common in the single-root teeth over a broad age-range (25). Areas of sclerotic dentine are more common in the apical third (26).
The results of this study showed that the intratubular penetration percentages in the canal perimeter of the sealer, independently of the technique used, were greater in the coronal section compared to the apical section.
One explanation for this finding could be due to a higher efficiency of irrigant administration and smear layer removal at the coronal levels. The smear layer sticks to the canal walls, forms physical barriers and creates contamination in the dentinal tubules, blocking sealer penetration (27). In addition, tubular diameter, density and number decrease at the apical levels, which explains the tendency for sealer penetration to decrease from the coronal to the apical region (20). In addition, the viscosity and flow of endodontic sealers may determine the efficiency with which they penetrate the dentinal tubules. Chen et al. (11) showed that HiFlow had a higher flow than BC Sealer at higher temperatures. It is important to create an adequate glide path to disinfect properly before obturating the apical third. Due to the morphological characteristics of the tooth, it is difficult to deliver irrigant and sealer. We must consider whether the taper of the master apical file allows these minimum criteria for disinfection and obturation to be adequately met. Apical preparation using 2 sizes larger than the initial apical binding file with a taper of 4% is insufficient and results in significantly lower success rates compared to larger preparation sizes and taper (28). The sealers penetrated into the dentinal tubules can maintain their bactericidal effect (29) and therefore favourable for the healing of the periapical lesion.
In conclusion, within the limitations of this study, for each type of gutta-percha and technique, dentinal tubule penetration was higher in the coronal section than in the apical section. The warm obturation techniques (continuous wave, vertical condensation and Guttacore) showed more intratubular penetration percentage in the canal perimeter of the sealer than in the single cone in all of the thirds studied. | 4,232.2 | 2022-08-01T00:00:00.000 | [
"Materials Science",
"Medicine"
] |
Flying with data: Openness, forms and understanding
: There is a concerted effort to make available large amounts of public and open data. This paper explores this much-vaulted idea in terms of how easy or difficult it might be to find and access this data, and how a non-specialist audience is able to read, comprehend and make sense of complex digital data in its conventional form. Following a discussion that introduces the concept of the datadriven physical object (the data-object), and the current issues pertaining to the access and use of open data, the paper traces the journey of two design researchers through the activity of locating and using publicly available healthcare statistics as source content for developing this new form of data interpretation. The documented ‘dataseeds’ case study suggests that making data publically available is only the first step in thinking about how digital data can be accessed and shared in meaningful ways by a range of different audiences.
It is considered that we respond to data both emotionally and cognitively (Kennedy, 2015), and that notions of the embodied technological experience form an important backdrop to current thinking around the Internet of Things (IOT), smart environments and the rapidly expanding data-sphere (Munster, 2006).In previous research (Gwilt, Yoxall, & Sano, 2012) it has been observed that when you represent data as a physical object there is a relationship established between the physical affordances of the object, such as shape, texture, scale and weight, and the perception of the interpretation of the data that object represents.For example, the amount of granularity or texture of a surface would appear to correlate with the perception of how much data that surface represents, e.g.textured surfaces suggest more data, smooth surfaces less and so forth.As Sennett has observed, the nuances of material cultures are extremely important when establishing and assigning value to the things we use (2009).
Choices in visual metaphor and form are also seen to impact on how people understand and relate to any suggested physical representation of data.However, the representation of data through a physical object is by no means a new idea; cultures and communities over time have adopted this technique in different ways to suite particular needs, for example Swiss shepherds used the tally stick (a piece of wood with notches carved into it) as a physical record to document Alpine grazing rights in 18th Century Switzerland.Pierre Dragicevic and Yvonne Jansen have put together a collection of over 250 different types of data driven objects dating back to 550Bc, however the majority of the examples in this archive have been created in the last decade (dataphys.org/list/).Andrew Vande Moere, an early commentator on the practice of data visualisation also comments on the use of the physical form to convey digital information and how we might approach representing abstract data that has no inherent spatial form in the material world (Vande Moere, 2008).Artists such as Nathalie Miebach and Annie Cattrell have worked with data, using both traditional and contemporary making techniques.In the case of Miebach, the artist uses weaving to create physical representations of weather patterns (Miebach, 2006), while Cattrell has employed 3D printing to represent neuroscientific data of what happens in the brain as we go through different emotional states (Cattrell, 2009).Abigail Reynolds 2013 work Mount Fear East London uses laser-cut pieces of corrugated cardboard to create a room sized 3 dimensional representation of violent crime statistics in different areas of London.This large data visualisation presents the audience with an imposing representation of data the meaning of which is enhanced by the use of roughly finished pieces of cardboard and through the physical scale of the work.In a more physically refined use of a dataobject concept Mitchell Whitelaw (2010) compiles 150 years of temperature data from Sydney, Australia to create a drinking beaker in a comment on global warming.Using 3D printing technologies, annual coils of data are placed one on top of the other to create the shape of the cup.Recent increases in the overall temperature patterns create a flared lip to the beaker in a serendipitous correlation with a convention that commonly uses the same flared-lip technique to make drinking more pleasant.
The employment of new digital making techniques such as the range of 3D printing methods now available, and the flexibility that this enables in terms of creating physical representations of data, is an important enabling factor.The other enabling factor in this story is the capacity of the computer and digital technologies to store, generate, analyse and cross-reference data at an ever increasing scale and speed.The dataseeds case-study outlined below is an example of the data-objects concept that utilises contemporary fabrication methods to translate complex digital data into a physical object that can be used to aid understanding and simulate conversation around a digital data set.
Making sense of data
Data and the use of data is rapidly becoming the new universal language.The rush to digitise all things physical in the late 20th Century led to the rise and rapid development of the human computer interface (HCI) in the many forms we see and use today (Johnson, 1997).In this new data driven revolution there is an equal and pressing need to develop and deploy interfaces that allow people and communities to explore and make use of digital data in a variety of contexts and for different purposes (Yau, 2013).Andy Kirk's book Data Visualisation A Handbook for Data Driven Design (2016) unpacks in some detail the variety of different ways that data can be represented in 2 Dimensional visual forms to help aid the reading and interpretation of data.But the notion of incongruent data where data has no inherent form (Vande Moere, 2008;Lima 2009) problematises what techniques we should be using to make data comprehensible and engender insight.If data has no naturally corresponding form what do we use to guide our choices when making a physical/visual representation of data?Unquestionably today's digital data comes in many forms and sizes, and terms such as Big Data, Open Data and the Quantified Self by degree refer to scales and accessible forms of data that are collected from the societal level to the personal (Prendiville, Gwilt, & Mitchell, 2017;MayerSchönberger & Cukier, 2013) 1 .In relation to the sharing of healthcare data in the UK NHS England has recently announced the establishment of a National Information Board to help manage and effectively utilise publically released open data, and to make progress on improving healthcare using data and technology (www.gov.uk/government/organisations/national-information-board).
The Dataseeds case-study
The following case-study describes an experiment to produce an object-based translation of a publically accessible open data source from the UK NHS healthcare sector as a praxis exemplar.It was devised as a practice-based method intended to reveal some of the key issues involved when translating digital data into a physical object that is representative of any underlying data set.As well as documenting the design process undertaken the case-study is also used to inform a set of general guiding principles for the creation of data-based objects.These principles are documented and discussed in the final section of the paper.
Moreover, the case-study operates as an example of how it is possible to interpret digital data as a physical object utilising a combination of design strategies and contemporary fabrication methods.It should be noted that as the project was conceived as a way of exploring the potentials of the data driven object as a way of communicating healthcare statistics the process we undertook was slightly unusual in that we did not start with a given or identified data set to work with.In most instances however it is imagined that an appropriate data set will have already been identified.The outline process that the case-study assumed was as follows: 1. find and select an appropriate data set (the data set would typically already be selected) 2. identify key information in the data 3. develop prototypes to test the design decisions in respect to communicating the data 4. develop a workable model that can be shared with potential users 5. evaluate the effectiveness of the data object in communicating the underlying data 6.
Selecting a data set
The data set we decided to use for the case-study came from NHS Digital (previously known as the Health and Social Care Information Centre), who are the national provider for information, data and IT systems, that support commissioners, analysts and clinicians in the health and social care sectors in the UK (https://digital.nhs.uk/).As mentioned there is a concerted effort to make data from the public sector available to the community, and as well as the NHS Digital resource an extensive repository of data from different sectors including, business, the environment, social metrics, transport, government and education statistics, can be accessed through data.gov.uk.The data sets in these digital repositories are typically presented and downloadable as statistical spreadsheets in commonly used formats such as MS Excel Spreadsheets, Xls or CSV files.These data sets are often accompanied by contextual reports.Although work is being undertaken to consolidate and simplify access to and navigation of these public resources, it can be quite difficult to know where to find information and to identify specific data which might be part of a more complex spread sheet; online tools to assist with this task are beginning to be provided in some cases.Information on how data is collected, data governance and good practice polices is an important part of official public open data and information pertaining to this can also be found at these locations.
Working with the data
Specifically, the data used in the case-study project comes from publically available NHS risk management statistics and makes up part of the data set 'The Health and Social Care Information Centre, Hospital Episode Statistics for England, inpatient statistics, 2012-13 (2016).This dataset documents over 350 different reasons why patients are admitted to NHS hospitals in England in 2012/3.Of all of these different causes we were particularly interested in 'falls' as a reason for admission to hospital.Within the statistics there were 15 subsets around falling accidents.These were as follows: • Fall on same level from slipping, tripping and stumbling We decided to use the falls on stairs and steps statistics, which accounted for over 3% (37,427) of all the 1.2million plus admissions for the year and was the 7th highest reason for admissions.For the purposes of the project the data was separated into four sub-sets: falls of people between the ages of 50 to 60 years, 60 to 70 years, 70 to 80 years and 80 to 90 years.
Designing with the data (designing the dataseeds)
The selected data set allowed us to develop a data-object concept based on the metaphor of falling (the dataseed).Drawing from nature we looked at the Sycamore seed as an aesthetically pleasing and functional solution (Figure 1.).The Sycamore seed form, and how it falls, is something that is universally engaging and as such we decided it would work well as a metaphor for human falls.To accurately represent the falls data as a data-object we needed to make a physical representation of a sycamore seed that could drop and spin at different rates to visually and dynamically interpret the data.To achieve this, we aimed to produce a standard seed body and spine with an adaptable wing profile that would parametrically alter based on the data instance, to change the descent and spin characteristics.A number of prototypes were created to replicate the angle and pitch of flight from a natural seed.
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Flying with data: Openness, forms and understanding Figure 1.The sycamore seed was identified as an appropriate analogy for the data-object we were constructing.
A selection of instances from the data set based on the number of falls in different age groups were used to calculate the surface area of the wing shape attached to a dataseed.These calculations dictated the spin and falling speed of each of the seeds, which meant that the data itself was manipulating the speed of descent of the seed.(Figure 2.).The design process was started through a process of 'quick-and-dirty' prototyping both on paper and digitally to create functional informative models.We created multiple seed forms from different data instances associated with the frequency and age demographics in the data set.SolidWorks, a CAD software was used to create 3D structures to develop the body and tail seed frames, and paper and adhesive tape were used for wing experimentation.Through this iterative process we were able to achieve a good representation of a Sycamore seed flight during falling.
The second part of the design process was to address how the speed of descent for each dataseed would work in relation to the data instance that it was representing.A flying dataseed that mimicked the natural fall pattern of the sycamore seed was developed over the course of a 2-week dynamic development design process, which looked at the wing design, and different materials and forms to achieve the optimum fall pattern results (Figure 3.).A range of materials was also tested for use in the wing section of the dataseed.This included testing materials such as masking tape, PTFE tape, cling film, copy paper and tracing paper.From these tests it was decided that the best material for weight for stability in flight was tracing paper.In addition, the surface area and shape of the wing was manipulated in a range of prototypes to alter the dynamic behaviour of each individual dataseed.A parametric design table was developed within SolidWorks that enabled the designers to alter the surface area of the seed to represent the actual data.
A short descriptive text was printed on each dataseed wing to contextualise the object and indicate which instance from the data set each individual seed represented.This addition was intended to facilitate comprehension of the data-object with end-users and to help any would-be data analyst to understand why the falling properties of seeds differed from one another (see Figure 4.).For the rigid spine and body of the dataseeds we used a fused filament fabrication (FFF) additive manufacturing, 3D printing process (see Figure 5.).A range of forms were experimented with to achieve the optimal design and biomimicry provided the best solution; this approach helped to replicate the natural descent angle of a sycamore seed 2 .We also experimented with a variety of fill densities, form patterns and scales.In terms of density, the best results were found with a 20% fill structure.In terms of form, we started by using an exact copy of a natural seed and wing size.In using our chosen manufacturing process and range of materials this did not allow us to replicate the natural falling behaviour of a Sycamore seed.However, scaling up the size of the seed, spine and wing did lead to a more natural falling motion when the size was around 200% of the conventional size of a UK sycamore seed.The length of the seed spine was adjusted to support the minimum dataset and maximum dataset without compromising the flight characteristics of the seeds.By changing wing surface area (dictated by the data for one of the age groups) the centre of gravity was altered, leading to a change in speed and rotation in decent.The final range of seeds produced incorporated a solid seed body and spine.
The developed dataseed prototypes were tested and recorded using a high-speed camera (see Figure 6.), and the rapid fabrication technologies used to make the data-objects allowed for the production of 200 dataseeds (representing a selection of data instances).These were 'drop' tested from a second-storey internal atrium to observe the flying characteristics and variance of the seeds.specific dataset and audience in mind and the authors have drawn up a sequence of guiding principles, and set of questions that should be considered before creating a data-object as a means to aid communication.
Guiding principles and questions for creating a data-object are as follows: • Consider what the creation/use of a data-object will contribute to the communication of the underlying data and to whom? (If you cannot answer this question stop here!)• Consider your audience and what their expectations from the data might be?
• Carefully select a relevant data set, paying attention to the credibility of the data source and the usability of the data.• Carefully examine the chosen data set to identify the significant key message/ messages in the data and to make sure that you understand what the data is communicating.• Carefully consider how the design choices of any physical form and/or use of visual metaphor relate to the underlying data?• Where possible involve your user community in all stages of the design and decision making processes.• Make sure the data object's form and physical qualities remain faithful to the statistical variance of the underlying data.To conclude, it is important to stress that the authors of this work do not envisage that the dataobject concept is a way of substituting other forms for communicating data.The data-object should be seen as a technique that when given the appropriate consideration has the potential to add to the understanding and cognition of any given data set.According to Luc Pauwels, editor of 'Visual Cultures of Science' (2006) visualisation techniques play an important role in not only facilitating knowledge but also are an important tool to how we understand and ratify the world around us.It is important to continue to develop and design appropriate methods to help interpret the complex and interrelated digital data-scape for all sectors of the community.
Figure 2 .
Figure 2. The data dictates the surface area of the wing of the dataseed, which in turn influences the spin and falling speed of the data-object.
Figure 3 .
Figure 3.A number of prototypes were developed to test materials, wing shapes, flight dynamics and so on.
Figure 4 .
Figure 4. Samples of prototype dataseeds that show the use of materials and the addition of text to indicate data set
Figure 5 .
Figure 5. 3D printing technologies used to fabricate multiple copies of the dataseeds body and tail sections.
2
The authors have since seen much larger Sycamore type seeds in other countries.S3869Downloaded by [Sheffield Hallam University] at 07:37 20 September 2017
•
Consider how the use of any fabrication techniques and choices in material might amplify or sympathetically reflect key trends in the data.Equally consider if there are any possible negative interpretations that might be drawn from your choices?• Consider where and how the data-object might be encountered and in what context?• Consider how the data-object might work with other forms of communication and fit into a long term communication strategy.
• Fall involving ice-skates, skis, roller-skates or skateboards • Other fall on same level due to collision with, or pushing by, another person • Fall while being carried or supported by other persons • | 4,355.4 | 2017-07-28T00:00:00.000 | [
"Computer Science"
] |
Polynomials defined by tableaux and linear recurrences
We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure atoms. The same technique can be applied to Hall-Littlewood polynomials and dual Grothendieck polynomials. The motivation behind this is that such recurrences are strongly connected with other nice properties, such as interpretations in terms of lattice points in polytopes and divided difference operators.
Introduction
Using a similar technique as in [Ale14], we provide a framework for showing that under certain conditions, polynomials encoding statistics on certain tableaux, or fillings of diagrams, satisfy a linear recurrence. We prove that several of the classical polynomials from representation theory fall into this category, such as (skew) Schur polynomials and Hall-Littlewood polynomials.
The main concern in this paper are the so called key polynomials, indexed by integer partitions, and atoms. The key polynomials are natural, non-symmetric generalizations of Schur polynomials and are specializations of the non-symmetric integer form Macdonald polynomials, see [Mas09] for details.
Let λ be a fixed diagram shape, (a partition shape, skew shape, etc.) and let P kλ (x), k = 1, 2, . . . , be a sequence of polynomials which are generating functions of fillings of shape kλ. For partitions, kλ is simply elementwise multiplication by k. There are several reasons why one would be interested in showing that a such sequence satisfies a linear recurrence: (1) To obtain hints about the existence or non-existence of formulas of certain type. For example, the Weyl determinant formula for Schur polynomials implies that the ordinary Schur polynomials satisfy a linear recurrence.
(2) To obtain evidence for alternative combinatorial interpretations of the tableaux involved. For example, the skew Schur polynomials can be obtained as lattice points in certain marked order polytopes, called Gelfand-Tsetlin polytopes. Such a polytope interpretation implies the existence of a linear recurrence relation.
(3) To prove polynomiality in k of the number of fillings of shape kλ.
(4) To obtain results about asymptotics. For example, in [Ale12] we used such recurrences to give a new proof of a classical result on asymptotics of eigenvalues of Toeplitz matrices.
In the last section, we provide several examples of polynomials that satisfy such linear recurrences. We also sketch two additional proofs in the case of key polynomials, to illustrate that several nice properties imply the existence of a linear recurrence relation. These methods are based on a lattice-point representation and an operator characterization of the key polynomials. There is no straightforward way to check if a family of polynomials have such characterizations, but it is easy to generate computer evidence that a sequence of polynomials satisfy a linear recurrence. Thus, proving the existence or non-existence of linear recurrence relations is an informative step towards alternative combinatorial descriptions of the family of polynomials.
Acknowledgements. The author would like to thank Jim Haglund for suggesting this problem. This work has been funded by the Knut and Alice Wallenberg Foundation.
Diagrams and fillings
A diagram D is a subset of {(i, j) : i, j ≥ 1} which realized as an arrangement of boxes, with a box at (i, j) for every (i, j) in D. Here, i refers to the row and j is the column of box (i, j) and we draw diagrams in the English notation. For example, D = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 2)} is shown as (1) is a filling of the diagram with shape (2, 4, 3, 1, 6)/(0, 2, 2, 1, 3), where the places marked × correspond to boxes in D β . The shape of a filling refers to the shape of the underlying diagram.
The jth column in a diagram D with l rows has a shape define as the integer composition (s 1 , . . . , s l ), where s i = 1 if (i, j) ∈ D and 0 otherwise. Thus, if α is an integer composition with only 0 and 1 as parts, then the first column of D α has shape α. Whenever α is an integer partition, D α is called a Young diagram and any filling of a Young diagram is called a tableau. A filling with shape α/β where both α and β are partitions, is called a skew tableau.
Given a diagram or a filling, we can duplicate or delete columns. For example, deleting the fourth column and duplicating the third column in the filling in Eq. (1) results in the filling 1 8 × × 9 9 9 × × 5 5 5 × × × × × × 2 7 . (2) Note that if the original filling T has shape D α/β , then duplication and deletion on T will result in some T of shape D α /β . This is straightforward to prove.
2.2. Column-closed families of fillings. In most applications, one are interested in a restricted family of fillings, perhaps tableaux or skew tableaux, together with some conditions on the numbers that appear in the boxes. Note that a filling T can be viewed as a concatenation of its columns -some of which might be empty. Obviously, T can only be expressed in one such way if we require that the last (rightmost) column is non-empty.
Definition 1.
A family of fillings, T , is said to be weakly column-closed if holds for every combination of integers m i where m i ≥ 1. The family T is said to be strictly column-closed if Eq. (3) holds for every combination where m i ≥ 0. That is, the family is closed under deletion of any column.
Less formally, T is weakly column-closed if it is closed under column duplication, and reduction of duplicate columns. The family is strictly column closed if it, in addition, is closed under removal of any column.
Combinatorial objects would not be interested if it weren't for combinatorial statistics. A combinatorial statistic on a family T is a map σ : T → N s . We will study a special type of statistics on fillings: for all choices of m i ≥ 1, where A and S i are vectors in N s . Similarly, σ defined on a strictly column-closed family T is linear if σ(m 1 C 1 , . . . , m l C l ) = S 1 m 1 + S 2 m 2 + · · · + S l m l for all choices of m i ≥ 0. Note that this is equivalent with the statement that σ(T 1 ∼ T 2 ) = σ(T 1 ) + σ(T 2 ) for every pair T 1 , T 2 of fillings such that T 1 ∼ T 2 is in T .
Note that the statistic given by w(T ) = (w 1 , w 2 , . . . , w n ) where w i are the number of boxes filled with i in T is a linear statistic. This is usually called the weight of T . Finally, two statistics σ 1 : T → N s1 and σ 2 : T → N s2 can be combined into a new statistic σ in the obvious manner as σ(T ) = (σ 1 (T ), σ 2 (T )), which map to N s1+s2 .
Properties of linear recurrences
We first recall some basic notions about linear recurrences. This can be seen as analogous to the theory of linear differential equations.
A sequence {a k (x)} ∞ k=0 of functions are said to satisfy a linear recurrence of length r if there are functions c 1 (x), . . . , c r (x) such that for all integers k ≥ r. The polynomial (in t) is called the characteristic polynomial of the recursion. If the characteristic polynomial factors as (t − ρ 1 ) m1 · · · (t − ρ r ) mr , where all ρ i (x) are different, then one can express a k (x) as for some functions g li (x), that only depend on the initial conditions, that is, the functions a 0 (x) to a r−1 (x). In the other direction, any sequence of functions which are of the form given in Eq. (5) satisfy a linear recurrence with χ(t) as characteristic polynomial. Notice that the c i are elementary symmetric polynomials in the ρ i , with some signs.
From now on, we are only concerned about sequences where the a k (x) and ρ j (x) are polynomials, which implies that the c i (x) are polynomials and the g li (x) are rational functions. Let a k (x) and b k (x) be sequences of polynomials with characteristic polynomials given by i (t − ρ i (x)) pi and i (t − ρ i (x)) qi respectively, where some of the p i or q i may be zero. Then, as sequences for k = 0, 1, . . . , • h(x)a k (x) satisfy the same linear recurrence as a k (x), where h(x) is any polynomial, • a k (x) + b k (x) satisfy a linear recurrence with characteristic polynomial given by • a k (x) · b k (x) satisfy a linear recurrence with characteristic polynomial given by However, if ρ i1 (x)ρ j1 (x) = ρ i2 (x)ρ j2 (x) for some (i 1 , j 1 ) = (i 2 , j 2 ), some roots of the characteristic equation can be removed -details are left as an exercise. As an example: with s a fixed positive integer satisfy a linear recurrence with characteristic polynomial given by The proofs for these statements follows from writing a k (x) and b k (x) in the form Eq. (5) and examining the expressions above. Note that if a k (x) and b k (x) have characteristic polynomials with simple roots, then so does Finally, the definition of a sequence satisfying a linear recurrence in Eq. (4) does not provide an easy method to check for a linear recurrence if the c i are unknown.
A useful shortcut might then be the following observation: a sequence {a k (x)} ∞ k=0 satisfy a linear recurrence of length r if and only if the following r × r-determinant vanish for all k ≥ r − 1: This classical trick can be found in e.g. [Lyn57].
Lemma 3. Let T be a weakly column-closed family of fillings and T = (C 1 , . . . , C l ) is a fixed filling in T , where no adjacent columns are equal. Let σ : T → N n be a linear combinatorial statistic such that σ(a 1 C 1 , . . . , a l C l ) = a 1 S 1 + a 2 S 2 + · · · + a l S l .
Define the sequence of polynomials Proof. Note that the definition of F k (z) implies that F k (z) ≡ 0 whenever 1 ≤ k < l, and that F l (x) = z S1+···+S l . These are l conditions and it is easy to see that if we have a characteristic polynomial of the form (6), then F 0 (z) must be equal to (−1) l+1 .
Any tableau of the form (a 1 C 1 , . . . , a l C l ) where a i ≥ 1 and a 1 + a 2 + · · · + a l > l, must have some a i ≥ 2. Thus, this tableau can be constructed from some (a 1 C 1 , . . . , (a i − 1)C i , . . . , a l C l ) by duplicating column C i . However, there might be several ways to do this. By using an inclusion-exclusion argument, it is straightforward to show that for all k ≥ 0. Note that the coefficients are the elementary symmetric polynomials, evaluated at z S1 , . . . , z S l , so factoring the characteristic polynomial gives exactly the expression in (6).
Lemma 4. Let T be a weakly column-closed family of fillings, and let the T (a) ∈ T be given as
where each T i is some fixed (possibly empty) filling and no adjacent columns in each (C i1 , . . . , C ili ) are equal. Furthermore, let σ : T → N n be an affine combinatorial statistic, such that σ(T (a)) = A + a 11 S 11 + · · · + a m,lm S m,lm .
Let α = (α 1 , . . . , α m ) be a fixed integer composition and define the polynomial Proof. This is immediate from the the definition of σ and the F i k (z), by simply substituting the definition of F i k (z) in the product and recognizing the expression for σ.
Note that the integer composition α should not be confused with some shape of a tableau. The composition α rather serves as the number of columns there are in each of the m "blocks" of columns in T (a). The functions G kα (x) can now be seen as the generating functions of σ, as the block sizes grows linearly with k, and each block i consists of column fillings with columns from {C i1 , . . . , C ili }, each present at least once. However, note that if all T i are empty fillings (no columns), then G kα (x) can be seen as generating function for fillings of shape kD for some fixed diagram D as in Fig. 1. In the proof of Proposition 6, the relation between α and D is explained in more detail.
Corollary 5. {G kα (z)} ∞ k=0 satisfy a linear recurrence with characteristic polynomial given by Furthermore, if σ is linear, then Eq. (7) can be expressed as Multiple roots can be disregarded if {S i1 , . . . , S ili } are all distinct for every i.
Proof. Each F i k (z) can be seen as generated by a linear statistic σ (T ) = σ(T ) − A. Therefore, each of these satisfy a linear recurrence, according to Lemma 3. The theory of linear recurrences now imply that the G kα (z) also does, with a characteristic polynomial as described above, since G α is essentially a product of the F i .
Eq. (8) follows from linearity of σ together with the definition of σ. Note that the value of σ(α 1 C 1j1 , α 2 C 2j2 , . . . , α m C m,jm ) is defined by linearity σ, but that the tableau we evaluate on might not be in T (if some α i = 0) unless this family is strictly column closed. The statement about simple roots follows immediately from the theory of linear recurrences.
So far, we have only treated generating functions of subsets of tableaux where the columns are from a specified subset and each column appear at least once. We will now treat the case where only the family of fillings and the diagram shape defines the generating function. To do that, it is natural to restrict ourself to a special type of families of fillings.
A family T is said to be well-behaved if every filling T ∈ T satisfies the following two properties: • if two columns in T are identical, then all columns in between are also identical to these two. • if two columns C 1 and C 2 are different and C 1 appears to somewhere the left C 2 , then C 1 never appears to the right of C 2 in some other filling T ∈ T .
For example, fillings such that every row is weakly decreasing (or increasing) are well-behaved.
Proposition 6. Let T be well-behaved weakly column-closed family of fillings and let σ be an affine statistic defined on T . Let D be a fixed diagram and define the polynomials where T (D, n) is the set of all fillings in T with shape D and for every box (i, j) in such a filling, we have 1 ≤ T (i, j) ≤ n. Then {H kD (z)} ∞ k=1 satisfy a linear recurrence. Furthermore, if σ is linear, then the characteristic polynomial of the recurrence is given by where T runs over all tableaux of shape D such that any adjacent columns of same shape in T are identical, and each T can be obtained from some T (kD, n) by deleting some columns. Note that T might not itself be an element in T . However, if T is strictly column closed, then each such T is in T (D, n).
Proof. Note that every column in kD has the same shape as some column in D.
Since we may only fill boxes with entries from [n], there is a finite number columns that can appear in T (kD, n). Furthermore, since T is well-behaved, there is a finite number of lists of columns, (C 1 , C 2 , . . . , C l ), such that all C i are different and C i never appears to the right of C j in some filling in T , whenever i < j. Thus, for every k, every filling in T (kD, n) can be obtained in a unique way from such a list, by duplicating some columns in that list. Hence, H kD (z) can be expressed as a finite sum over such lists (C 1 , C 2 , . . . , C l ), where each term corresponds to fillings T of shape kD where each column in T is in the list and every column in the list appears at least once in T .
More specifically, let the diagram D be expressed as the concatenation D = (α 1 s 1 , α 2 s 2 , . . . , α m s m ) where the s i are column shapes and s i = s i+1 (here, we use the same notation as for filled columns). Then every filling in T (kD, n) can be obtained in a unique way as where each C ij has shape s i and a i1 + · · · + a i,li = α i . Hence, H kD (x, t) can be expressed as a sum over polynomials of the same form as G kα in Lemma 4. Corollary 5 tells us that each G kα satisfy a linear recurrence, so the sum of such sequences must too. This proves the first statement in the proposition.
The second statement follows from Corollary 5 and observing that the S ij in Eq. (7) can be replaced by σ(C ij ), since σ is linear. The observation that it is enough to only consider tableaux where adjacent columns of same shape have identical fillings is a consequence of the combinatorial interpretation of the F i kαi (z) in Lemma 4a block of size kα i must have α i copies of some column if k is sufficiently large and now a similar inclusion-exclusion reasoning apply as in Lemma 3.
Corollary 7. Let (σ, τ ) be an affine statistic, such that the restriction to σ is linear and σ(C 1 ) = σ(C 2 ) ⇒ C 1 = C 2 for any pair of columns that appear in a filling in T . Then the characteristic polynomial in (9) can be taken to have only simple roots.
Proof. The fact that σ(C 1 ) = σ(C 2 ) ⇒ C 1 = C 2 implies that the values of the S ij in (7) are all distinct. Since {F kD (z)} ∞ k=1 can be expressed as a sum of sequences, each of which has simple roots in its characteristic polynomial, the statement follows by using the theory in Section 3.
Augmented fillings
This section introduce the diagram fillings that are responsible for key polynomials, Demazure atoms and Hall-Littlewood polynomials. We follow the terminology in [HLMvW11,Mas09], with a few minor modifications.
Let β = (β 1 , . . . , β n ) be a list of n different positive integers and let α = (α 1 , . . . , α n ) be a weak integer composition, that is, a vector with non-negative integer entries. An augmented filling of shape α and basement β is a filling of a Young diagram of shape (α 1 , . . . , α n ) with positive integers, augmented with a zeroth column filled from top to bottom with β 1 , . . . , β n . Similarly, an inversion triple of type B is an arrangement of boxes, a, b, c, located such that a is immediately to the left of b, and c is somewhere above a, and the row containing a and b is strictly longer than the row containing c and Warning! This definition slightly different from what is stated in [HLMvW11]. However, the definitions coincides whenever the rows in the filling are weakly decreasing and we are only concerned with that special case.
Definition 10.
A semi-standard augmented filling, (ssaf) of shape α and basement β is an augmented filling of shape α and basement β with weakly decreasing rows and without any inversion triples.
Note that this definition implies that there are no attacking boxes in an ssaf. In particular, all entries in every column are different.
Example 11. Here is an example of a semi-standard augmented filling, with basement (1, 3, 2, 5, 4). 1 3 3 1 1 2 2 5 5 5 5 4 4 4 3 2 We can for example check the underlined entries for the type B inversion triple condition -since 4 ≤ 1 ≤ 3 is not true, they do not form such a triple. It is left as an exercise to check that no other triples are inversion triples.
Lemma 12. The semi-standard augmented fillings is a weakly column-closed, wellbehaved family.
Proof. It suffices to show that duplication of a column in a ssaf T do not introduce any inversion triples and it is enough to check that there are no inversion triples in adjacent and identical columns.
Assume that a, b, c form an inversion triple, as in Eq. (10) (either type). Since the columns are identical, T (a) = T (b) which implies T (a) = T (c) = T (b). However, this is means that two boxes in the same column are identical, so they are attacking. This contradicts the fact that the filling is a ssaf.
Let ssaf(β, α) be the set of all semi-standard augmented fillings with basement β and shape α. Note that ssaf(β, α) is a finite set. Given an augmented filling T , let w(T ) = (w 1 , . . . , w n ) where w i count the number of boxes with content i not including the basement. The generalized Demazure atoms are defined as The special case when β i = i corresponds to the ordinary Demazure atoms, introduced by Lascoux and Schützenberger in [LS90] under the name standard bases.
Let nawf(α) denote the set of all non-attacking augmented fillings of shape α with weakly decreasing rows and basement given by β i = i. The non-symmetric, integral form Hall-Littlewood polynomials, E α (x 1 , . . . , x n ), may be defined as where coinv(T ) is the number of triples in T which are not inversion triples, and dn(T ) is the number of pairs of adjacent boxes, (i, j) and (i, j + 1) such that T (i, j) = T (i, j+1) (different neighbors). This formula was first given in [HLMvW11]. It is straightforward to show that the nawf form a weakly column-closed and wellbehaved family. They show that the ordinary Hall-Littlewood polynomials P µ (x; t) can be expressed as where λ(γ) is the unique integer partition that is obtained from the weak integer composition γ by sorting the parts in decreasing order.
Lemma 13. The statistics dn and coinv are affine statistics.
Proof. It follows immediately from the definition of dn that if dn(C 1 , . . . , C l ) = A, then dn(m 1 C 1 , . . . , m l C l ) = A for all m i ≥ 1, so this is affine. The fact that coinv is affine is also quite straightforward and is left as an exercise to the reader.
Note that Eq. (13) implies that the ordinary Hall-Littlewood P polynomials satisfy a linear recurrence. These are usually (see [Mac95]) defined as where λ = (λ 1 , . . . , λ n ), some parts might be zero and m λ (i) denotes the number of parts of λ equal to i, and σ act on the indexing of the variables.
Observe that from this definition, it is quite clear that {P kλ (x; t)} ∞ k=1 satisfies a linear recurrence, since for a fixed σ in (14), the expression is of the form g(x; t)σ(x) λ where g is independent under λ → kλ. Now compare with Eq. (5) above.
Key tableaux and key polynomials.
Let α = (α 1 , . . . , α n ) be a weak integer composition. To any such composition, construct a composition with unique entries, β, and a partition λ as follows: Create an augmented Young diagram with shape α and fill the zeroth column with the numbers 1, . . . , n in decreasing order. Remove all rows for which α i = 0 and sort the remaining rows according to the number of boxes, in a decreasing manner. If two rows has the same number of boxes, preserve the relative order 1 . The resulting diagram has the shape of a partition, λ, which we denote λ(α), and the zeroth column will be our basement β(α). It is easy to show that this process can be reversed, that is, to any pair (β, λ), there is a corresponding α. Finally, note that β(kα) = β(α) and λ(kα) = kλ(α) for non-negative integers k.
This correspondence is illustrated in Eq. (15), for α = (0, 2, 3, 4, 2, 0, 1) and the tuple β = (4, 5, 6, 3, 1), λ = (4, 3, 2, 2, 1). The key polynomials generalizes the Schur polynomials and are indexed by integer compositions. They can be defined as Note that the key polynomials are a subset of the generalized Demazure atoms. This motivates the definition of a key tableau as a semi-standard augmented filling of partition shape, and we let ktab(β, λ) = ssaf(β, λ) to emphasize that this subset is of special interest. Note that we only need to be concerned about inversion triples of type A since we are dealing with partition shapes.
Given a column (β 1 , . . . , β n ) and a set of entries {c 1 , . . . , c n }, there is at most one one way to arrange the entries c 1 , . . . , c n in a column next to β such that the result fulfills all properties of a key tableau. First of all, it is easy to see that a necessary condition is that β i ≥ c i for all i, for some enumeration of the c i , in order to have decreasing rows in the result.
Secondly, the lack of inversion triples in a key tableau implies that the order of the entries in the second column is unique; if (a, b, c) is an inversion triple of type A, then transposing the entries in box b and c yield a non-inversion triple. This defines a total order among the elements in the second column, so there can be at most one filling where the second column (as a set) consists of the entries c 1 , . . . , c n .
The following lemma shows that under the obvious condition that if β i ≤ c i for all i, then the c i can be arranged in such a way that the columns form a proper key tableau with basement β. We prove a stronger statement: Lemma 15. Let T be a Young diagram of partition shape 1 + λ, filled with positive integers in such a way that each row is weakly decreasing, and each column contains unique entries, and the first column is given by β. Then each column in T can be sorted in a unique way such that the result is a key tableau of with shape λ and basement β.
Proof. We do the proof in several steps. The first case we cover is the case when all parts in λ has the same size, that is, all columns of T has the same height. It is easy to see that in this case, we only need to show the statement for two columns. Thus, assume (β 1 , . . . , β n ) and (c 1 , . . . , c n ) are given, with β i ≥ c i for all i.
We now perform the following sorting procedure on the second column. Let c i be the largest entry in the second column such that β 1 ≥ c i , and transpose c 1 and c i . Since c i ≥ c 1 , the rows are still weakly decreasing after this transposition. Note that β 1 and c i cannot be involved in an inversion triple later on: if there is some c j such that β 1 ≥ c j > c i , this would violate the maximality of the choice of c i .
We now proceed recursively on the remaining entries of the two columns, (β 2 , . . . , β n ) and (c 2 , . . . , c n ) where we have performed a transposition in the second column.
To handle tableaux with more than two columns, simply apply the permutation that takes the original column c to the result on all subsequent columns. The result will now still be a tableau with weakly decreasing rows, but the first two columns do not contain any inversion triples. Proceed with the same method on column 2 and 3, then 3 and 4, and so on.
Note that if c 1 < c 2 < · · · < c r ≤ β i for all i, and c r < c j for all j > r, then the second column after the above procedure will end in the sequence c r , c r−1 , . . . , c 1 , reading from top to bottom. Thus, to turn an arbitrarily shaped tableau T into a key tableau, we first augment each column with negative integers, such that all columns have the same height, and a new entry on row i will get the value −i. After performing the sorting procedure, the above observation implies that we can remove all boxes with negative entries from the result and recover a key tableau with the same shape as T .
Note that Lemma 15 implies that if T is a key tableau, then one can remove any column from it, reorder the entries in each column and obtain another key tableau. In some sense, key tableaux behave similarly to a strictly column-closed family of tableaux.
Example 16. Here we illustrate the sorting procedure described in Lemma 15. We start with the tableau T which is then augmented with negative integers. Removing the boxes with negative entries now yield a proper key tableaux with the same shape and basement as T .
Remark 17. Note that Lemma 15 does not generalize to arbitrary semi-standard augmented fillings. For example, it is impossible to remove the first column in Example 11 and reorder the entries in the remaining non-basement columns into a valid SSAF -the 1s always appear in some attacking configuration.
Key polynomial recurrence.
We are now ready to state one of the main result of this paper.
Theorem 18. The sequence of polynomials {K kα (x)} ∞ k=1 satisfy a linear recurrence with as characteristic polynomial, where the product is taken over all key tableaux of shape α such that columns of equal height have the same filling and multiple roots in the product are ignored.
Proof. This follows almost immediately from Proposition 6, except that ktab is not a strictly column-closed family. However, Lemma 15 implies that the tableaux that appear in the product Eq. (9), can be rearranged to key tableaux, while preserving the weight of the tableau.
The polytope side
In this section, we show that the integer point transform of polytopes with the integer decomposition property, (IDP), satisfy a linear recurrence. In particular, this can be used to give an alternate proof of Theorem 18.
An integral polytope is the convex hull of a finite set of integer points in R d . The k-dilation of a polytope P is defined as kP = {kx : x ∈ P} where k is a non-negative integer, and it is easy to see that this is an integral polytope if P is. Furthermore, a polytope P is said to have the integer decomposition property if for every integer k ≥ 1, every lattice point x ∈ kP ∩ Z d can be expressed as x = x 1 + · · · + x k with x i ∈ P. Note that only integral polytopes can have the integer decomposition property and that every face of a polytope with IDP is also a polytope with the IDP.
The following proposition shows that certain polynomials obtained from polytopes satisfies a linear recurrence. The argument is very similar to that in Lemma 3.
Proposition 19. Let P be an integrally closed polytope in R d and let p k (z) be the polynomial defined as Then the sequence p j (z) for j = 0, 1, . . . satisfies a linear recurrence with characteristic polynomial given by Proof. Since P has the IDP, one can easily show that every lattice point in kP can be expressed as a sum of a lattice point in (k − 1)P plus a lattice point in P. Therefore is a polynomial with only negative coefficients corresponding to points in kP that are expressible in more than one way as x + y with x in (k − 1)P ∩ Z d and y in P ∩ Z d . Hene is again a polynomial with positive coefficient corresponding to lattice points in kP expressible in at least three different ways. Repeating this argument using the principle of inclusion-exclusion then yield the desired formula.
The polynomial defined in Eq. (17) for k = 1 is commonly known as the integerpoint transform of P.
The intersection of two faces of a polytope is also a face (of possibly lower dimension) of the polytope. This enables us to generalize Proposition 19 slightly: Corollary 20. Let P be a polytope with the integer decomposition property and let F 1 , . . . , F l be faces of P. Define the sequence of polynomials Then the sequence p j (z) for j = 0, 1, . . . satisfies a linear recurrence with characteristic polynomial given by Proof. The integer point transform of each face F i satisfy a linear recurrence under dilation by k, and the polynomials in Eq. (18) can be expressed (via inclusionexclusion) as a linear combination of such integer point transforms of faces.
In [KST10], it was proven that key polynomials (Demazure characters) can be expressed as (a certain specialization of) the integer point transform of a union of faces of a Gelfand-Tsetlin polytope. Such polytopes are known to have the integer decomposition property, see e.g. [Ale14], so Corollary 20 implies a weaker version of Theorem 18. Note that the linear recurrences allow us to define K 0α (x) and it follows from the polyhedral complex interpretation that this always evaluates to 1 (there is exactly one lattice point in the union of faces with dilation 0, namely the origin). It would be interesting to see a direct proof of this fact without using the polytope interpretation.
After extensive computer experimentation, it is hard not to ask the following question: Question 21. Does the polynomial k → K kα (1 n ) always have non-negative coefficients?
The case when α is a partition corresponds to a Schur polynomial and it is known that where n is the number of variables. This gives a positive answer to the question in this case.
The operator side
Some families of polynomials, such as the Schubert and key polynomials can be defined via divided difference operators. Let s i denote the transposition (i, i + 1) and let such transpositions act on Z[x 1 , . . . , ] by permuting the indices of the variables. Define the divided difference operators Given a permutation ω ∈ S n , it can be expressed as a product of transpositions, ω = s i1 · · · s i l . When the length l is minimal, we say that i 1 i 2 . . . i l is a reduced word of ω. Then, let ∂ π = ∂ i1 · · · ∂ i l and π ω = π i1 · · · π i l . It can be shown that these operators does not depend on the choice of the reduced word.
The key polynomials may now be defined [RS95] as K α (x) = π u(α) x λ(α) , where λ(α) is the partition obtained by sorting the parts of α in decreasing order and u(α) is a permutation that sorts α into a partition shape. That this indeed is equivalent to the definition above was proved in [Mas09]. We will now give yet another proof that the key polynomials satisfy linear recurrences. First, note that x kλ is a geometric series as k = 0, 1, . . . and thus satisfy a linear recurrence with characteristic polynomial t − x λ . Now note that if {f k (x)} ∞ k=0 satisfy a linear recurrence, then so does The result is now a consequence of induction.
The Schubert polynomials, S ω (x), indexed by permutations in S n , are defined in a similar fashion, where ω 0 is the longest permutation in S n , namely (n, n − 1, . . . , 1) in one-line notation. Using a similar reasoning as for the key polynomials, one can produce sequences of Schubert polynomials that satisfies linear recurrences.
Appendix: Some families of column-closed fillings
In this section, we review some common families of column-closed fillings, related combinatorial statistics and generating functions over subsets of such families. Some statements here are well-known or very easy to show, so we present them without proof. Proposition 6 implies that all these polynomials we define below satisfy linear recurrences.
7.1. Flagged skew semi-standard Young tableaux. Let λ and µ be partitions with at most l parts, such that λ ⊇ µ. Let ssyt(λ/µ, n) be the set of fillings of D λ/µ with entries in [n], such that each row is weakly increasing and each column is strictly increasing. Then for every l and n, the families λ⊇µ ssyt(λ/µ, n) and λ ssyt(λ, n) are strictly column-closed families, where the unions are taken over shapes with at most l rows. On any filling T with entries in [n], we define the statistic w(T ) : T → N n such that if w(T ) = (w 1 , . . . , w n ), then w i is the number of boxes in T filled with i. It is evident that w is a linear statistic.
Finally, the skew Schur polynomials in n variables, indexed by skew partition shapes λ/µ, are defined as Even more general, let λ ⊇ µ be a shapes with at most l rows and let a and b be increasing sequences of integers of length l, such that a i ≤ b i for all i. Let ssyt(λ/µ, a, b, n) ⊆ ssyt(λ/µ, n) be the subset of fillings T , such that a i ≤ T (i, j) ≤ b i for every box (i, j) ∈ D λ/µ . Then for each n, λ⊇µ ssyt(λ/µ, a, b, n) is a strictly column-closed family, where the union is taken over all λ ⊇ µ with at most l rows. The row-flagged Schur polynomials, s λ/µ,a,b (x) in n variables are defined as s λ/µ,a,b (x) = T ∈ssyt(λ/µ,a,b,n) x w(T ) , see e.g. [Wac85] as a reference.
7.2. Symplectic fillings. The following definition is taken from [Kin76] and these polynomials are related to representations of Sp(2n). The symplectic Schur polynomials, sp λ (x), in the variables x ±1 1 , x ±1 2 , . . . , x ±1 n are defined via fillings of the Young diagram λ using the alphabet 1 < 1 < 2 < 2 < · · · < n < n such that rows are weakly increasing, columns are strictly increasing, and entries in row i are greater than or equal to i. Then, for a partition λ with at most n parts, where w(T ) is the weight only counting unbarred entries and w(T ) only counts the barred entries. It is quite clear that the symplectic Young tableaux form a strictly column-closed family, and that the statistics w and w are linear. Consequently, {sp kλ } ∞ k=1 satisfies a linear recurrence for every fixed partition λ.
7.3. Set-valued tableaux and reverse plane partitions. The Grothendieck polynomials 2 G λ (x) can be defined (see [Buc02]) as where the sum is taken over set-valued Young tableaux. These are defined as fillings of a diagram of shape λ, but now each box contains a set of natural numbers. For two such sets A, B we have A < B if max A < min B and similar for A ≤ B.
With this notation, svt(λ) is the set of all set-valued tableaux (subsets of [n]) such that rows are weakly increasing, and columns are strictly increasing. Here, the ith component of w(T ) is now the total number of sets where i appears, and |T | is the sum over all cardinalities of the sets in the boxes. Note that the lowest-degree part of G λ (x) is the usual Schur polynomial s λ (x).
There is also an operator definition of the more general Grothendieck polynomials which are indexed by permutations and similar to the Schubert polynomials and introduced by Lascoux and Schützenberger in 1982.
To show that G λ (x) satisfy a linear recurrence, one needs to use the more general version of Lemma 4, since the family of set-valued Young tableaux is not a weakly column-closed family; only columns where each set is a singleton can be duplicated. However, we note that the family is well-behaved and that every tableau T ∈ svt(kλ) contains duplicate columns for every k sufficiently large. These observations together with Lemma 4 allows us to deduce that the Grothendieck polynomials also satisfy a linear recurrence. We leave the details as an exercise to the reader. This can also be proved using the divided difference operator definition, similar to the Schubert polynomials.
Lam and Pylyavskyy [LP07] proved that the dual stable Grothendieck polynomials, g λ (x) in n variables can be defined as where rpp(λ) is the set of reverse plane partitions of shape λ, that is, fillings of λ with numbers in [n] such that rows and columns are weakly decreasing. The statistic ev(T ) i is the total number of columns where i appears. Evidently, ev is a linear statistic and reverse plane partitions is a well-behaved, strictly column-closed family of fillings. Consequently, we get a linear recurrence in this case.
A note on Jack and Macdonald polynomials.
A consequence of satisfying a linear recurrence, is that the sequence of polynomials must satisfy a linear recurrence under every specialization of the variables. In particular, if we pick a specialization such that all roots of the characteristic polynomial become equal to 1, then the resulting sequence is a polynomial. For example, k → K kα (1 n ) is a polynomial in k.
This observation allows us to deduce that the Jack polynomials J λ (x, a) do not satisfy a linear recurrence for general values of a, the sequences J kλ (1 n , a) are not of the form given in Eq. (5). This observation holds for both standard normalizations of Jack polynomials.
It follows that there are no linear recursions for Macdonald polynomials either, since the Jack polynomials are a specialization of the Macdonald polynomials. | 10,621.8 | 2015-05-11T00:00:00.000 | [
"Mathematics"
] |
Studies in Asian Nervilia ( Orchidaceae ) VII : Nervilia kasiensis , a new Lao endemic
You are free to share to copy, distribute and transmit the work, under the following conditions: Attribution: You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Non-commercial: You may not use this work for commercial purposes. No derivative works: You may not alter, transform, or build upon this work. For any reuse or distribution, you must make clear to others the license terms of this work, which can be found at http://creativecommons.org/licenses/by-nc-nd/3.0/legalcode. Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this license impairs or restricts the author’s moral rights. Blumea 62, 2017: 1–5 ISSN (Online) 2212-1676 www.ingentaconnect.com/content/nhn/blumea https://doi.org/10.3767/000651917X694732 RESEARCH ARTICLE
RESEARCH ARTICLE InTRoduCTIon
The Old World terrestrial orchid genus Nervilia continues to grow, with the addition of at least one new species per year for the last five years (Averyanov 2011a, Hsu et al. 2012, Jalal et al. 2012, Gale et al. 2013, 2014, 2015, 2016, Lin & Chang 2013, Lin 2014).All of these recent discoveries occur in tropical or subtropical Asia, and each is referable to one of a series of species complexes whose ecology and evolution remains only poorly understood.The few molecular and cytological studies carried out to date suggest that small morphological differences within these complexes -even between species inhabiting the same site -can mask significant genetic distances and variation in ploidy level (Gale et al. 2010, 2015, Eum et al. 2011).This suggests the occurrence of considerably more cryptic diversity than presently recognised.
In a cladistic analysis focusing on African members of the genus, Pettersson (1991) circumscribed an alliance of closely related one-flowered species unified by the combination of an elongating fruiting scape, a glabrous, angular leaf and a pubescent column, as epitomised by the African N. adolphi Schltr.and the Indonesian N. punctata (Blume) Makino.The concept of the so-called 'Nervilia adolphi/punctata species alliance' has since been further examined in Asia by Gale et al. (2013Gale et al. ( , 2015)), with the addition of a slender, entire and predominantly white labellum with violet markings as a typical character.The alliance accounts for at least 26 of the approximately 70 species presently accepted in the genus, with representatives distributed throughout most of the generic range, from sub-Saharan Africa, through tropical, subtropical and warm temperate Asia to the Southwest Pacific Islands.Most occur in deep shade as elements of the forest understorey (Gale et al. 2015).
As for the genus as a whole, members of the alliance exhibit a hysteranthous annual cycle in which the solitary scape emerges at the onset of the growing season, followed by the single, deciduous leaf once the flower has either withered or fructified (Pridgeon et al. 2005, Gale et al. 2006).This temporal separation of the flowering and leafing phases, as well as the seasonal dormancy that follows senescence of the leaf at the end of the annual growth cycle, has been interpreted as an adaptation to a strong wet /dry seasonality (Pettersson 1991), with the few recorded exceptions to this characteristic pattern tending to occur in moister habitats or regions with a less marked transition between dry and wet seasons.Thus overlapping reproductive and photosynthetic phases have been noted for N. punctata in lowland evergreen forest in Java (Backer & Bakhuizen van den Brink 1968), for N. borneense (J.J.Sm.)Schltr. in mossy montane forest in East Malaysia (S.Gale pers.observ., voucher: A. Lamb 2089/2011, SAN) and for N. muratana S.W.Gale & S.K.Wu in humid broadleaved forest in South China and northern Vietnam (Gale & Wu 2008, Averyanov 2011b); all three of these species belong to the N. adolphi/punctata alliance.
To date, only five species of Nervilia have been recorded from Laos (Schuiteman et al. 2008, Gale et al. 2016).Given that 11 species are known from Thailand (Gale & Watthana 2014, Gale et al. 2016) and eight are known from Vietnam (Averyanov & Averyanova 2003, Averyanov 2011a, b, Gale et al. 2016), this is likely to be an underestimate due in part to insufficient botanical exploration (Newman et al. 2007), as well as to the inconspicuous and ephemeral nature of the plants themselves (Gale et al. 2014) and the potential presence of cryptic taxa (Gale et al. 2015).During a recent survey of remnant primary forest fragments in the north of the country, the present authors discovered an unidentified member of the N. adolphi/ punctata alliance that was striking for its unusually large, faintly tessellated leaf.Subsequent analysis of plants that flowered in cultivation confirmed that they represent an undescribed species morphologically allied to N. muratana.Reinforcing this affiliation, seasonal dormancy was absent, with the leaf undergoing senescence only after emergence of the flower in the following growth cycle (Fig. 1b).
Key words
Hysteranthy Laos new species Orchidaceae species complex Abstract A new species belonging to the terrestrial orchid genus Nervilia is described from Kasi District, Vientiane Province, northern Laos.Referable to the widespread and species-rich N. adolphi/punctata alliance on account of its solitary flower, slender white and violet-marked labellum and glabrous, angular leaf, N. kasiensis is morphologically most closely allied to N. muratana of southern China and northern Vietnam.As in that species, the flowering and leafing phases overlap, an unusual feature among members of the genus.The new species can be distinguished from N. muratana by its shorter inflorescence, its weakly spreading perianth with beige sepals, its narrower labellum with a central pubescent strip on the epichile, its arched column, and by its faintly tessellated leaf.A morphological description, line drawing and notes on the species' ecology and conservation status are presented.
Published on 12 January 2017 dESCRIPTIon Nervilia kasiensis S.W. Gale & Phaxaysombath,2,3 This new species most closely resembles N. muratana S.W.Gale & S.K.Wu in the outline of its labellum, in the shape of its leaf and in its non-hysteranthous growth habit.However, N. kasiensis is distinguished from N. muratana by its much shorter inflorescence (up to 4.3 cm in the former vs 6.5 -10.0 cm in the latter), its weakly spreading perianth (vs widely spreading in the latter) with beige sepals (vs white in the latter), its narrower labellum (up to 6.4 mm wide in the former vs 9-12 mm wide in the latter) with a central pubescent strip on the epichile (vs shortly and sparsely hairy along the main veins in the latter), its arched column (vs straight in the latter), and by its tessellated leaf (vs uniformly dark green in the latter).Etymology.Named after Kasi District, northern Laos, in which this species was discovered.
Inflorescence emerging while the plant is in leaf, erect, terminal, warty at base near junction with subterranean stem, terete above, 2.5 -4.3 cm long to origin of floral bract, 2.0 -2.2 mm diam, olive green flushed brown, bearing 1 short papery sterile bract at base and 1 sheathing cataphyll above; cataphyll olive green flushed brown with irregular purple blotches, 1.8-2.8cm long, enclosing the base of the floral bract, apex acute; floral bract olive green with irregular purple blotches, narrowly elliptic, 4.8 -5.5 mm long, 1.4 -1.6 mm wide, exceeding the pedicel, apex acute.Flower solitary, resupinate, nodding, perianth not spreading widely; pedicel concealed within the base of the floral bract, up to 2.0 mm long; ovary narrowly conical, 4.9-5.2mm long, c. 2.5 mm diam, olive green with irregular purple blotches; sepals and petals similar, outer surfaces cream-beige with irregular pink-violet flecks, glossy white inside, narrowly elliptic-lanceolate, acuminate; dorsal sepal 22.4-26.8mm long, 3.5-4.2mm wide, 5-veined; lateral sepals slightly oblique, slightly inflated and slightly saccate at base, 21.8-24.6mm long, 2.8-3.5 mm wide, 3-veined; petals slightly oblique, 21.0 -23.5 mm long, 1.8 -2.8 mm wide, 3-veined; labellum white with irregular pink-violet flecks and blotches, not spurred but slightly concave at base, narrowly obovate-spathulate, 20.7-21.5 mm long, divided above the middle by a narrow waist into a hypochile and epichile; hypochile oblong, 11.2-12.0mm long, 3.5-4.2mm wide, lateral margins raised and embracing the column, terminating in a pair of short, ovate, obtuse auricles up to 0.4 mm long; epichile ovate-orbicular, 9.5-9.8mm long, 5.9-6.4mm wide, apex acute; disk bearing a central lanate band that divides in 2 below the auricles and then merges again at the base of the epichile to form a raised pubescent strip that terminates within 1.5 mm of the apex, shortly papillate elsewhere on the epichile.Column white, slender, clavate, arched towards the apex, 10.2 -11.5 mm long, with a patch of short hairs below the stigma; anther cap helmet-shaped, c. 1.8 mm long; pollinia enclosed behind the stigma, 2.6 -2.8 mm long; stigma shield-shaped, slightly concave; rostellum forming a prominent ridge along the apex of the stigma.Distribution -At present known only from the type collection, which comes from fragmented primary hill forest in northern Laos (Fig. 3).Its discovery in similar habitats elsewhere in Laos as well as in neighbouring parts of Thailand and Vietnam might be expected, although primary forest in the region continues to dwindle rapidly.
Ecology -Nervilia kasiensis is an understorey herb that grows in shade in deep organic soils in moist, evergreen hill forest over limestone at c. 750 m altitude.The flowering shoot emerges in March, while its tuber is still connected by a runner to the previous year's leafy shoot.The old leaf withers and a new leaf emerges from a separate runner after anthesis.Multiple runners are produced both from nodes of the tuber itself and from the subterranean stem of leafy shoots.The presence of a prominent rostellum at the apex of the stigma (Fig. 2h) suggests that N. kasiensis is outcrossing (cf.Gale 2007).
Conservation status -Only a small population of fewer than ten emergent shoots was found at the type locality.The availability of suitable habitat throughout the Khoun Lang Nature Reserve offers hope that more plants occur nearby.However, on-going destruction of primary moist broadleaved forest in northern Laos, as well as in neighbouring parts of Indochina, indicates that this apparently restricted and rare species is under considerable threat due to habitat loss.Pending surveys to better gauge its distribution and abundance, N. kasiensis is for now considered Data Deficient (DD; IUCN 2012).
Note -On account of its glabrous, angular leaf and the narrow, white and violet-marked labellum of its single flower, N. kasiensis is immediately recognisable as a member of the N. adolphi/punctata alliance.In addition to the characters noted in the diagnosis that differentiate it from N. muratana, its closest morphological ally, N. kasiensis is also distinguished by its relatively broader tepals as compared to those of that species.In its non-spreading perianth, the slightly concave base of its lip and the rounded hypochile auricles, N. kasiensis is also similar to N. alishanensis T.C.Hsu, S.W.Chung & C.M.Kuo, a species of Taiwan and Hainan Province in southeast China (Hsu et al. 2012, Gale et al. 2015).However, overall dimensions of the leaf and flower parts are otherwise markedly different, added to which N. alishanensis lacks a functional rostellum and is reported to be self-pollinating (Hsieh et al. 2013).
Fig. 1 Fig. 2
Fig. 1 Nervilia kasiensis S.W.Gale & Phaxaysombath.a. Plants in leaf at the type locality in northwest Laos showing the faint silver-grey mottling on the adaxial surface; b. plant in flower showing the non-hysteranthous growth habit; c. close-up of inflorescence; d. lateral view of flower showing slightly saccate base of the lateral sepals; e. front view of flower showing the weakly spreading perianth.
Fig. 3
Fig.3Primary, moist evergreen forest at the type locality in Kasi District, Vientiane Province, northwest Laos. | 2,671.2 | 2017-05-01T00:00:00.000 | [
"Biology"
] |
Ferronematics Based on Paramagnetic Nitroxide Radical Liquid Crystal
We have prepared novel ferronematics based on a paramagnetic liquid crystalline (LC) material. Our ferronematics can disperse a higher volume fraction of magnetic nanoparticles compared to classical ferronematics because paramagnetic nature of the host LC material prevents the aggregation of magnetic nanoparticles. The interactions between the magnetic nanoparticles and the LC material enhance a magnetic anisotropy of ferronematics and improve the magnetic responsivity.
Introduction
The orientational direction of liquid crystalline (LC) phases can be controlled by applying an external electric or magnetic field because of their anisotropic dielectric permittivity or magnetic susceptibility [1].Since a strong magnetic field (B~1 T) is required to realize the magnetic-field-induced OPEN ACCESS molecular reorientation, in practice most LC devices such as displays are driven by an electric field.This is because most LC materials have a small anisotropy of magnetic susceptibility (Δχ~10 −7 ) [2].However, the magnetic-field-induced molecular reorientation should be suitable for devices consisting of LC materials like ionic LC materials, to which the electric-field-induced molecular reorientation is not applicable [3].In actual use, the responsivity of LC materials to a magnetic field needs to be improved in some way.
In 1970, Brochard and de Gennes theoretically proposed the way to improve the magnetic responsivity of LC materials [4].They demonstrated that LC materials doped with magnetic particles at very low volume fractions could exhibit high responsivity to applied magnetic field; the composite systems are known as "ferronematics".The high responsivity induced by an orientational coupling between the magnetic particles and the LC director field gives possibilities of the magnetic field-driven LC devices.In 1983, Chen and Amer experimentally succeeded in the reorientation of ferronematics by a few milli-tesla of magnetic field [5].A number of ferronematics have been reported [6,7]; they exhibit the high magnetic responsivity [8] and unusual magnetic behaviors such as linear responses of birefringence [9] and capacitance [10] in a low magnetic field region (far below the Frederiks threshold).
In contrast to the previously reported ferronematics consisting of diamagnetic LC materials as the hosts, we see a great future for some ferronematics with paramagnetic liquid crystalline (PLC) hosts.This is because PLC hosts are expected to work as dispersion media for magnetic particles better than diamagnetic LC hosts and to exhibit the coupling between the magnetic moments of magnetic particles and paramagnetic susceptibility of PLC molecules.They are classified into two categories; the majority is metal-complex LC compounds containing paramagnetic transition or lanthanide metal ions [11,12], and the minority is all-organic radical LC compounds.Despite the existence of large magnetic anisotropy of the former metal-complexes, their high viscosity derived from the polar character frequently renders the magnetic-field-induced reorientation difficult.In contrast, the latter all-organic radical LC materials with the small magnetic anisotropy do not show such high viscosity.As one of the most stable all-organic radical PLC materials, a nitroxide radical LC compound 1 with an enantiotropic nematic phase has been reported to exhibit the magnetic-field-induced molecular reorientation in the nematic phase at below 1 T of magnetic field [3,13].If the magnetic responsivity is improved by doping magnetic particles, the all-organic radical LC materials would be more suitable for the hosts of ferronematics.Here, we demonstrate the preparation of the ferronematics consisting of Fe3O4 magnetic nanoparticles (MNPs) to the nematic phase of 1 and discuss the MNPs dispersibility and the magnetic-field-induced Frederiks transition of the new ferronematics.
Experimental
The studied ferronematics were based on the PLC material 1, which was prepared as the previous reported procedure [14].The chemical structure and phase transition temperatures of the thermotropic nematic compound 1 are shown in Figure 1.In spite of the existence of a radical moiety, 1 is thermally stable up to about 150 °C in air.The ferronematics were simply prepared by adding a toluene solution of Fe3O4 MNPs coated with oleic acid (Sigma Aldrich, St. Louis, MO, USA) to 1.Then, the mixture was left at the temperature of ~120 °C so that the solvent could evaporate and 1 would show an isotropic phase.The size and morphology of the MNPs were determined by TEM.They were almost spheres of mean diameter of ~20 nm.The MNPs in the prepared ferronematics have volume fractions ϕ = 0, 1 × 10 −5 , 1 × 10 −4 , 1 × 10 −3 , which are named 1, 2a, 2b and 2c, respectively.Phase transition temperatures of each sample were determined by differential scanning calorimetry (DSC) (SHIMADZU DSC-60) at a scan rate of 2 °C/min.The Frederiks thresholds were measured for 1 and 2a-c by a polarization-optics method.The ferronematics were introduced by capillary action into about 10 μm thick (D) handmade sandwich cells (7.5 mm × 10 mm) in which the inner surfaces of the two glass substrates were coated with polyimide (AL1254, JSR, Tokyo, Japan).The polyimide surfaces in the cell were rubbed horizontally 10 times using a velvet roller before bonded together.The magneto-optical measurements were performed at the temperature of 80 °C (far below the magnetic transition temperature of MNPs [15]) with our experimental setup shown in Figure 2. The easy axis of molecular direction n and the analyzer direction were parallel to each other, and a magnetic field B perpendicular to n and parallel to the cell plane was applied.To discuss the molecular reorientation induced by the magnetic field B, we monitored the intensity of transmitted light of laser beam with wavelength of 532 nm.
Results and Discussion
We carried out simple tests of the dispersibility of MNPs into LC matrices with the use of optical transmission microscopy at the temperature where samples exhibits the isotropic phase.We compared the size of aggregates in PLC material 1 with that in a conventional diamagnetic LC material 4-cyano-4′-heptyloxybiphenyl (7OCB) doped with the same MNPs (ϕ = 1 × 10 −3 ).A lot of large aggregates were observed in 7OCB as shown in Figure 3a.In contrast, such phenomena were suppressed in our ferronematics based on 1 as shown in Figure 3b.The aggregation of MNPs tends to be promoted in LC phases and they do not disperse again even if the temperature is elevated up to ~120 °C where they exhibit isotropic phase.This difference of the dispersibility can be attributed to the magnetism of each LC material.On the one hand, diamagnetic LC molecules are repelled by MNPs; on the other hand, PLC molecules are attracted by the same MNPs.In fact, the droplets made of PLC material 1 floating on hot water are attracted by a magnet [16].Therefore, PLC material 1 is desirable as a host material of ferronematics.In a certain diamagnetic nematic material MLC-6609 (Merck, Darmstadt, Germany) doped with ferroelectric BaTiO3 nanoparticles, the nanoparticles induce the increase of the orientational order parameter resulting in 9 °C rise of nematic-isotropic phase transition temperature, TNI [17,18].Since the similar effect might occur for our ferronematics due to the magnetic moments of MNPs and paramagnetic susceptibility of the PLC molecules, we measured TNIs of the samples 1 and 2a-c by DSC analysis.As a result, the more concentrated the MNPs become, the lower the phase transition temperature becomes as shown in Table 1.Therefore, above-mentioned increase of orientational order leading to the rise of TNI was not observed in our ferronematics.Thus, these results suggest that the orientational order is not induced by MNPs or the effect is too small to observe and the impurity effect of the MNPs to disturb the orientational order is dominant.In particular, the depression of TNI obviously appears in 2c with the highest volume fraction of MNPs.This result indicates that the molecular alignment of 2c is somewhat disturbed by the doped MNPs especially nearby TNI.Molecules in the LC cell started to align along B as shown in Figure 4 at a certain critical value of the magnetic field, Frederiks threshold BC, which can be described for undoped nematic LC cell as [2]: where μ0 is magnetic permeability and K2 is LC twist elastic constant.The magnetic-field-induced molecular reorientation of LC materials is mainly caused by Δχ, which is the sum of the paramagnetic component (Δχpara) and the diamagnetic one (Δχdia) for PLC materials unlike the conventional diamagnetic LC materials.This twist deformation of molecular orientation caused an increase of transmitted light intensity under crossed nicols.The relative intensity I/I0 for the samples 1 and 2a-c is plotted as a function of the magnetic field B in Figure 5, where I0 is transmitted light intensity measured under parallel nicols.For the undoped sample 1, the molecular reorientation started at about 0.8 T. Due to doping MNPs, magnetic responsivity of the PLC material was enhanced; the Frederiks threshold decreased, or the larger orientational deformation was induced at the same magnetic field.These ferronematics showed the same order of magnitude of the magnetic responsivity compared to the classical ferronematics.It is because Δχpara hardly affects the magnetic responsivity because Δχ dia ≫ Δχ para (Δχ dia = 6.5 × 10 −5 emu• mol −1 and Δχ para = −1.7 × 10 −6 emu• mol −1 at 300 K [3]).The free energy density for the ferronematics with respect to the elastic deformation is written as [19,20]: where n is the nematic director, v is the particle volume, m is the magnetic director of MNP, K1 and K3 are the LC splay and bend elastic constants, MS is the MNP magnetization and W is the coupling energy density between the MNP and the LC orientation.Equation (2) represents the nematic director field interacts with the magnetic moments of MNPs under applied magnetic field.The first three terms represent the usual Frank energy density of the elastic deformations of the nematic director field, the fourth term is the magnetic energy of the nematic director field.The last three terms are specific to ferronematics: the contribution of the mixing entropy of their ideal solution, the magnetic energy of the MNPs and the coupling energy between the MNPs and the nematic director.Since the measurements were carried out at the same temperature far below the TNIs, the change of orientational scalar order parameter S induced by doping MNPs and temperature dependence on interactions between MNPs and LC host are ignorable.Since the effects of the last three terms of Equation ( 2) derived from the doping MNPs influence the Frederiks threshold BC of Equation ( 1), they are combined into Δχ causing the Frederiks transition as: where θ only contains the magnetic effects derived from doping MNPs.Namely, the coupling between MNPs and nematic director induced by the applied magnetic field increases θ and enhances the effective magnetic anisotropy.Then, adding the contribution of θ into Equation (1), Frederiks threshold decreases.Assuming that D and K2 are constant, θ(ϕ) is derived from Equations ( 1) and (3) as: where C (ϕ) is defined as the magnetic field when we observed I/I0 = 0.01.Using Equation (4), we calculated θ(ϕ) from C (0) and C (ϕ).As shown in Figure 6, the interactions between the MNPs and the nematic director increase as a function of ϕ.In a small ϕ region, MNPs doping effects are drastically large.The addition of MNPs into the PLC material results in 1.8-fold enhancement of the magnetic responsivity of the PLC material.
Conclusions
We have fabricated novel ferronematics based on the PLC material 1.The aggregation of MNPs is reduced by the paramagnetic nature of 1. Similar to classical ferronematics based on the diamagnetic LC materials, the response to applied magnetic field can be enhanced by doping MNPs.MNPs interact with the nematic orientational order and increase the magnetic anisotropy Δχ of PLC material, which causes the decrease of the Frederiks threshold.Furthermore, if the paramagnetic anisotropy Δχpara is increased or the LC elastic constants are decreased by molecular modification and more anisotropically shaped MNPs are doped into PLC hosts with larger paramagnetic susceptibility χpara, the ferronematics based on PLC materials would be more useful than the conventional ferronematics based on a diamagnetic one.
Figure 1 .
Figure 1.Chemical structure of one of the enantiomers of 1 (2S, 5S) and phase transition temperatures (°C) of racemic 1.The temperatures were determined by differential scanning calorimetry (DSC) upon heating.Standard notation gives the transition temperatures between the crystalline (Cr), nematic (N) and isotropic (Iso) phases.
Figure 2 .
Figure 2. (a) Experimental setup for magneto-optical measurements; (b) Top view of the liquid crystalline (LC) cell in the initial state.
Figure 4 .Figure 5 .
Figure 4. Schematic illustration of twist deformation of molecular alignments induced by applied magnetic field.Molecules in closer to the center reorient along to magnetic field. | 2,857.4 | 2015-04-27T00:00:00.000 | [
"Chemistry",
"Materials Science",
"Physics"
] |
Exact black holes in string-inspired Euler-Heisenberg theory
We consider higher-order derivative gauge field corrections that arise in the fundamental context of dimensional reduction of String Theory and Lovelock-inspired gravities and obtain an exact and asymptotically flat black-hole solution, in the presence of non-trivial dilaton configurations. Specifically, by considering the gravitational theory of Euler-Heisenberg non-linear electrodynamics coupled to a dilaton field with specific coupling functions, we perform an extensive analysis of the characteristics of the black hole, including its geodesics for massive particles, the energy conditions, thermodynamical and stability analysis. The inclusion of a dilaton scalar potential in the action can also give rise to asymptotically (A)dS spacetimes and an effective cosmological constant. Moreover, we find that the black hole can be thermodynamically favored when compared to the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole for those parameters of the model that lead to a larger black-hole horizon for the same mass. Finally, it is observed that the energy conditions of the obtained black hole are indeed satisfied, further validating the robustness of the solution within the theoretical framework, but also implying that this self-gravitating dilaton-non-linear-electrodynamics system constitutes another explicit example of bypassing modern versions of the no-hair theorem without any violation of the energy conditions.
I. INTRODUCTION
In the pursuit of a comprehensive understanding of gravitational phenomena in the cosmos as well as gravity itself, the theoretical examination of black holes stands as an essential frontier.The General theory of Relativity (GR), while highly successful in describing the macroscopic behavior of these celestial entities, becomes subject to scrutiny under extreme conditions.This investigation prompts the exploration of modified gravitational theories and theories with extra dimensions.Among the theories attempting to unify fundamental interactions, String Theory stands as the leading contender.In particular, the heterotic string theory stands as an essential branch within the broader scope of String Theory, distinguished by its capability to unify gravitational interactions with other fundamental forces.Notably, it excels in synthesizing these interactions into a cohesive framework.A focal point of interest lies in the derivation of an effective four-dimensional theory, offering insights into quantum corrections that modify Einstein's theory of gravity.These corrections can potentially incorporate terms ranging from the Gauss-Bonnet, quadratic-curvature term [1][2][3][4] to non-linear electromagnetic corrections (see e.g.[5][6][7][8] and references within).
Drawing therefore inspiration only from the aforementioned corrections introduced by string/brane theory, in this article, we aim to elucidate the implications of departing from the conventional electromagnetic framework and embracing the intricacies of non-linear electrodynamics (NED) and scalar fields within the context of black hole solutions.In addition to the above, it is important to mention that four-dimensional scalar-vector-tensor theories can be also obtained via an appropriate reduction from a higher-dimensional Lovelock theory [9].Under this perspective, scalar-tensor-vector theories can be understood as natural extensions of the scalar-tensor theories that have been extensively studied in the last decades [4,.Such scalar-vectortensor theories offer a very fruitful framework for finding novel compact-object solutions, eluding the constraints imposed by the "no-hair" theorems .This departure from traditional limitations is attributed to the dilaton field, which, notably, introduces no additional independent free parameter into the resulting solution [85].Instead, these solutions manifest a distinct feature known as "secondary hair", intricately determined by the compact object's mass, charge, and angular momentum.
Despite the motivation coming from higher-dimensional theories, there are also additional reasons that lead us to explore nonlinear electrodynamics.First and foremost, in regions with strong gravitational fields, such as those near black holes, traditional linear theories may break down.Non-linear electrodynamics becomes important in these strong field regimes, where the intensity of electromagnetic fields can become comparable to the strength of gravitational fields.Studying how non-linearities affect the behavior of electromagnetic fields in these regimes is crucial for understanding the physics of objects like black holes, neutron stars, and other astrophysical phenomena.Moreover, non-linear electrodynamics is expected to lead to phenomena that are absent in linear theories.In the early universe for example, when energy densities were extremely high, the interplay between gravitational and electromagnetic fields was significant.NED can be crucial in modeling the behavior of these fields during cosmological evolution.Consequently, NED allows us to investigate how electromagnetic interactions influenced the dynamics of the early universe and whether non-linear effects played a role in the formation of cosmic structures.Understanding these cosmological implications helps build a more complete picture of the evolution of the universe.For a review on non-linear electrodynamics and its applications, see [86] and references therein.
In this paper, we embark on a comprehensive exploration of a gravitational theory extending the classical Euler-Heisenberg (EH) electrodynamics coupled to a non-trivial dilaton field.Our motivation for this study stems from the rich theoretical landscape it promises, building upon the established framework of self-gravitating dilaton-linear-electrodynamics.This extension allows us to delve into intriguing phenomena, notably exemplified by the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole [87,88], a significant exact solution within this domain.In our investigation, we examine the intricacies of our proposed model and unravel its associated black-hole solution in detail.One of our key insights lies in the strategic assumption of a specific profile governing the dilaton coupling to the Euler-Heisenberg terms.This choice results in an exact analytic black-hole solution, facilitating a straightforward examination of its physical characteristics.
Having the solution at hand, we then commence a rigorous analysis encompassing various facets of our model's implications.This includes a thorough examination of the geodesics of massive test particles within the black-hole spacetime, followed by a meticulous scrutiny of the energy conditions.Subsequently, we delve into the thermodynamic aspects of the black hole, computing the relevant thermodynamic quantities, such as the temperature, the entropy, and the magnetic potential (Φ m ), to demonstrate the validity of the first law of thermodynamics.Moreover, within the parameter space of solutions, we unveil the existence of pairs consisting of two distinct black holes characterized by different ratios Q m /M , both more compact than the Schwarzschild solution yet sharing identical horizon radii.Intriguingly, despite their geometric similarity, a thermodynamic analysis reveals clear distinctions, with one black hole exhibiting thermodynamic stability while its doppelgänger proves to be thermodynamically unstable.Additionally, we explore the radial stability of the black-hole solution under linear perturbations and also its scalar quasi-normal modes, shedding light on its potential as an astrophysical entity.Furthermore, we extend our discussions to encompass other solutions and extensions of our model theory, including asymptotically (Anti-)de Sitter (AdS) spacetimes and more general dilaton couplings, providing a comprehensive overview of the theoretical landscape.In conclusion, our work offers a thorough investigation into the gravitational theory of non-linear EH electrodynamics coupled to a non-trivial dilaton field, unraveling a plethora of intriguing phenomena and paving the way for further exploration and theoretical advancements in this domain.
The structure of the current article is the following: In the next section II we motivate our study by discussing a gravita-tional theory of non-linear Euler-Heisenberg (EH) electrodynamics coupled to a non-trivial dilaton field.This generalises the corresponding self-gravitating dilaton-linear-electrodynamics case, known to admit the GMGHS black hole [87,88] as an exact solution.In the subsequent section III, we discuss our model and its associated black hole solution.By assuming a specific profile for the dilaton coupling to the EH terms, in such a way that, additionally to non-trivial dilaton couplings, one has also dilaton-independent EH terms, we demonstrate the possibility of studying analytically the corresponding black-hole solution.In section IV we first discuss the geodesics of test particles in such black hole spacetimes, and then demonstrate the satisfaction of the energy conditions for appropriate sets of the parameters of the solution.In section V, we study the thermodynamics of the black hole, and show explicitly, by computing the relevant thermodynamical quantities, that the first law of thermodynamics is satisfied in a coordinate-independent way, as should have been expected.In the parameter space of solutions, it is possible to obtain two distinct black holes with different ratios Q m /M that are more compact than the Schwarzschild solution and share the same horizon radius.However, these black holes even though they have the same horizon radius, from a thermodynamic point of view, are quite distinguishable, since the solution with a greater value for the ratio Q m /M is thermodynamically stable, while its doppelgänger with a lower value for the ratio Q m /M is thermodynamically unstable.In section VI, we demonstrate the radial stability of the black-hole solution under linear perturbations, and study its scalar quasi-normal models, which provide insights into its properties as a potential astrophysical object.Other solutions of (extensions of) our model theory (3.1), including asymptotically (Anti-)de Sitter (AdS) spacetimes, as well as solutions corresponding to more general couplings exp(−2γϕ), of the dilaton to the Maxwell term in the action, rather than the γ = 1 in closed strings, are discussed in section VII.Finally, conclusions and outlook are given in section VIII.
II. STRING INSPIRED NON-LINEAR ELECTRODYNAMICS
One of the particular aspects of string/brane-induced non-linear electrodynamics effects is that the higher order in the Maxwell tensor can be combined into an all-order expression, the so-called Born-Infeld (BI) Lagrangian [89][90][91][92][93][94], as a result of resummation of open string excitations (attached to, e.g., 3-brane worlds in the D-brane extension of string theory, in which case the world-volume of (d = 3)-brane leads to the DiracBI (DBI) action (see [95][96][97] and references therein).In such models, the BI electrodynamics in four spacetime dimensions originates from the higher (d = 10)-dimensional superstring action upon either compactification or appropriate restriction on a 3d-brane volume.It is important to note that in all such string-inspired models the BI Lagrangian couples to the inverse of the open-string coupling g s = e ϕ , where ϕ is the (dimensionless) dilaton field, so the corresponding four-dimensional action in a curved four-dimensional background metric (in the Jordan or σ-model frame), g J µν , reads where F µν is the Maxwell tensor the Regge slope (M s the string mass scale, which in general is different from the four-dimensional Planck scale).One may go away from string/brane theory and define the BI action as a starting point of an effective modified electrodynamics field theory.In such a case the string tension T 4 may be considered as an arbitrary phenomenological dimensionful parameter which is not related to the Regge slope α ′ .We term such a parameter the BI parameter.
We next remark that, in four spacetime dimensions, the determinant in the argument of the square root in the BI action (2.1) can be expanded exactly to yield: where F µν = 1 2 ε µνρσ F ρσ is the dual of the Maxwell tensor, with ε µνρσ the Levi-Civita fully antisymmetric symbol in curved spacetime with metric g J µν .Expanding the (square root in the) four-dimensional BI action (2.2) in inverse powers of the BI parameter T 4 , leads to effective dimension 8 (and higher) operators in the effective field theory, which make contact with the generic Euler-Heisenberg (EH) non-linear electrodynamics (NED) [94,98,99]: Hence, ignoring for the moment the dilaton, to fourth order in the field strength F µν one obtains (up to the dilaton factors) a special case of the generic EH NED with dimension 8 operators, with Lagrangian: where the BI Lagrangian corresponds to [98,99] (2.5) The reader should notice that the ratio of c 2 /c 1 = −4 exactly, which is a characteristic prediction of the BI theory.Phenomenologically, assuming a constant dilaton and flat Minkowski spacetime, the BI parameter T 2 4 can be constrained in collider physics, via light-by-light scattering, for which there is clear experimental evidence these days at LHC experiments (see [100][101][102]).Such light-by-light scattering studies [98] can place a lower bound on the BI parameter T 4 ≳ 100 GeV.In the case of string theory, this would lead to a (weak) lower bound of the string mass scale M s ≳ 0.25 TeV.Notably, extra dimension collider (LHC) searches place currently this bound to M s ≳ O(10) TeV.Forecasts for much larger values of the lower bounds of the BI parameter in future colliders, in particular FCC, have been given in [99].Embedding the BI (or more generally Euler-Heisenberg) theory into curved spacetime, and fully incorporating the dilaton effects, leads to a whole new area of tests of NED by employing the entire machinery of modern gravitational experiments technology.
The BI action S BI (2.1) and (2.2) in curved background metrics can be augmented, at an effective field theory level, by including the dynamics of the gravitational (g J µν ) and dilaton (ϕ) fields.In this respect, we recall that the D-brane action is by construction in the so-called Jordan (or σ-model) frame.Passing into the Einstein frame in four dimensions, via the transformation of the metric: g J µν → g µν = e −2ϕ g J µν , we write for the pertinent gravitational action (in geometrized units c = G = 1, in which we work from now on): where the quantities I E i , i = 2, 4 are given by the corresponding ones in (2.3), but the indices contraction is made by the Einstein-frame metric g µν .
Departing from the case of the brane DBI action (2.1), one may consider higher-order (in derivatives, that is in a Regge slope α ′ expression) electromagnetic terms in effective low energy field theories stemming only from closed strings, e.g. the heterotic string [1].In such theories, unlike the DBI brane or open-string case, there is no resummation in closed form of the gauge terms.Nonetheless, some authors have generalised the BI effective action in a curved (3 + 1)-dimensional spacetime, by considering the following form of dilaton couplings to the electromagnetic fields in a BI NED setting [103][104][105]: where the notation has been defined above, γ defines the dilaton coupling, and now β BI plays the role of the generalised BI parameter, with mass dimensions +2 (which is identified with T 2 4 in the case of strings, in which case, to match with the corresponding O(α ′ ) Maxwell terms of the heterotic-string effective action [1], e −2ϕ F 2 , one should fix γ = 1).
The above considerations deal with tree-level in string loops, that is first quantised actions on world-sheet with trivial topology (2d sphere for closed string sectors, and disc for open one).In general, string loop effective actions are not known in closed form.In simplified phenomenological scenarios such effective actions can be expressed in the generic form, e.g. in the closed string sector in the string (or σ-model frame with metric g µν in (3 + 1)-dimensions, after string compactification) [106]: where the (...) symbol above a tensorial quantity implies contraction of the world-indices with the string-frame metric g µν , F µν denotes the field strength of the gauge field, D µ is the gauge covariant derivative, ψ are fermionic matter fields and the . . .denote other matter fields as well as (an infinity of) higher-derivative (higher order in α ′ ) terms, The quantities B i (Φ), i = g, Φ, F, ψ are non-derivative functions of the dilaton which arise from summing over (closed) world-sheet topologies, that is these functions involve powers of the string coupling g s = exp(Φ) of the form g −χ s , where χ = 2−2N where N denotes the number of handles, is the genus of the world-sheet surface (sphere has N = 0, torus (one string loop) = 0 etc.Thus, where the constant quantities c i pertain to effects of string loops, so that the expressions (2.9) involve a power series in the square of the string coupling g 2 s = exp(2Φ).The first term on the right-hand side of (2.9) leads to the standard closed string expression for the gauge field Maxwell terms in the low-energy effective action, e −2ϕ F 2 for standard dilaton kinetic term normalization in the Einstein frame [1][2][3]). 1 Passing to the Einstein frame, via appropriate redefinitions of [106]: the metric g µν → g µν = C B g (Φ) g µν , where C are numerical normalization constants, the dilaton Φ → ϕ = dΦ 3 4 , where the prime denotes d/dΦ, and the fermionic matter fields, ψ → ψ = C −3/4 B −3/4 g B 1/2 ψ ψ, leaving the gauge fields as they are, yields the effective action: where the reader should notice the potential existence (depending on the specific type of string theory considered) of constant (dilaton-independent) terms involving F 2 terms (cf. the c (F ) 0 terms on the right-hand side of (2.9)).In case we consider more general theories involving a combination of closed and open strings (the latter attached, e.g. to brane universe)s, for which one obtains effective actions in the Einstein frame that include both closed-and open-string sectors (the latter leading to DBI terms of the form appearing in the second integral on the right-hand side of (2.6)), then, the inclusion of string loops can lead, following similar arguments to the closed-string case (2.10), to generalised situations, in which the (string-loop corrected) effective action acquires the form in the Einstein frame [107] where the functions B F i (ϕ), i = 2, 4 admit a power series expansion in the string coupling, summing up terms of the generic form where χ = 2 − 2N − N H , with N H the number of holes (or boundaries) (eg disc has genus χ = 1, since N = 0, N H = 1 etc), where finite parts of dilaton tadpoles contribute to the coefficients c . In heterotic strings, which do not involve branes, the higher derivative EH electrodynamics terms do not appear in a closed BDI form.In that case a more general action, involving EH terms, after summation over string loops, might then be considered, in the Einstein frame: where the ellipsis (. . . ) includes possible string-loop generated dilaton-potential terms, whose precise form is not known at present, as this is a highly string-model-dependent issue, and the functions B F 2 (ϕ), B F 4 (ϕ) in this case are given by power series expansions of even powers of the string coupling, of the form (2.9), as only closed world-sheet surfaces are involved.The Euler-Heisenberg Lagrangian L EH is given by (2.4), but the coefficients c i , i = 1, 2 no longer satisfy (2.5), given that the DBI action no longer describes the electromagnetic self-interactions in closed form.In this work we shall use the framework (2.14) to discuss black hole solutions in a phenomenological manner, keeping the coefficients c i of the EH Lagrangian as arbitrary.As already mentioned, in such a framework, for some sufficiently high string-loop order one can conjecture that there would exist a dilaton independent term in the function B F 4 (ϕ).As we shall discuss in the next section, such a constant term plays a crucial rôle in our phenomenological analysis in this paper in yielding analytic black hole solutions of a dilaton-EH theory that could be the low energy limit of an appropriate underlying string theory.However in our work, we shall be more general, and our analysis will be presented independent of strings. 1 We note for completion that a similar factor accompanies the quadratic gravitational curvature (Gauss-Bonnet (GB)) terms in the action at string-loop tree level.This is a remnant of the corresponding situation of the ten-dimensional target-spacetime heterotic-string effective field theory action, which in the extra (compact) dimensional sector leads to the celebrated anomaly cancellation by equating the extra-dimensional (non-Abelian) gauge with the corresponding quadratic-curvature gravitational GB terms d 6 x −G (6) e −2Φ TrF 2 − R 2 GB → 0 (with the Tr being a group-index trace), which leads to the Heterotic string selecting the E 8 × E 8 gauge group as the unique target-space group before compactification to (3+1)-dimensions [2,3]. 2 Indeed, if only Abelian gauge fields are considered then only open world-sheet surfaces are taken into account, in order to evaluate the pertinent contribution to the effective action, as discussed explicitly in [107] where it was shown that the loop corrected effective action acquires the form in the sigma-model frame (ignoring antisymmetric tensor fields contributions, which are of no interest in the present discussion): where d i , i = 1, 2, . . ., denote finite parts of the dilaton tadpoles, and the dots denote contributions from higher derivative corrections, as well as higher string loops (that is higher powers of the string coupling gs = exp(ϕ).Passing onto the appropriate Einstein frame leads to actions of the form (2.12).
III. THEORETICAL FRAMEWORK AND BLACK-HOLE SOLUTIONS
In the geometrised unit system (c = G = 1), the Einstein-frame action functional that we will occupy us in this article is a simplified version of (2.14) and reads Such a field theoretic gravitational actions also arises as part of a non-diagonal reduction of the Gauss-Bonnet action [9] and admits the GMGHS black hole [87,88] as an exact solution when f (ϕ) = 0.
is the usual Faraday scalar, and F4 ≡ F µν F µν F αβ F αβ , where F µν stands for the usual field strength F µν = ∂ µ A ν − ∂ ν A µ and α, β are coupling constants of the theory, with dimensions (length) 2 , which in our discussion are treated phenomenologically.The scalar field ϕ and the associated scalar function f (ϕ) are both dimensionless. 3For the moment we do not consider a potential for the dilaton, but only its non-linear interactions with the EH terms.The addition of a pure dilaton potential V(ϕ) can lead to interesting alternative solutions, including a cosmological constant, which we discuss in section VII.
The field equations emanating from (3.1) are of the following form By taking into account the higher-order electromagnetic invariants F 4 and F α β F β γ F γ δ F δ α , we are interested in extending the GMGHS solution [87,88].To do so, we introduce the most general spherically symmetric metric ansatz in the form where B(r), R(r) are two unknown functions to be determined from the field equations, while dΩ 2 = dθ 2 + sin 2 θ dφ 2 . 4 Moreover, we consider both electric and magnetic charges, via the following four-vector, which is compatible with spherical symmetry, where Q m stands for the magnetic charge carried by the black hole.This ansatz for the electromagnetic field solves by construction the φ component of the Maxwell equations iff one considers that the scalar field inherits the spacetime symmetries, namely ϕ ≡ ϕ(r).Interestingly, one can see that the combination will vanish if one does not consider both electric and magnetic configurations in the case of α = β.In the above, prime denotes derivation with respect to r. Maxwell's equation is very difficult to be integrated for the dyonic case and as a result we will consider pure magnetic fields, that is V (r) = 0. Consequently, both these non-linear electrodynamics terms will contribute iff α ̸ = β.We will begin our analysis for the scalar free scenario ϕ = 0, f (ϕ = 0) = 1, for which the solution reads and R(r) = r.This solution resembles the Einstein-Euler-Heisenberg black hole [108].The interesting thing to notice in (3.8) is that the non-linear electromagnetic terms F α β F β γ F γ δ F δ α and F 4 affect the spacetime geometry in a similar way.It is solely the values of the coupling constants α and β that determine whether this contribution survives or not.Note that in the case of α = β the higher-order electromagnetic term does not contribute at all.However, in the case where α ̸ = β, we notice that depending on the signs of the parameters α and β, the non-linear electromagnetic terms can act either attractively or repulsively.Black holes with a scalar hair in the Euler-Heisenberg theory have been discussed in [67], and it was found that the scalar hair results in a more compact black hole (having a smaller radius for the event horizon) when compared to the non-hairy Einstein-Euler-Heisenberg black hole.
Let us now assume a non-trivial profile for the coupling function f (ϕ).In particular, we consider Notice here that the coupling function f (ϕ) contains the dilatonic coupling e 2ξϕ with ξ = ±1 as well as a constant (dilaton independent) term.At this point the reader is invited, for completion, to compare such couplings with the string-loop corrected coupling functions B F 4 (ϕ), in the framework of string-inspired models (2.14), discussed in the previous section II.In such a stringy context, the exponential dilaton terms in the coupling function (3.9) can be written as f (ϕ where g s = exp(ϕ) is the string coupling.As discussed in section II, the g −2 s is the standard tree-level dilaton-Maxwell term coupling [1][2][3], while the g 2 s indicates two-string-loop corrections (genus-χ = 2 world-sheet surfaces).The crucial, for our subsequent discussion, dilaton-independent term in f (ϕ) might be the result of appropriate combinations of higher-string-loop corrections in the Einstein-frame effective action.
It is now straightforward to solve the field equations of (3.1), with (3.9), in order to determine the geometry of the spacetime and the functional expression for the scalar field.By doing so, one obtains a simple exact, magnetically charged black-hole solution, for which it holds that We observe that in this case, for α = β we obtain the GHS solution [88], while the radial coordinate r ∈ (Q 2 m /M, +∞) in order to have R ∈ (0, +∞).In this case, it is also intriguing to observe that the sign of the combination α − β among the coupling constants determines whether the higher-order electromagnetic terms in the theory will contribute attractively or not.
To obtain a better understanding of the spacetime geometry, one may express the line element (3.5) in terms of the physical coordinate system with R playing the role of the radial coordinate.By doing so, one finds that with functions B(R), W (R), and ϕ(R) being given by In the physical coordinate system (t, R, θ, φ), one can verify that the curvature invariant quantities R, R µν R µν , and R αβγδ R αβγδ possess a single spacetime singularity residing at R = 0, while the function B(R) satisfies the following expansions (3.17 All parameters are dimensionless, and the horizontal axis in both figures is logarithmic. From (3.16), it becomes apparent that the spacetime (3.12) is practically indistinguishable from that of a magnetically charged Reissner-Nordström black hole for an observer at infinity, with the parameter M corresponding to the ADM mass of the solution.
However, an observer much closer to the black hole (3.12) would perceive a completely different picture.Indeed these quantumgravity corrections are important near the singularity, since the geometry there is determined by their behavior.The radial null-trajectories for the spacetime (3.12), lead to the relation which by its turn means that the roots of the function B(R h ) correspond to black-hole horizons.In Fig. 1, one can observe the behavior of the metric function B(R) in terms of the dimensionless quantity R/(2M ).We see that the solution (3.12) describes a black hole with a single horizon when (α − β)/M 2 = 1, while for (α − β)/M 2 = −1 the black-hole horizons can range from two to none.It is essential to note that the previous assertion holds in general for (α − β)/M 2 being either greater or lower than zero.Analysis of Fig. 1a reveals that a positive value for the combination (α − β)/M 2 results in black-hole solutions featuring a single horizon.To facilitate comparison, we have also included the Schwarzschild solution which can be obtained by simply setting Q m = 0.One can readily observe that within our theory's solution spectrum, black holes can exhibit either greater compactness or sparsity relative to the Schwarzschild solution.In astrophysical scenarios where Q m is relatively small compared to the mass, our solution appears more compact.Conversely, when the fraction (α − β)/M 2 takes a negative value, the solutions range from black holes with two horizons to naked singularities.The transition from one class of solutions to the other occurs continuously as the magnetic charge Q m increases, as depicted in Fig. 1b.Consequently, in this scenario, there always exists a specific value for the ratio Q m /M that renders the black hole extremal, meaning the inner and outer horizons coincide.
It is crucial to highlight here the intriguing behavior observed in the realm of single-horizon black-hole solutions, for which α − β > 0. Specifically, there exists a minimum value for the ratio R h /(2M ), which is below unity, resulting in more compact black holes compared to the Schwarzschild solution.Starting from Q m = 0 (Schwarzschild) and increasing the magnetic charge, the resulting black holes become progressively more compact until reaching the point where R h /(2M ) attains its minimum value.Beyond this point, further increase in the ratio Q m /M causes R h /(2M ) to rise again, eventually reaching R h /(2M ) = 1, albeit now with Q m ̸ = 0. Subsequently, any additional increase in the ratio Q m /M yields a solution more sparse than the Schwarzschild counterpart.This particular behavior is elucidated by analyzing Fig. 2, where the relationship between the ratio of the black hole horizon (R h ) to twice the black hole mass (2M ) and the ratio Q m /M is depicted for various values of the dimensionless parameters (α − β)/M 2 .Conversely, it is observed that when α − β < 0, the outer horizon radius of the resulting black holes is consistently smaller than that of the corresponding Schwarzschild black hole with the same mass.Furthermore, it is important to note that in this scenario, the graph reaches a termination point.This occurs because, beyond a certain threshold of the ratio Q m /M (which is less than unity), there is a significant transition in the nature of the compact object.Specifically, the object transitions from being an extremal black hole to a naked singularity.Consequently, for this particular choice of parameters, there is no horizon to be depicted.These observations are further corroborated by the findings depicted in Fig. 1b.Returning now to the case α − β > 0, the discovery of black-hole solutions sharing identical horizon radii yet varying in the ratios Q m /M unveils a realm of doppelgänger black holes within the framework of theory (3.1).While it is typical to find black holes stemming from different theoretical paradigms with shared horizon radii but differing physical attributes such as mass, electric charge, or secondary scalar hair, such occurrences are notably rare when considering black holes that arise from the same theory.Even more remarkable is the fact that these two doppelgänger black holes, despite having identical horizon radii, exhibit distinguishable thermodynamic behaviors.One is thermodynamically stable while the other is unstable.This distinctive feature is thoroughly explored in Section V.
A. Geodesics
In this subsection, we will examine the geodesic curves of massive particles and the effective gravitational potential generated by the spacetime geometry given by eqs.(3.5) and (3.10).We choose to work with the (t, r, θ, φ) coordinate system, as it facilitates a straightforward derivation of the effective gravitational potential V eff through a well-established procedure.This will help us to better comprehend the geometry of the aforementioned black hole solutions.To do so, we introduce the effective Lagrangian the Euler-Lagrange equations of which yield the geodesic equations.In the above, τ is an affine parameter of motion which can be identified with the proper time of a particle, dot denotes derivation with respect to τ , while 2L eff = −1 corresponds to massive particles which follow a timelike path.Note that massless particles will not follow the geodesics induced by the geometry g µν , instead they will follow the geodesics induced by an effective geometry that accounts for photon-photon interactions, introduced by the non-linear electromagnetic terms in our action.Upon inspecting the Lagrangian (4.1), it becomes evident that there is no explicit dependence on the coordinates (t, φ).As a result, the Euler-Lagrange equations for t and φ yield two conserved quantities: the energy E and the angular momentum J of the particle under consideration, respectively.Hence, we have 3) The equation of motion for θ reads All parameters are dimensionless, and the horizontal axis is logarithmic.
and by choosing θ = π/2 ( θ = 0), the particles stay fixed at the equatorial plane.Now plugging these results back to (4.1) we obtain the radial equation of motion with the effective potential induced by the geometry being and the functions B(r) and R(r) given by (3.10) .As we have already mentioned in the previous section, the radial coordinate r ranges from Q 2 m /M to plus infinity because the physical radial coordinate R ∈ (0, +∞).In Fig. 3, we depict the behavior of the effective potential V eff in terms of the dimensionless parameter r/M , considering three distinct values for the fraction (α − β)/M 2 .Upon close examination, it becomes evident that the scenarios where α = β and (α − β)/M 2 = 2 share a strikingly similar pattern in the effective potential.In both cases, the potential curve features one maximum and one minimum value, corresponding to unstable and stable circular orbits, respectively.On the other hand, in the case where (α − β)/M 2 = −2, an additional minimum emerges, exhibiting local behavior that closely resembles the Newtonian potential.To understand the origin of this difference, we have to examine the expansion of the potential V eff in the limit r → Q 2 m /M , where one can verify that We observe that the first term, which dominates in this particular regime, depends explicitly on the sign of the quantity α − β.When α − β > 0, the potential tends toward negative infinity, whereas for α − β < 0, the potential tends toward positive infinity.This alignment precisely mirrors our observations in Fig. 3. Finally, from Fig. 3, it is also clear that for r/M > 2, the effective potential in all cases exhibits the same profile, independently of the relative values of the coupling constants α and β.This can be naively understood through the expansion of the potential at infinity, which is of the following form It is obvious that in the asymptotic regime, the coupling constants α and β cease to influence the potential profile, as their first contribution comes into play only in the seventh term of the expansion.Consequently, even at medium distances, we anticipate that beyond a certain point, the coupling constants will have negligible impact on the potential's behavior.
B. Energy Conditions
We will now turn our attention to the energy conditions associated with the stress-energy tensor of our theory.In the physical coordinate system (t, R, θ, φ) the stress-energy tensor is described by an anisotropic fluid which in a covariant form can be written as In the above, ρ E is the energy density of the fluid measured by a comoving observer with the fluid, p R is its radial pressure, p θ is its tangential pressure, while u µ and n µ are its timelike four-velocity and a spacelike unit vector orthogonal to u µ and also to both angular directions.The four-vectors u µ and n µ satisfy the following relations: ) Given eqs.(3.2), (3.9), (3.12)-(3.15),and (4.9)-(4.11),one can readily compute that ) For the anisotropic fluid of (4.9), the energy conditions take the following expression: • Null Energy Conditions (NEC): In Figs.4a and 4b, we illustrate the graphs of the quantities ρ E , ρ E + p R , ρ E + p θ , and ρ E + p R + 2p θ each plotted against the dimensionless parameter R/M .The free parameters of our model and solution have been chosen to be Q m /M = 0.5, while the combination (α − β)/M 2 takes values of 1 and −1, respectively.It is evident from Fig. 4 that all the aforementioned quantities maintain positive values within the causal region of spacetime and as a result, all energy conditions are satisfied.These results imply, therefore, the existence of a dilaton hair in the black hole's exterior, while the energy conditions are satisfied, thereby leading to a bypass of the pertinent (modern version of the) no-hair theorems [109,110] in the spirit of [111].The situation can be understood as a consequence of the fact that the stress-energy tensor of our theory (3.1), with (3.9), is such that the tangential component of the pressure (p θ = T θ θ ) dominates over its radial one (p R = T R R ) (in the (t, R, θ, ϕ) coordinate system), outside the horizon.That is, the following quantity is positive in the exterior region of the black hole, where G = ρ E + T θ θ and J ≡ ρ E + T R R .Note that the condition (4.15) follows from NEC.As discussed in detail in [111], the quantity 2G/R is the effective gradient pressure force, and its positivity (i.e. that of G, since R > 0) explains in a physical way the existence of scalar hair in the black-hole's exterior, without any violation of the energy conditions.The validity of the condition (4.15) can also be explicitly checked in our model from Eqs. (4.13) and (4.14).Thus, the exact black hole solution of the self-gravitating scalar-EH (non-linear) electrodynamics examined in this paper constitutes another explicit example of the general considerations of [111] for bypassing the no-hair theorem without any violation of the energy conditions.
V. THERMODYNAMIC ANALYSIS
In this section, we will discuss the thermodynamics of both the GMGHS and our black-hole solution by considering their Euclidean actions.We will consider the Grand Canonical Ensemble and enclose the black hole spacetime in a cavity with a large radius r c .In the Grand Canonical Ensemble, the black hole is allowed to exchange energy/mass and charge with its environment, so these two quantities are allowed to flow in and out through the boundary keeping the temperature and the magnetostatic potential of the boundary fixed.This effectively means that T (r h ) = T (r c ) and Φ m (r h ) = Φ m (r c ) and the system black hole-cavity is in thermodynamic equilibrium.Note that T is the black-hole temperature and Φ m is the magnetostatic potential.The quantum partition function for the system is then given by where S is the Lorentzian action, I E is the Euclidean action and ψ denotes all other possible fields included besides the metric tensor.The two actions are related via I E = −iS [112].The quantity g µν is the Lorentzian metric with signature (− + ++), which corresponds to a R 3,1 spacetime, while g µν is the Euclidean metric with signature (+ + ++), which is obtained from the Lorentzian one by performing a Wick rotation [113] of the time coordinate (τ = it).In the standard Matsubara formalism of finite-temperature systems, the Euclidean metric corresponds to a space R 3 × S 1 βτ , where the radius β τ of the S 1 is the inverse temperature T −1 in units of the Boltzman factor k B = 1.Hence, the second integral in (5.1) is evaluated over all possible field configurations that have an imaginary time τ with period β τ .From the partition function, using standard thermodynamic relations one can obtain the Free Energy G of the system as By using the saddle point approximation (Laplace's method) we will consider that the classical action contributes the most and as a result we may drop the integral in the partition function Z. Then the Euclidean action I E can be related to the free energy evaluated on shell through the following relation Having the expression of the free energy for the black hole solution, we will compare it with the free energy of the grand canonical ensemble in order to extract the mass (internal energy), the entropy, and the magnetostatic potential of the black hole.For more information in the discussion that follows, we refer the reader to the original work of Gibbons and Hawking [114].
A. GMGHS black hole
We start our analysis with the thermodynamics of the GMGHS solution.The Euclidean action, including the appropriate boundary terms, is given by (5.4) In the Euclidean signature, the GMGHS black hole is described by the following metric: where B(r) = 1−2M/r, while R(r) has the same form as in eq.(3.10).In this coordinate system, the Euclidean time coordinate is periodic and takes values in the range 0 ≤ τ ≤ β τ .For the derivation of the thermodynamic quantities, we assume that we have enclosed the black hole in a large cavity with radius r c .Therefore, the radial coordinate takes values in r h ≤ r < r c .Finally, the two angular coordinates take their usual values.The boundary term K represents the trace of the extrinsic curvature, which in our case reads where n α = 1/B(r) δ r α is a normalized spacelike vector field.The K term in the above hypersurface integral represents the Gibbons-Hawking-York boundary term, ensuring a well-defined variational principle.The second boundary term K 0 serves as a subtraction term to render the action finite for flat space (in the absence of the black hole).For flat space, K 0 equals 2/r, obtained by setting B(r) = 1 and R(r) = r in the above relation.Utilizing these relations, one can readily compute the Euclidean action (5.4) to be (5.7) In the above, we have used that the horizon radius is given by r h = 2M .In the Grand Canonical Ensemble, the Euclidean action is identified with the free energy of the thermodynamic system as I E = β τ G, thus, we can rewrite (5.7) as where S is the entropy and Φ m is the magnetostatic potential, Φ m = Q m /r h .For the derivation of the above equation, we have used the fact that β τ = 8πM ≡ 1/T with T being the temperature of the black hole.By combining now eqs.(5.7) and (5.8) we can evaluate the black-hole entropy S, which is given by the following relation where A denotes the horizon area.It is evident that in this case, the entropy function has the well-known form of the Bekenstein-Hawking entropy.For validation, the same result may also be obtained using Wald's formula or even using the Arnowitt-Deser-Misner (ADM) formalism [115].For a comprehensive analysis of the ADM formalism, readers are directed to [116].
Additionally, for its explicit application in black-hole solutions, we refer the interested reader to [117].In the subsequent subsection, we will utilize the ADM formalism for the thermodynamic analysis of our black-hole solution.
The inclusion of the Gibbons-Hawking-York boundary term ensures that the Euclidean action attains an extremum within the class of fields considered here, δI E = 0 .As a result, it is evident that the first law of thermodynamics in the Grand Canonical Ensemble (keeping the temperature and the magnetic potential fixed) takes the form derived from (5.8), and holds by construction.The first law is also evident by taking the variation of the entropy with respect to the primary black-hole charges.The temperature of this black hole is the same as that of the Schwarzschild black hole, as pointed out in [118], since the Euclidean continuation does not care about the angular part.Consequently, the heat capacity C for constant charge will also be negative, C = −1/(8πT 2 ); hence, these types of black holes cannot reach thermal equilibrium.
B. Black hole with non-linear electrodynamics
We will now focus on our black-hole solution, emanating from the action (3.1) and characterized by the line element (3.12)- (3.14).The scalar and the gauge fields are of the form ϕ = ϕ(R)-with R being the physical radial coordinate-and A µ = (0, 0, 0, A(θ)), respectively.In this case, to determine the thermodynamic quantities associated with the resulting black-hole solution, we will make use of the Euclidean signature and also utilize the ADM formalism [115,116].Hence, we consider the line element of the form where the Euclidean time takes values in the range 0 ≤ τ ≤ β τ , while the radial coordinate R ∈ [R h , +∞).To obtain the temperature, that is the period of the Matsubara frequency τ , in our case, we follow the calculation of [37].To this end, we first ignore the angular part of the line element and perform a series expansion near the horizon.Thus, we are left with a twodimensional line element which is compared with the line element of two-dimensional space expressed in polar coordinates dS = d R2 + R2 dΘ 2 .By doing so, we obtain (5.12) (5.13) The coordinate Θ is periodic with a period 2π which implies that τ is also a periodic coordinate with a period β τ given by: where T is the temperature of the black hole.For completeness, we also remark at this point that we have also checked that, as expected, the temperature will take on the same values at the event horizon regardless of the coordinate system we are using (r or R).
The Euclidean action is related to the Lorentzian action via I E = −iS and we will consider the following variational problem which basically consists of the theory (3.1) alongside a boundary term denoted by B E which we will consider in order to have a well-defined variational principle δI E = 0. Thus, we have Here L denotes the Lagrangian of the theory which is a function of R, θ coordinates.After canceling total derivatives, the Euclidean action reads with (5.17) Following the ADM formalism, we have to vary the above Euclidean action with respect to each one of the dynamical fields Q i to obtain the field equations.By doing so, we obtain none other than the well-known Euler-Lagrange equations, namely Let us now apply the above equation for the dynamical field Q 1 = N (R).Upon substituting the expression of L from (5.17) into (5.18),we find that the second term vanishes identically, while ∂ L/∂N = L/N .As a result, the equation for N (R) indicates that L = 0, which in turn implies I E = B E .This outcome is anticipated in the ADM formalism, where the metric construction (5.11) is specifically tailored to yield this result.Additionally, by solving the field equations (5.18) for all dynamical fields Q i , one can determine the unknown functions and verify that the resulting solution is the one obtained in Sec.III with line element (3.12)-(3.14),alongside a constant N which without loss of generality we may set equal to 1.It is important to mention at this point, that during the derivation of the Euler-Lagrange equations, certain boundary terms were omitted.These terms are of the following form and . (5.20) The variation of the boundary term δB E will account for the neglected boundary terms, ensuring the attainment of a welldefined variational principle δI E = 0. Utilizing the fact that the variation of A yields δA = (δQ m ) cos θ, and substituting the expressions for the functions in (5.20), one can integrate and derive the following expression: Now, the variation of the dynamical fields at infinity yield while at the horizon we have that Note that the parameters α, β are fixed by the theory and thus not allowed to vary, while M and Q m are pure integration constants allowed in the variation.As previously mentioned, to ensure a well-defined variational procedure, it is desirable to have δI E = 0.For clarity and convenience, we will partition the variation of the boundary term δB E into two components: one at infinity and another at the event horizon, expressed as: (5.28) Evaluating now (5.19) at infinity and considering the variation of the boundary term at infinity we find that a zeroth order contribution survives, which according to the variations of the fields leads to On the other hand, eq. ( 5.19) at the horizon, alongside the variation of the boundary term at the horizon and (5.21) results in which might be written equivalently as where we have used the fact that the area of the black hole is given by A = 4πR 2 h and we have defined the magnetic potential as Considering now that we are dealing with the Grand Canonical Ensemble, we keep the temperature and the magnetic potential of the system fixed and as a result we can drop the variations to obtain Therefore, the value of the Euclidean action is given by and since the Euclidean action is related to the free energy G of the system via can identify, by comparison the conserved black hole mass and the entropy of the black hole as Finally, the First Law of Thermodynamics (5.10) holds by construction as in the GMGHS black hole.With the confirmation that the black-hole thermodynamic quantities in our case adhere to the standard relations, we can now proceed to analyze the black hole's temperature.In Fig. 5, we depict the black-hole temperature as a function of the dimensionless quantity R h /(2M ).Notice that the temperature is scaled by the temperature of the Schwarzschild black-hole to form a dimensionless quantity, ensuring its independence from the chosen unit system.In Figs.5a and 5b, we explore the effects of the higher-order electromagnetic contributions on black-hole temperature, considering fixed (yet distinct) values for the coupling constants α and β, along with varying magnetic charge (Q m ) values, but maintaining the same value for the black-hole mass.Both Figs.5a and 5b were generated using the following procedure: For each value (α − β)/M 2 and the ratio Q m /M , we numerically evaluate the value of the ratio R h /(2M ) using eq.(3.13).Subsequently, employing equation (5.14), we calculate the temperature of the black hole for each parameter pair.Finally, for each (α − β)/M 2 we plot the points from the list {R h /(2M ), T (R h )/T sch }.Note that we use the same mass parameter M for the temperature calculation of the Schwarzschild black hole T sch .In both figures, we have also incorporated a distinctive dot symbolizing a constant value for the quantity T (R h )/T sch , irrespective of the ratio R h /(2M ).Apparently, this is not coincidental, as it mirrors the characteristics of the Schwarzschild black hole, where the horizon radius precisely equals 2M and its temperature is determined by the established formula T = 1/(8πM ).
Focusing now on the thermodynamical characteristics of our solution, we observe that regardless of the value (α − β)/M 2 , for Q m = 0, our solution reduces to the Schwarzschild black hole and therefore all graphs in Fig. 5 have as a starting point the Schwarzschild point.However, when we depart from this limit, we notice that for α − β > 0, as illustrated in Fig. 5a, the temperature of the resulting black holes consistently surpasses that of the Schwarzschild black hole, whereas for α − β < 0 (Fig. 5b), the opposite effect occurs.Furthermore, this temperature increase, in the α − β > 0 scenario, is independent of whether the black hole under examination possesses a smaller or larger horizon radius compared to the corresponding Schwarzschild black hole.As previously observed in Fig. 2 and discussed in Sec.III, it becomes evident in Fig. 5a that there are consistently pairs of black-hole solutions, more compact than the Schwarzschild solution, that share the same horizon radius R h but with different ratios Q m /M .However, now we see that although these solutions possess the same horizon radius, their temperatures differ significantly.This can be understood through the relation (5.14)where it is evident that the formula determining the temperature of a black hole depends on the first derivative of the function B(R).This means that black-hole solutions which for different ratios Q m /M result in the same horizon radius R h through the equation B(R h ) = 0, their temperatures are not necessarily the same since B ′ (R h ) could differ in these two cases.
Moreover, we can deduce the thermodynamic stability of these black holes by examining how the temperature changes with a change in the mass.In Fig. 5a it is evident that there are two distinct branches of black-hole solutions.In the first branch we have black-hole solutions that get colder as the mass is decreasing, while in the second branch we have black holes that are getting hotter as the mass is getting smaller.This implies that the heat capacity C ≡ dM/dT for the first branch is positive since both dM, dT are negative and the black holes are thermally stable, while the second branch, for which the temperature rises with the decrease of mass, exhibits negative heat capacity and are thermally unstable.Notice also the fact that the Schwarzchild black hole lies in the second (unstable) branch which is a well-known result.Furthermore, the parameter space of these black holes exhibits a point where dT = 0 indicating the divergence of the heat capacity and as a result a phase transition from hot to cold black holes.In Fig. 5b, we can see that as the black holes lose mass they get colder which implies that they are thermally stable since they possess positive heat capacity.These results are in agreement with the studies in [119], where the black holes are viewed as defects in the thermodynamical spacetime [120].
In the next section, we proceed to study the stability of the black holes from a linear-perturbation point of view, which, in general, is distinct from the thermodynamic stability.Indeed, as we shall demonstrate explicitly below, such a linearised stability analysis does not necessarily imply thermodynamical stability, in the sense that the thermodynamically unstable branches found above exhibit stability under linear perturbations.
VI. LINEAR PERTURBATIONS A. Radial Stability
In this section, we investigate the stability of our solution under radial perturbations.For simplicity, we focus on linear and radial perturbations.Therefore, we use the following ansatz: where For the stability analysis, it is more convenient to work within the physical coordinate system; hence, in the above equations B(R), ϕ(R) and H(R) = B(R)/W 2 (R) are given in eqs.(3.13-3.15),and correspond to the background/unperturbed spacetime.Note that the radial perturbations are associated with the L = 0 perturbation 5 in the even sector of the gravitational perturbations.Therefore, in the electromagnetic part, only the electric-type perturbations contribute, as the magnetic-type corresponds to the odd sector [124,125].The dimensionless constant ϵ determines the order of the perturbation.Finally, ω specifies the decomposition of the modes with fixed energy.A direct calculation reveals that both the spacetime and the matter field perturbations are determined from the function ϕ 1 .Consequently, the investigation of the system is simplified to a single equation for the perturbation of the scalar field.This specific equation can be expressed in the conventional Schrödinger form: 5 L is the "angular momentum" index in the spherical harmonics function Y M L L (θ, φ).For more information about the decomposition of the perturbations in spherical harmonics, see [121][122][123][124]. where we have defined a new perturbation function as Ψ ≡ Rϕ 1 and the tortoise coordinate is . The potential of the Schrödinger equation has the following form Considering our emphasis on the stability of black-hole solutions, there is no need to solve eq.(6.4).The time evolution factor, exp (−iωt), simplifies the task, requiring us only to ascertain whether the frequency, ω, is purely imaginary or not.In the scenario where the frequency ω is purely imaginary, the mode undergoes exponential growth due to the presence of the term exp (−iωt) making the solution unstable.Therefore, a negative eigenvalue, ω 2 < 0, that signifies an unstable mode, corresponds to a bound state in the Schrödinger equation (6.4).A general result in quantum physics is that for a potential that vanishes in both asymptotic regions, has a barrier form, and is positive definite.Therefore, eq.(6.4) does not exhibit bound states.In Fig. 6, we depict the potential of the Schrödinger equation for two families of solutions.The first one corresponds to (α − β)/M 2 = 1, while the second one corresponds to (α − β)/M 2 = −1.By carefully examining the parametric space of the solutions, we deduce that the potential always takes a form similar to the potentials in Fig. 6.Therefore, we conclude that our solutions are stable under radial perturbations.Although radial stability is a strong indication regarding the stability of a particular solution, a more careful and general perturbation analysis has to be performed to extract a stronger result, which, however, lies beyond the scope of this work.Moreover, as shown in the previous section V, linear stability does not necessarily imply thermodynamical stability for the black hole, in the sense that the latter, although linearly stable, nonetheless it possesses thermodynamically unstable branches.
B. Scalar Quasi-Normal Modes
Quasi-normal modes (QNMs) play a crucial role in the study of black holes and other astrophysical objects [126][127][128].These modes represent the characteristic vibrations or oscillations of a black hole after a perturbation, such as a gravitational wave or a scattering event.QNMs are characterized by complex frequencies, i.e. eigenvalues of the Schrödinger equation, consisting of a real part and an imaginary part.The real part corresponds to the oscillation frequency, while the imaginary part reflects the damping or decay of the mode.The study of QNMs provides valuable insights into the nature and properties of black holes, offering a unique window into their internal dynamics.
For simplicity, we will consider the propagation of a test scalar field Φ in the background of our black hole and extract its QNMs.We begin our analysis from the following action functional for the scalar field, where m is the mass of the test scalar field.The variation of the above action with respect to the scalar field yields the Klein-Gordon equation in the black hole background Note that the test scalar field Φ, as a perturbation field, does not back-react on the spacetime metric and is a function of all spacetime coordinates Φ = Φ(t, R, θ, φ).For clarity, we choose to work in the physical coordinate system.Therefore, the background metric is given by eq.(3.12).We can apply the separation of variables as follows where Y M L L (θ, φ) represents the spherical harmonics function.By using the tortoise coordinate, , one can rewrite the perturbation equation in a Schrödinger form as: where V (R) is the effective potential of the Schrödinger equation and is given by The background metric functions B and H = B/W 2 are given in eqs.(3.13-3.14).
In the pursuit of calculating the QNMs, the WKB (Wentzel-Kramers-Brillouin) approximation stands as a valuable method.Particularly useful in the context of wave-like phenomena, the WKB approximation provides an efficient and semi-classical approach to estimating the complex frequencies associated with QNMs.By treating the Schrödinger-like equation governing the perturbations as a semiclassical wave equation, the WKB method allows for the determination of QNM frequencies without the need for an exact solution.The WKB method was initially developed for quantum mechanical problems; however, Schutz and Will were the first to apply this method to the problem of scattering around black holes [129].Later, Iyer and Will extended this approach to the third WKB order beyond the eikonal approximation [130], and Konoplya further advanced it to the sixth order [128,131].Interestingly, the sixth order yields a relative error of approximately two orders of magnitude lower than that of the third WKB order [128,131].However, for simplicity, in this work, we will employ the first-order WKB approximation, in which the QNM frequencies are obtained from the solution of the following equation The expression in the right-hand part of the above equation is evaluated at the maximum of the potential r * max while n is the overtone number of the QNMs.
In Tables I and II, we present the dimensionless QNM frequencies, denoted by (M ω), for two distinct scenarios: when m = 0 and m/M = 0.4, respectively.Notably, as Q m approaches 0, our solution converges to the Schwarzschild black hole, irrespective of the (α − β)/M 2 parameter.This convergence is evident in the first row of both tables, where Q m /M = 0.01, as the QNM values remain constant across varying (α − β)/M 2 .Furthermore, as (α − β)/M 2 tends toward 0, our solution adopts the characteristics of the GMGHS black hole.Consequently, the QNMs in the first row of both tables, specifically when (α − β)/M 2 = 0.01, align with those of the GMGHS black hole.The subsequent rows in the tables provide additional insights into the characteristics of our solution.For instance, in the second and third rows, where Q m /M = 0.3 and 0.6, respectively, we observe a systematic variation in the QNM values with changes in both Q m /M and (α − β)/M 2 .This behavior highlights the sensitivity of the QNM frequencies to the parameters characterizing the black hole solution.Furthermore, by comparing these results to the Schwarzschild and GMGHS cases, we discern how our solution deviates from these benchmark scenarios.Additionally, the tables reveal intriguing patterns in the imaginary parts of the QNMs.For varying Q m /M and (α − β)/M 2 , the imaginary parts exhibit non-trivial changes, reflecting the impact of the black hole's charge and the parameter (α − β)/M 2 on the damping behavior of the perturbations.
VII. OTHER SOLUTIONS A. Asymptotically (A)dS spacetimes
Let us now, briefly discuss asymptotically (A)dS spacetimes.Following [132], introducing a scalar potential V(ϕ) in the action and considering with a V(ϕ) of the form we can obtain B(r) as while ϕ(r), R(r) will remain the same.Note here that the potentials V(ϕ) and f (ϕ) are almost identical, and they are both Liouville-type potentials [73]. 6
B. Solutions for general γ
Assuming that the coupling term between the dilaton and the Maxwell term is of the form e −2γϕ we can obtain the same geometry with the γ = 1 case with the coupling function f (ϕ) now being given by f In this case, the charge-to-mass ratio is fixed by the theory.As a result, such black holes are described by a constrained phase space of free parameters, since this situation reduces the number of primary black hole hairs from two to one.A more physical result would be to let the form of the dilaton field to be affected by the change of the coupling function with the Maxwell term, however, we were not able to derive exact results in this case, so one has to employ numerical techniques.Such endeavors may be undertaken in subsequent works.
VIII. CONCLUSIONS
In the quest to comprehend gravitational phenomena and the nature of gravity itself, the theoretical exploration of black holes stands as a pivotal frontier.The predictions of General Relativity (GR) are in good agreement with current observations related to black holes.This is attributed to the large mass of the observed objects and therefore their large horizon radius and small horizon curvature.Additionally, a plethora of cosmological observations indicates instances where GR exhibits limitations, with the most notable challenges being the Dark Energy Problem and GR's inability to account for the inflationary epoch in our universe.Therefore, the validity of General Relativity is expected to come under scrutiny in extreme conditions.General Relativity is commonly acknowledged as an effective theory applicable only within the realm of low energies.Consequently, such observations motivate us to explore modified gravitational theories, especially in extreme conditions where GR's validity may be compromised.Among these theoretical frameworks, modifications originating from String Theory, particularly the heterotic string theory, emerge as leading contenders.Notably, String Theory offers insights into high-order corrections, ranging from the Gauss-Bonnet term to non-linear electromagnetic effects, and provides a rich avenue for exploring the behavior of black holes under diverse conditions.
One intriguing aspect of string/brane-induced non-linear electrodynamics is the emergence of the Born-Infeld (BI) Lagrangian, which encapsulates higher-order corrections to Maxwell's theory.This Lagrangian arises from the resummation of open string excitations, particularly in the context of D-brane worlds in string theory.The coupling of the BI Lagrangian to the dilaton field in curved spacetime leads to an effective four-dimensional action, offering a novel perspective on electromagnetic interactions in the presence of gravity.Furthermore, considerations of higher-order electromagnetic terms, originating from closed string sectors, broaden the theoretical landscape.The inclusion of string loops leads to generalized effective actions, incorporating both closed and open string contributions, and potentially revealing novel phenomena beyond conventional electromagnetic frameworks.Departing from traditional electromagnetic theories, the exploration of non-linear electrodynamics within the context of black hole solutions offers a rich avenue for understanding strong-field regimes and cosmological implications.Non-linear effects become crucial in regions with intense gravitational fields, such as those near black holes, shedding light on phenomena absent in linear theories.Moreover, non-linear electrodynamics holds relevance for early universe cosmology, where the interplay between gravitational and electromagnetic fields played a significant role.
In this work, we considered a string-inspired theory that involves a scalar field ϕ coupled to the electromagnetic field via a non-linear function f (ϕ).The action encompasses higher-order electromagnetic invariants, contributing to the field equations and leading to novel black hole solutions.Furthermore, we investigated the impact of a non-trivial coupling function f (ϕ), considering a specific functional form motivated by string-inspired models.The resulting exact, magnetically charged black hole solution revealed significant departures from the classical General Relativity predictions, with the scalar field and the electromagnetic field configurations exhibiting non-trivial behavior.We explored the implications of different coupling constants α and β on the spacetime geometry and electromagnetic field configurations.The solutions obtained exhibit intriguing features, including dependence on the sign of α − β which determines whether the higher-order electromagnetic terms contribute attractively or repulsively to the spacetime geometry.Additionally, we examined the horizon structure of the black hole solutions, observing transitions from single to multiple horizons and even to naked singularities as the parameters varied.Notably, the compactness of the black holes relative to the Schwarzschild solution depended on the the magnetic charge to mass ratio.Our findings suggest a rich interplay between the scalar field, electromagnetic field, and spacetime geometry, highlighting the potential implications of such theories in astrophysical contexts, and the search for potential signatures of string theory in black hole physics, at least those signatures that can be manifested through effective string-inspired field theory models.It goes without saying, however, that the present work does not deal with a detailed experimental sensitivity analysis of such objects, which still remains to be done.
The examination of geodesics and energy conditions delves into the intricate dynamics of particles moving within the spacetime geometry described by the black hole solutions under investigation.By analyzing the geodesic equations we unveil the behavior of massive particles in the vicinity of these black holes, elucidating the role of the effective gravitational potential.Notably, the effective potential exhibits distinct features depending on the relative values of the coupling constants, offering insights into the stability and nature of orbits around the black holes.Additionally, the examination of energy conditions associated with the effective stress-energy tensor reveals intriguing properties of the spacetime, indicating the existence of a dilaton hair in the black hole's exterior while satisfying all energy conditions.This observation challenges the traditional no-hair theorems, underscoring the nuanced interplay between gravitational theories, non-linear electrodynamics, and scalar fields in modified theories.Our thermodynamic analysis provided valuable insights into the properties of black holes in both the GMGHS solution and our black-hole solution with non-linear electrodynamics.Our analysis allows for the extraction of important thermodynamic quantities such as mass, entropy, magnetostatic potential, and the extraction of the first Law of Thermodynamics.Notably, the entropy of both black hole is consistent with the Bekenstein-Hawking entropy formula.By examining the behavior of the temperature, we concluded that when the non-linear electrodynamics terms act attractively, there exist two distinct branches of black holes, one that is getting colder as the mass is decreasing and therefore is thermally stable, and another one that is getting hotter as the mass is decreasing which is thermally unstable.On the other hand, when the non-linear electrodynamics terms have a repulsive effect, the black holes are getting colder as the mass is decreasing and as a result are thermally stable.
Finally, our analysis of linear perturbations and scalar quasi-normal modes (QNMs) provides valuable insights into the stability and dynamic behavior of black hole solutions with non-linear electrodynamics.Through a rigorous investigation of radial stability, we demonstrated that our black hole solutions remain stable under linear and radial perturbations.This finding underscores the robustness of our black hole solutions against radial perturbations, supporting their viability as physically meaningful configurations within the framework of non-linear electrodynamics.Furthermore, our examination of scalar QNMs yielded intriguing results regarding the characteristic vibrations and oscillations of the black hole spacetime.Moreover, the analysis of scalar QNMs revealed the intricate interplay between the black hole parameters, such as charge and (α − β)/M 2 , and the frequency and damping behavior of perturbations.By systematically varying these parameters, we observed distinct patterns in the QNM frequencies, indicating the sensitivity of the black hole's dynamic properties to its intrinsic characteristics.Notably, our results exhibited convergence to the Schwarzschild black hole in the limit of vanishing charge and alignment with the GMGHS black hole in specific parameter regimes.These observations highlight the rich phenomenology associated with black holes in our string-inspired theory. )
4 FIG. 2 :
FIG. 2:The ratio R h /(2M ) in terms of the ratio Q m /M for various values of the dimensionless parameter (α − β)/M 2 .Both axes are logarithmic.
FIG. 4 :
FIG.4:The energy conditions for Q m /M = 0.5 with (a) a positive and (b) a negative value assigned to the dimensionless quantity (α − β)/M 2 .The vertical lines correspond to the horizon of the black hole determined by these parameters.
FIG. 5 :
FIG.5:The black-hole temperature for (a) attractive and (b) repulsive higher-order electromagnetic contributions, with varying values of the magnetic charge (Q m ), while keeping the mass (M ) the same.The axes in both figures are logarithmic. | 16,202.2 | 2024-02-19T00:00:00.000 | [
"Physics"
] |
How the Social Relations Affect Performance in Chinese High-tech New Ventures: The Role of Legitimacy Acquisition and Symbolic Strategy
Existing research on the relationship between social relations and new venture’s performance remains inconsistent. From the perspective of institutional theory, we introduce legitimacy acquisition and symbolic strategy to develop a theoretical model to explain the disparities in the Chinese transition economy. Based on the survey data of 242 small and medium-sized enterprises (SMEs) in China’s strategic emerging industries (SEIs), this paper (1) investigates the role of legitimacy acquisition as the mediator through which the two sub levels of social relations (political and business) affecting new venture’s performance. (2) Explores the moderating role of symbolic strategies to further illustrate the conditional nature of legitimacy acquisition. The results show that legitimacy acquisition plays a complete mediating role in the relationship between social relations and new venture’s performance. Symbolic strategy improves the positive effect of political ties on legitimacy acquisition, but weakens the positive effect of business relations on legitimacy acquisition. The findings contribute to the entrepreneurial literature and make significant empirical implications. Plain Language Summary Social Relations, Legitimacy Acquisition, Symbolic Strategy and Firm Performance Purpose: The study aimed to understand how social relations impact the performance of new ventures in China, emphasizing the roles of legitimacy acquisition and symbolic strategies. Methods: Through a survey of 242 small and medium-sized enterprises in strategic emerging industries in China, the study examined how legitimacy acquisition mediates the effect of social relations on venture performance, and how symbolic strategies moderate this mediation. Conclusions: It was found that legitimacy acquisition significantly mediates the link between social relations and venture performance. Symbolic strategies, however, had a mixed effect: enhancing the positive impact of political relations on legitimacy acquisition, but diminishing the effect of business relations. Implications: The results suggest that new ventures can improve their performance by gaining legitimacy through social relations. However, employing symbolic strategies may have varied effects depending on the nature of the social relations. Limitations: The study is bound to China, limiting generalizability. Other potential mediators or moderators impacting the relationship between social relations and venture performance were not explored. Additionally, the detailed impact of political versus business relations on legitimacy acquisition was not fully examined.
Introduction
Entrepreneurial activities have been considered as one of the most important ways to enhance economic vitality (Urbano et al., 2019).However, as the pioneers of new industries and new entrants of existing institutions, the ''liability of newness and smallness'' faced by new ventures create difficulties to access resources (Aldrich & Fiol, 1994;Fisher et al., 2017).In addition, because entrepreneurial activities are subject to risk factors and uncertainties, new businesses have few resources to meet their development goals (Hersel & Webb, 2018).Therefore, new ventures are forced to seek external cooperation (Boh et al., 2020; M. W. Peng & Luo, 2000), which may establish various relationships with external actors (H.Peng et al., 2016).Drawing upon social capital theory, researches suggested that social relations facilitate firms to access external resources that are beneficial for firm's performance (Feld, 1981;Tilly, 2015).Extant researches mainly indicate that social relations positively influence the performance of new venture (H.Li & Zhang, 2007;Zhu et al., 2017), however, it has also been researched that social relations can negatively affect firm's performance (Avgerou & Li, 2013).As an example, Uzzi (1997) argues that if a focal firm goes bankrupt, the business performance of its surrounding friends is also negatively affected.J. J. Li et al. (2009) found that political ties could decrease firm's profitability as the connections with governmental officials are too close.Further, in the entrepreneurial context, as new ventures seek to establish social relations with powerful partners, it may force them lowering their ethical standard (Warren et al., 2004).
These inconsistent findings lead to explore how social relations influence new venture's performance.Existing research focuses on analyzing the direct factors of how performance was affected by social relations (Su & Yang, 2018).However, others found that social relations that new firms established are unlikely to convert into good performance directly (Zhang et al., 2021).The recent study focuses on analyzing whether there are confounding factors between social relationships and performance, namely the mediator, such as adaptive capacity factors (Zhu et al., 2017), dynamic capabilities (Pinho & Prange, 2016), and resource bundling capabilities (F.Jiang et al., 2018, X. Jiang et al., 2018).Despite these efforts, the mechanisms of how social relations affect the performance of new ventures remain ambiguous (G.D. Bruton et al., 2018;H. Peng et al., 2016).
In order to provide deeper insight on the mechanisms of how social relations affect new venture's performance, we introduce the mediating role of legitimacy acquisition to explore how social relations enhance new venture's performance.The study based on institutional theory found that new firms are confronted with ''liability of newness'' in the process of creation and development (Stinchcombe, 1965), which creates difficulties for survival and development.By acquiring legitimacy from their external audiences, such as government players and business players, new ventures may gain resources needed for survival and development (Liu & Wang, 2022) and thus overcome the difficulties.
Meanwhile, the value of social relations is conditional on contingency factors (J.J. Li et al., 2008).By facilitating new venture to acquire legitimacy from social relations, symbolic strategies (Marquis & Qian, 2014) adopted by new ventures may serve as an important contingency factor.Symbolic strategy was frequently utilized to chase ''ulterior'' purpose by the new ventures (Zott & Huy, 2007) especially in SEIs 1 of Chinese transition economy.For example, a senior manager reported in the interview: ''once the high-tech new venture certification was granted, we will receive honors, subsidies and pay less taxes.itcannot reflect the real technological strength of our firm.becausemany patents we applied are junk patents, just for the need of applying for high-tech new venture certification.''Therefore, we proposed that the symbolic strategies have a significant effect on the relationship between social relations and new venture's performance.
By using 242 survey sample from SEI's of China's transition economy, we analyze the mediating role of legitimacy acquisition between social relations and new venture's performance, as well as the moderating role of symbolic strategies and further explain the conditional nature of the value of social relations.Specifically, for one thing, the empirical results show that legitimacy acquisition plays a fully mediating role between social relations and entrepreneurial performance when viewed from two dimensions of social relations, namely political and business relations.For another, the findings suggest that while symbolic strategies enhance the positive impact of political relations on legitimacy acquisition, they depress the active impact of business relations on legitimacy acquisition.
This paper emphasizes on the importance of resource management as social relations transfer into superior performance in Chinese transition economy.We further explore the realistic scenarios in which the theories applying, which helps to integrate social capital theory and institutional theory.
Hypothesis and Conceptual Model Development
Theory New Venture's Social Relations.Social relations represented as informal, interpersonal social connections between the focal firm's top managers and their external actors (Feld, 1981) which are based on trust and shared values between each other ( (Tilly, 2015).Scholars classified the type of social relations mainly as business relations (connections with business actors) and political relations (connections with government officials) (Luo et al., 2012).Accordingly, in Chinese transition economy, top managers in new ventures may foster ''Guanxibased relations'' with business and government actors (Burt & Burzynska, 2017).We adopted the existing concepts of social relations that contain political and business relations.On the one hand, political relations refer to ''guanxi''-developing contact with government officials.(Tilly, 2015).Firms develop contacts to complement formal institutions in order to escape institutional voids and to obtain preferential treatment as well as project approval (Burt & Opper, 2020;Luo et al., 2012).However, business relations refer to the process of developing relationships with market players, such as suppliers, customers, and competitors (Ellis, 2011).Social relations are helpful to gain customers, new business opportunities, avoiding threats accessing resources and building trust (Avgerou & Li, 2013;De Carolis et al., 2009;Zhu et al., 2017).The combination of both types of social relations forms an important basis for new venture to access various resources and achieve business goals.
Legitimacy Acquisition.Legitimacy facilitates new businesses to take on ''liability of newness'' and to achieve organizational stability, which is one of the core concepts in institutional theory (Scott, 1995;U ¨berbacher, 2014).According to Suchman (1995, p. 574), legitimacy is defined as ''a generalized belief or assumption that the actions of an entity are desirable, proper, or appropriate within some socially constructed system.''Kostova and Zaheer (1999) predigested the definition of legitimacy as ''being accepted by the environment.''However, due to the different interests of public demands within the environment, new ventures should to obtain the recognition from various audiences (Fisher et al., 2017).In other words, when key audiences perceived the behavior of new ventures in an acceptable way, they may be gifted as legitimate.Thus, legitimacy acquisition was regarded as new ventures' efforts to obtain the recognition of their audiences (Fisher et al., 2017), which facilitating themselves to overcome the obstacles in the entrepreneurial process (U ¨berbacher, 2014;Yin et al., 2021).
Social Relations and Legitimacy Acquisition
Political relations are likely to improve firms' ability to deploy public resolution approach that may produce favorable outcomes for new ventures (W.Shi et al., 2014).This effect is more pronounced in transition economies, especially in China (J.Shi et al., 2020).Chinese economy exhibits weaker institutional environment where government plays key role in resource allocation (G.Bruton et al., 2021).Accordingly, researches have emphasized the role of political relations that may offset the negative impacts of institutional burdens in Chinese economy (Bai et al., 2019;Ellis, 2011;M. W. Peng et al., 2008).Firms closely linked with the government (e.g., attendance at Congress and personal connections with government officials) have institutional advantages over those without these links (Q.Tang et al., 2021).Therefore, political relations help firms to access governmental authority which place the focal firm in a good position to acquire reputation, prestige and other resources outside their boundaries (Q.Tang et al., 2021).Specifically, through the establishment of political relations with government, new ventures interact frequently with government departments and regulative institutions.Such good relationship with government departments could in turn serve as endorsement for new ventures (G.D. Bruton et al., 2018).The endorsement by the government gifted the new venture with reputations, which may results in high-level of legitimacy (Bai et al., 2019).
For the role of business relations, given new ventures are unfamiliar with the prevailing norms and practices in the marketplace, they may suffer from ''liability of newness'' (Jacob & Duysters, 2017;U ¨berbacher, 2014).Business relations may promote resonance between the focal firm and their audiences in the marketplace which help new venture to overcame the difficulties (Wang et al., 2020).To be specific, through formal and informal communication with business actors, new ventures could establish various connections, such as friendship, business clubs, alliances, professional associations (Wang et al., 2020), with business actors and audiences (like customers, opponents, and distributors) which enhance mutual understanding between each other.As the relationship deepens, the business activities of new ventures will be widely accepted by the audiences (Fisher et al., 2017), which may facilitating new ventures to acquire legitimacy.Thus, the new venture could overcome ''liability of newness and smallness'' by legitimacy acquisition (Neumeyer et al., 2019;U ¨berbacher, 2014).
In summary, the following hypotheses are put forward H1a: Political relations have a positive impact on legitimacy acquisition.
H1b: Business relations have a positive impact on legitimacy acquisition.
Legitimacy Acquisition and Performance
For new ventures, legitimacy acquisition is an important basis for them to obtain other resources (Dı´ez-Martı´n, Blanco-Gonza´lez, & Dı´ez-de-Castro, 2021; Zimmerman & Zeitz, 2002).Only when firms recognized by their audiences can they gain a foothold in the marketplace (Fisher et al., 2017).Hence, legitimacy is a certain type of resources, which help new ventures to attract customers, investors, partners, suppliers and other audiences (Dı´ez-Martı´n, Blanco-Gonza´lez, & Prado-Roma´n, 2021; U ¨berbacher, 2014).As such, high-level of legitimacy offers support to access resources for new venture creation.For example, Deeds et al. (2004) empirically examined that legitimacy acquisition can help biopharmaceutical firms to attract investors.Chan and Makino (2007) have also found that organizations with higher legitimacy can obtain better resources than those with lower legitimacy.In fact, most new venture's failure is not due to lack of market potential, but because they hardly gain the trust and support of audiences (Fisher et al., 2017).Due to the nature of novelty and uncertainty in new ventures, audiences are unwilling to take risks and invest resources in them (Liu & Wang, 2022).Therefore, new ventures need to cultivate ''guanxi'' relations with government players and market players, such as officials, industrial bureaus, customers, investors, suppliers, and competitors (Liu & Wang, 2022).As the new ventures is recognized, trusted, and supported by the audiences, it will enhance their ability to obtain resources (Fisher et al., 2017).Thus, legitimacy acquisition is helpful for new ventures to promote products and services and increase market share (Liu et al., 2022).
In general, legitimacy acquisition plays a mediating role between social relations and new venture's performance.On the one hand, it allows political relations to be settled in a way that has a positive impact on legitimacy acquisition and, consequently, on the new venture's performance.On the other hand, it allows business relations to be settled in a way that has a positive impact on legitimacy acquisition and, consequently, on the new venture's performance.We propose the following, H2a: Legitimacy acquisition mediates the relationship between political relations and new venture's performance.H2b: Legitimacy acquisition mediates the relationship between business relations and new venture's performance.
Symbolic Strategy as the Moderator
Although social relations offer opportunities to legitimacy acquisition, these opportunities do not automatically lead to legitimacy acquisition (Fisher et al., 2017).Drawing on the Chinese transition economy context, new ventures prefer to implement symbolic strategies to facilitate resource acquisition (Marquis & Qian, 2014).Symbolic strategies, which was defined as the actions that convey the meaning of social construction beyond its ontological function (Zott & Huy, 2007).Such strategies always be utilized by firms to chase ''ulterior'' purpose (Marquis & Qian, 2014).From a practical view of point, symbolic strategy delivers positive information to the audiences that is likely to construct favorable and legitimate image (Nagy et al., 2012).Firms utilize symbolic strategies that convey the firm's credibility, organizational achievement to their audiences, which may serve as contingency factors as firms to acquire legitimacy and resources from various social connections (U ¨berbacher, 2014).
According to the seminal work of Marquis and Qian (2014), we proposed that symbolic strategies of new ventures may moderate the relationship between social relations and legitimacy acquisition.Because there exists information asymmetry when firms deal with different actors (political vs. market) (Cohen & Dean, 2005), we predict that different type of symbolic strategies may be utilized by the new venture to acquire legitimacy from different audiences (Marquis & Qian, 2014).For one thing, firm's symbolic strategy for the government audiences may signals that their products/services are qualified by the customers, investors and other audiences for the marketplace (Marquis & Qian, 2014).However, in Chinese transition economy, the government's evaluations for firm's qualifications are mainly based on indicators responded from the market (Burt & Opper, 2020), such as the satisfaction of customers and stakeholders, credit rating by third-party agencies, etc. (Burt & Burzynska, 2017).Therefore, it may facilitating firms to gain legitimacy as they established ties with government actors (Verhaal et al., 2017).Thus, we predict that symbolic strategy for the government may strengthen the influence of political relations on legitimacy acquisition.For another, symbolic strategy for the business audiences may serve as certain type of symbolic function (Christmann & Taylor, 2006), because new ventures in Chinese transition economy need to respond to government instructions (Marquis & Qian, 2014).For example, a senior manager reported in our semi-structured interview: ''once the high-tech new venture certification was granted, we will receive honors, subsidies and pay less taxes.itcannot reflect the real technological strength of our firm.becausemany patents we applied are junk patents, just for the need of applying for high-tech new venture certification.''As they establish business relations with market actors, firm's symbolic strategy will be stigmatized by market actors within the category (Hampel & Tracey, 2017).Such dishonorable behaviors will result in legitimacy deficit.
Overall, the symbolic strategy plays a moderating role in the relationship between the two dimensions of social relations and new venture's performance.We propose the following, H3a: Symbolic strategy for the government audiences positively moderates the influence of political relations on legitimacy acquisition.H3b: Symbolic strategy for the business audiences negatively impact the legitimacy of business relations.
Questionnaire Design
We identify variables and constructs based on previous literature and modified them according to the feedback of in-depth interviews with SEIs senior managers in various Chinese Cities.Then, we organized three pilot-scale interviews from October to December, 2020 to identify the fitness of each item.We have translated each item within the questionnaire into Chinese language to pledge the interviewees can completely understand it.Likert 5 scale was utilized to measure the value of each item.For the point of the scale, ''5'' point equal the degree of very high (or the attitude of fully agree) and ''1'' point equal the degree of very low (or the attitude of completely disagree).
Data Collection
We have drawn our sample from Chengdu Tianfu Software Park, Sichuan, China.As the park is one of the largest professional software parks in China, thus the sampling source is well representative.The age of targeted firms are \8 years.The respondents were mainly the founders, CEOs, co-founders and other senior managers.The sampling method was simple random sampling.According to the enterprise directory provided by the park management committee, we randomly selected enterprises, conducted field visits in the Tianfu Software Park, and invited the top managers to fill in the questionnaire.For the targeted enterprises which had not been visited on the spot, we contacted the enterprises by telephone and e-mails.Based on the consent of targeted enterprises, we emailed our questionnaire to senior managers.We distributed 800 questionnaires in December 2020 and received 389 responses in April 2021.The invalid responses have been eliminated which makes our sample size 242.The effective sample recovery rate was 30.25%.The detailed sample was shown in Table 1.
Private owned enterprises account for the 84.71% of our sample.Seventy-one enterprises are \2 years of age accounting 29.34% while 89 enterprises are between the 3 and 5 years of age whereas 82 firms are aged from 6 to 8 years which account for 36.78% and 33.88% of our sample size respectively.From the industrial attribute of the sample distribution, 163 enterprises belong to SEIs, accounting for 67.40% of the total sample.Besides, the
Measures
Social Relations.Considering the relationship between focal firms and different actors we divide social relations into two dimensions: political relations and business relations.Referring to M. W. Peng and Luo (2000) and Zhu et al. (2017), political relations include four items including (1) we have maintained good relationships with local government departments and government officials; (2) we have maintained good relationships with regulatory departments of the industry; (3) we have maintained good relationships with local industrial and commercial bureau, and taxation administration; (4) we have maintained a good relationship with the local park management According to H. Li and Zhang (2007), business relations include three items, including (1) we maintained good relationships with customers; (2) we have maintained good relationships with suppliers and retailers; (3) we have maintained good relationship with peers within the category.New Venture's Performance.The financial indicators of achievement can improve the effectiveness of the measurement.That information about performance of leads to the insufficient use of indicators (Zhu et al., 2017).Therefore, we determine the performance of new business according to H. Li and Zhang (2007) to reflect the growth, profitability and innovation of new ventures.This index considers four items including: (1) compare with competitors, our firm's growth rate of total sales and market shares are higher; (2) compare with competitors, our firm's ROI and ROA are higher; (3) compare with competitors, our firm invested and developed more new products or services; (4) compare with competitors, our company has promised to bring new products or services to market faster.
Legitimacy Acquisition.Legitimacy acquisition is the mediator factor of the study.We measure the constructs according to the connotation of the variable that whether the focal firm are recognized and accepted by the environment.Accordingly, Certo and Hodge (2007) created a subjective scale to survey legitimacy based on the recognition of important audiences.We adopted the measurement and altered the scales as per Chinese context (Liu & Wang, 2022).The measures include five items, namely (1) government praise for the manage processes and daily operations of the focal firm; (2) customers praise for the products and services of the focal firm; (3) distributors and suppliers want to work with the focal firm; (4) companies within the category want to treat the focal firm with respect; (5) investors want to invest in the focal firm.Symbolic Strategies.New ventures in the strategic emerging industries (SEIs) of Chinese transition economy often apply for two types of certifications namely the product/service quality certification granted by the market and the high-tech new venture certification granted by the government (Xie et al., 2022).We measure symbolic strategy for government audiences as whether the focal firms applying for product/service quality certifications.Because this type of certification was granted by the market, which could testify the quality of firm's products/services.If the firm was granted by such type of certification, then the value equal 1, otherwise the value equal 0. We measure symbolic strategy for market audiences as whether the focal firms applying for hightech new venture certifications.Because this type of certifications was granted by government, which was mainly utilized as to gain fiscal subsidies and reduce taxes.Similarly, If the firm was granted by such type of certification, then the value equal 1, otherwise the value equal 0.
Sample Analysis
Validity and Reliability.We conducted the software of SPSS 22.0 and Amos 22.0 to test the validity and reliability of each construct.The results of validity and reliability each construct was shown in Table 2.
Referring to the criteria of most previous studies, 0.7 is taken as the critical value of Cronbach's alpha reliability coefficient in this study.The Cronbach's a value of each construct is ..8, which has a good reliability.Considering that the questionnaire in this study has passed the exploratory factor analysis (EFA) in the presurvey stage, which shows that the scale has a good construction validity.The confirmatory factor analysis (CFA) results show that factor loadings were between 0.561 and 0.926, which fulfill the requirement of factor loading that falls between 0.5 and 0.95.Moreover, the convergent validity of our factors of average variance extracted (AVE) is reported in Table 2. Results show that AVE values are well above the recommended value of 0.5.In addition, every dimension of variables demonstrates higher than 0.8 combination reliability (CR).Thus, the convergent validity of the data was satisfied with good result.
We further estimate the discriminant validity by using the Fornell-Larcker criterion to observe how greater the square root value of AVE of each construct in comparison to the correlations between each variable.The square root of AVE and the diagonal coefficient for all structures of non-diagonal elements were shown in Table 3.We can find that the diagonal elements are larger than the off-diagonal ones, which means the results the discriminant validity of the data was satisfied.
Common Method Variance (CMV).The sample might be the subject of common method variance (CMV) problem.Thus, to avoid CMV, we utilized multivariate questions to measure each item in our questionnaire.Afterward, in order to lessen the retrospective bias of respondents, we also reversed and misplaced the items of each latent variable.Subsequently, we employ Harman single factor test to examine the common method deviation.This considers that there have a single factor explains the covariance between most of the independent variables and the dependent variables (More than 40%), it indicates that there exists a CMV problem.In this study, principal component analysis was used to check CMV problem.The first factor explained 27.936% of the variation when the axis was not rotated, so there was no single factor that could explain most of the variation, which means the CMV problem has resolved.
Mediating Mechanism of the Regression
The variance of inflation factor (VIF) value was tested before the regression analysis.Since the VIF value in all models were between [1.021, 1.982] which is far more \10.Therefore, no multicollinearity problem occurs in the study.Table 4 contains the results of regression analysis of mediating effects.First, the effect of control variables on the dependent variables was examined in model 1.Next, the effect of independent variables, namely political relations and business relations, on the dependent variable was tested in model 2. Result show that both political relations (M2: b1 = .191,p \ .01)and business relations (M2: b2 = .375,p \ .001)shows a positive correlation with new venture's performance.Next, we examined the effects of political relations and business relations along with control variables on legitimacy acquisition in model 3b.Moreover, we investigate the effect of legitimacy acquisition and control variables on new venture's performance in model 3a.As a result, it became clear that the two sub-dimensions of social relations have positive effects on legitimacy acquisition (M3b: b1 = .162,p \ .001;b2 = .563,p \ .001),and legitimacy acquisition has a significantly positive impact on new venture's performance (M3a: b3 = .711,p \ .001).Further, we examine the mediating role of legitimacy acquisition in model 4. We take took into account all variables (including political relations, business relations and control variables) to examine their effect on new venture's performance.The result show that legitimacy acquisition has a positive and significant impact on performance, however, there is no significant impact of political relations and business relations on new venture's performance.(M4: b1 = .085,p ..1; b2 = .036,p ..1; b3 = .659,p \ .001).In combination, the regression results indicate that legitimacy acquisitions fully mediate the relationship between the two dimensions of social relations and new venture's performance.Thus, H1a, H1b, H2a, and H2b are supported.
Results of Moderating Mechanism
To examine the moderating effect, the moderated hierarchical regression was adopted to test the interaction between social relations and symbol strategies.To avoid multicollinearity of the regression model, all explanatory variables were mean-centered (H.Tang et al., 2023).The regression results were presented in Table 5.First, the effect of control variables on legitimacy acquisition was examined in model 5. Next, we add independent variables in models (6-9), afterward, we add moderating variables in models (7-10).Subsequently, the moderation and interactions terms have been introduced in models (8-11).
It was shown that political relations have a significantly positive relationship with legitimacy acquisition in model 6 (M6: b = .316,p \ .001).In Model 8, the interaction between political relations and symbolic strategy results in an active effect on legitimacy acquisition (M8: b = .179,p \ .05).Results in Model 9 suggest that business relations are significantly positive related to legitimacy acquisition (M9: b = .629,p \ .001).In model 11, the interaction between business relations and symbolic strategy is significantly negative related to legitimacy acquisition (M11: b = 2.207, p \ .05).Thus, H3a and H3b are corrective.
To more directly represent how symbolic strategies moderate the impact of social relations on legitimacy acquisition, we plotted this result numerically in Figures 2 and 3. Figure 2 shows the interaction effects of political relations and symbolic strategy for the government on legitimacy acquisition.When the value of interaction term (symbolic strategy multiply with political relations, abbreviated to Sym_Gov) is 0, the slope is relatively low; while when the value is 1, the slope is relatively high, presenting a positive effect of political relations on legitimacy acquisition.Figure 3 shows the results of the interaction between symbolic strategy and business relations on legitimacy acquisition.When the value of interaction term (symbolic strategy multiply with business relations, abbreviated to Sym_Mkt) is 0, the slope is relatively high; while when the value is 1, the slope is relatively low, showing a negative effect of the interaction term on legitimacy acquisition.Figures 2 and 3 provide support for Hypotheses 3a and 3b.
Conclusions
Employing a data set of 242 new ventures of SEIs in China, this paper explored the role of legitimacy acquisition and the role of symbolic strategies within the ''social relations-performance'' linkages.The empirical analysis illustrated several main findings.Firstly, the two sub-dimensions of social relations (political and business) have a positive impact on legitimacy acquisition.Secondly, the acquisition of legitimacy plays a full mediating role within the ''social relations-performance'' linkage.Finally, symbolic strategy plays a moderating role in determining the relationships between the two sub-dimensions of social relations and legitimacy acquisition.Specifically, the symbolic strategies of government audiences positively moderate the impact of political relations on legitimacy acquisition, however, it has a negative moderating effect on the impact of business relations on legitimacy acquisition.Overall, the findings offer significant contributions both theoretically and empirically.
Contributions
Theoretical Contributions.Firstly, we offer a new perspective for understanding the relationship between social relations and the performance of new ventures.This paper highlights the indispensable role of legitimacy acquisition as new ventures acquire resources and promote performance through social relations.Due to the nature of ''liability of newness'' for new ventures (Gimenez-Fernandez et al., 2020), it is the first priority for new ventures to acquire legitimacy through social relations than any other resources or capabilities (Soublie`re & Gehman, 2020).Therefore, it enriches the internal mechanism of linkage between social relations and performance in entrepreneurial context.Moreover, this paper holds that legitimacy is certain type of resources for new ventures (Liu & Wang, 2022;Zimmerman & Zeitz, 2002), previous literature explained the resource acquisition of new ventures mainly from the perspective of social capital theory (F.Jiang et al., 2018), which has paid little attention to the institutional factors, namely legitimacy.This paper hold that only when new ventures obtained legitimacy resources can they promote the performance, which contributes to the integration of social capital theory and institutional theory (Rigolini & Huse, 2021).
Secondly, by exploring the significance of symbolic strategy (Marquis & Qian, 2014), the study asserts the conditional nature in the relationship between social relations and legitimacy acquisition.This finding deepens the research that how new ventures interact with their audiences when they strive for legitimacy.By straight out the pros and cons of symbolic strategy, it takes the theory a step further (Soto-Simeone et al., 2020).Previous literature proposed that symbolic strategies may be utilized by firms to chase ''ulterior'' purpose, however, it is not clear that such strategy is good or bad for new ventures (Hampel & Tracey, 2017).By categorized the types of symbolic strategy according to different audiences, this paper makes this point clear.Therefore, the findings shed light on the role of symbolic strategy in entrepreneurial context, which contribute to the entrepreneurial theory.
Empirical Significance.The findings make significant implications for practice.
Firstly, we suggest that there exists a mediator as firm's social relations transformed into performance.Different from established firms, new ventures often confronted with the problem of liability of newness and smallness, which makes them hardly to growth.Hence, new ventures should take efforts to recognized by customers, competitors, suppliers, retailors, government departments and other audiences.Because, for new ventures, to some extent, the legitimacy is much more important than the technological and financial resources.Once the legitimacy was granted by their audiences, it will form a mechanism of cooperation on the basis of mutual trust.Such mechanism may reduce the cost of new product development and technological innovation.The trust relationship makes new ventures closely cooperate with their partners, which reduces the opportunistic tendency and risks, thus improve the performance.
Secondly, we advise that firms should take symbolic strategy in a proper way.Different from western developed economies, the Chinese transition economy has institutional defects, that large number of enterprises will try to utilize the defects, such as engage symbolic strategy to accelerate the business process.Although the strategy may beneficial for firms in some ways, the findings also illustrate the dark side of symbolic strategy.Even if the symbolic strategy can fulfill other purposes that beneficial for new ventures, it could stigmatize the reputation of new ventures recognized by market actors.Thus, new ventures should avoid themselves falling in the ''myopic trap'' that they should take care of the negative effects of such strategy.
Limitations
This study, while insightful, presents certain limitations that open avenues for further investigation.Firstly, the research is geographically bounded to China, which poses questions on the generalizability of the findings to other institutional settings.Future research could extend this inquiry to different socio-economic contexts to ascertain the universality of the observed relationships.Secondly, the study elucidates the mediating role of legitimacy acquisition between social relations and venture performance; however, there might be other mediating or moderating variables at play, unexplored in this study.Future research could delve into identifying other mechanisms that might explain the complex relationship between social relations and new venture performance.Lastly, this study lays the groundwork for a deeper exploration of the varying impacts of political and business relations on legitimacy acquisition.Further studies could dissect these sub-dimensions of social relations more thoroughly, potentially revealing a more intricate understanding of how different facets of social relations contribute to the legitimacy and success of new ventures.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Figure 1
Figure 1 of theoretical framework depicts all hypotheses.
Figure 2 .
Figure 2. Moderating effects of symbolic strategy for the government.
Figure 3 .
Figure 3. Moderating effects of symbolic strategy for the business.
Table 1 .
Descriptive Statistics (N = 242).number of employee and income can reflect the size of the enterprise.According to the criteria of SMEs published in 2017 for the breakdown of SMEs of each industry by the state statistical office of China, the study of the sample meets the requirement of SMEs.
Note.Diagonal elements (in bold) are square roots of the AVE.Off-diagonal elements are the correlations of the main variables of the study.N = 242.a Poli_Rel = political relations; Busi_Rel = business relations; Legi_Acq = legitimacy acquisition; Sym_Mkt = symbolic strategy for the market; Sym_Gov = symbolic strategy for the government.* p\.05.**p\.01 (two-tailed).
Table 2 .
Validity and Reliability of the Constructs. | 7,859.6 | 2023-10-01T00:00:00.000 | [
"Business",
"Economics"
] |
Detecting Respiratory Pathologies Using Convolutional Neural Networks and Variational Autoencoders for Unbalancing Data
The aim of this paper was the detection of pathologies through respiratory sounds. The ICBHI (International Conference on Biomedical and Health Informatics) Benchmark was used. This dataset is composed of 920 sounds of which 810 are of chronic diseases, 75 of non-chronic diseases and only 35 of healthy individuals. As more than 88% of the samples of the dataset are from the same class (Chronic), the use of a Variational Convolutional Autoencoder was proposed to generate new labeled data and other well known oversampling techniques after determining that the dataset classes are unbalanced. Once the preprocessing step was carried out, a Convolutional Neural Network (CNN) was used to classify the respiratory sounds into healthy, chronic, and non-chronic disease. In addition, we carried out a more challenging classification trying to distinguish between the different types of pathologies or healthy: URTI, COPD, Bronchiectasis, Pneumonia, and Bronchiolitis. We achieved results up to 0.993 F-Score in the three-label classification and 0.990 F-Score in the more challenging six-class classification.
Introduction
Today, respiratory pathologies are a common problem all over the world.Although smoking is the most common cause of respiratory pathologies, sometimes they are caused by genetics, as well as environmental exposure [1].The ICBHI (International Conference on Biomedical and Health Informatics) respiratory dataset [2] includes seven pathologies, such as chronic obstructive pulmonary disease (COPD), asthma, upper respiratory tract infection (URTI), lower respiratory tract infection (LRTI), bronchiectasis, pneumonia, and bronchiolitis.
Chronic obstructive pulmonary disease (COPD) is a chronic pathology which is difficult to detect.The main cause of COPD is smoking [3].It causes symptoms, including shortness of breath and cough, which are also common in Asthma disease.Furthermore, these symptoms can be interpreted as a simple aging process.
Bronchiectasis is a chronic condition in which the airways of the lungs become abnormally widened.These damaged air passages allow bacteria and mucus to build up and pool in your lungs.This results in frequent infections and blockages of the airways.All these symptoms can be interpreted also as a bronchiolitis or just a cold [4].The main difference between both diseases is that bronchiolitis most often affects young children and it can be cure, whereas bronchiectasis is a chronic disease.
Upper respiratory tract infection is a non-chronic disease that can happen at any time, but it is more common in the fall and winter.The vast majority of upper respiratory infections are caused by viruses [5].The symptoms of this disease can be confused with those of pneumonia [1].Most people with pneumonia can recover in a short time, but for certain people, it can be extremely serious and even life-threatening so the diagnosis is crucial.
Symptoms of lower respiratory tract infections (LRTI) vary and depend on the severity of the infection.Less severe infections can have symptoms similar to those of bronchiectasis or bronchiolitis.
As we can see, the symptoms of all these diseases are very common and can cause a bad diagnosis by the doctor.For all this, it is very interesting to be able to determine the disease using the sound of the breaths without taking into account the rest of the symptoms.
Respiratory Sounds Detection
Lung auscultation provides valuable information regarding the respiratory function of the patient, and it is important to analyze respiratory sounds using an algorithm to give support to medical doctors.There are a few methods in the literature to deal with this challenge.Typically, wheezing is found in asthma and chronic obstructive lung diseases.Wheezes can be so loud you can hear it just by standing next to the patient.Crackles, on the other hand, are only heard using a stethoscope, and they are a sign of too much fluid in the lung.Crackles and wheezes are indications of the pathology.
Islam et al. [6] detected asthma pathology by basing their research on the fact that asthma detection from lung sound signals rely on the presence of wheeze.They collected lung sounds from 60 subjects in which the 50% had asthma and using a data acquisition system from four different positions on the back of the chest.For the classification step, ANN (Artificial Neural Networks) and SVM (Support Vector Machine) were used with the best results (93.3%) obtained in the SVM scenario.
Other studies based on the detection of wheezes and crackles [7] used different configurations of a neural network, obtaining results of up to 93% for detecting crackles and 91.7% for wheezes.The same goal is pursued in Reference [8], but the dataset used in this case consists of seven classes: normal, coarse crackle, fine crackle, monophonic wheeze, polyphonic wheeze, squawk, and stridor.The best results were achieved using a Convolutional Neural Network (CNN).Chen et al. [9] proposed ResNet with an OST-based (Optimized S-Transform based) feature map to classify wheeze, crackle, and normal sounds.In detail, three RGB -maps (Red-Green-Blue) of the rescaled feature map is fed into ResNet due to the balance between the depth and performance.The input feature map is passed through three steps of the ResNet structure and finally, the output corresponds to the class (wheeze, crackle, or normal).The results are compared with ResNet-STFT (Short Term Fourier Transform) and ResNet-ST (S-Transform), with the best accuracy achieved using their proposal ResNet-OST.
In Reference [10], the authors propose a methodology to classify the respiratory sounds into wheezes, crackles, both wheezes and crackles, and normal using the same dataset as that used in our work: ICBHI [2].The procedure consists of a noise suppression step using spectral subtraction followed by a feature extraction process.Hidden Markov Models were used in the classification step obtaining 39.56% using the score metric, defined as the average of sensitivity and specificity.These results are not promising but in Reference [11], Perna et al. proposed a reliable method to classify in healthy, chronic disease, or non-chronic disease based-on wheezes, crackles, or normal sounds using deep learning and, more concretely, recurrent neural networks and again using the ICBHI benchmark [2].
In Reference [12], Jacome et al. also proposed a CNN to deal with respiratory sounds for detecting breathing phase with a 97% of success in inspiration detection and a 87% in expiration.
Early models of RNNs suffered from both exploding and vanishing gradient problems.Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU) were designed to address the gradient problems successfully.The authors exploited the LSTM and GRU advantages and obtained promising results of up to 91% of the ICBHI Score calculated as the average value of sensitivity and specificity [11].
Deep learning techniques have also been used to detect some kinds of pathologies such as bronchiolitis, URTI, pneumonia, etc., which supposed a more challenging problem than classifying wheezes and crackles.In Reference [13], the authors try to distinguish between pathological and non-pathological voice over the Saarbrücken Voice Database (SVD) using the MultiFocal toolkit for a discriminative calibration and fusion.The authors carry out a feature extraction step, and these features (Mel-frequency cepstral coefficients, harmonics-to-noise ratio, normalized noise energy and glottal-to-noise excitation ratio) are used to train a generative Gaussian Mixture Models (GMM) model [14].
Deep Learning Techniques
In the literature, many deep learning techniques have been used to resolve all kinds of problem.This, gives us an idea of how useful artificial intelligence is.
Today, one of the most used techniques for all kinds of purposes are autoencoders and CNNs.Sugimoto et al. [15] try to detect myocardial infarction using the ECG (electrocardiogram) information using a CNN.In their experiments, the classification performance was evaluated using 353,640 beats obtained from the ECG data of MI (myocardial infarction) patients and healthy subjects.ECG data was extremely imbalanced, and the minority class, including abnormal ECG data, may not be learned adequately.To solve this problem, the authors proposed to use the convolutional autoencoder in the following way: The CAE model is constructed for each lead and outputs reconstructed input ECG data if normal ECG data is inputted.Otherwise, the waveform is distorted and outputted.After this process, k-Nearest Neighbors (kNN) is used as a classifier.
A CAE (Convolutional autoencoder) is also used in Reference [16] to restore the corrupted laser stripe images of the depth sensor by denoising the data.
In Reference [17], Kao et al. propose a method of classifying Lycopersicons based on three levels of maturity (immature, semi-mature, and mature).Their method includes two artificial neural networks, a convolutional autoencoder (CAE), and a backpropagation neural network.With the first one, the ROI in the Lycopersicon is detected (instead of doing it manually).Then, using the extracted features, the neural network employs self-learning mechanisms to determine Lycopersicon maturity obtaining an accuracy rate of 100%.
A variational autoencoder is used in Reference [18] for video anomaly detection and localization using only normal samples.The method is based on Gaussian Mixture Variational Autoencoder, which can learn the feature representations of the normal samples as a Gaussian Mixture Model trained using deep learning.A Fully Convolutional Network (FCN) is employed for the encoder-decoder structure to preserve relative spatial coordinates between the input image and the output feature map.
In Reference [19], a non-linear surrogate model based on deep learning is proposed using a variational autoencoder with deep convolutional layers and a deep neural network with batch normalization (VAEDC-DNN) for a real-time analysis of the probability of death in toxic gas scenarios.
Advances in indoor positioning technologies can generate large volumes of spatial trajectory data on the occupants.These data can reveal the distribution of the occupants.In Reference [20], the authors propose a method of evaluating similarities in occupant trajectory data using a convolutional autoencoder (CAE).
In Reference [21], deep autoencoders are proposed to produce efficient bimodal features from the audio and visual stream inputs.The authors obtained an average relative reduction of 36.9% for a range of different noisy conditions, and also, a relative reduction of 19.2% for the clean condition in terms of the Phoneme Error Rates (PER) in comparison with the baseline method.
In 2019, variational autoencoders have been widely used to analyze different kind of signals and monitoring them [22,23].In addition, in Zemouri et al. [24], variational autoencoders have been used for train a model as a 2D visualization tool for partial discharge source classification.So, today autoencoders and CNNs are widely used in the literature to solve all kinds of problems.We take advantage of both methods and proposed the use of a variational convolutional autoencoder to balance the data, as well as a CNN to carry out the classification step.
For this paper, we proposed a technique to classify healthy, chronic disease, and non-chronic disease and six different pathology classes: Chronic obstructive pulmonary disease (COPD), upper respiratory tract infection (URTI), bronchiectasis, pneumonia, bronchiolitis, and healthy.Our procedure outperforms the state-of-the-art proposals.
The rest of the paper is organized as follows: In Section 3, we describe the methodology, including data preprocessing, data normalization, and data augmentation, using our Variational Convolutional autoencoder and finally data classification using a CNN.Experiments and results are detailed in Section 4, taking into account two types of classification, and finally, we conclude in Section 5.
Data Normalization
Data normalization is an important step before carrying out any machine learning strategy.There are multiple alternatives to normalize data.In this paper, we evaluated our data with MinMax normalization, which got the data in the [0,1] range.
Data Augmentation: Variational AutoEncoder (VAE)
In all fields of research, but more frequently in ehealth, it is very common to have unbalanced data in the datasets.That means that the number of elements (cardinal) of one class is much bigger than all the cardinal of the rest of the classes.To solve this, there are multiples techniques which try to replicate samples of the minority classes.Synthetic Minority Oversampling Technique (SMOTE) [25], Adaptive Synthetic Sampling Method (ADASYN) [26], and Variational Autoencoders (VAE) [27] are some examples of generative methods.We evaluated our dataset with all of these oversampling methods obtaining the best results with VAE, as shown in the results section.
VAE are part of a kind of neural network known as autoencoders.Vanilla autoencoder architecture consists of a number of dense hidden layers with two main peculiarities:
•
One of these hidden layers has a very few neurons (latent space).
•
The output of the vanilla autoencoder tries to replicate the input.
Taking into account these two considerations, when an autoencoder is trained, the net learns to encode data information in its latent space and decode them after that to reconstruct the original data.
However, VAE is a probabilistic model focused on learning the distribution of data to be able to create new samples which would belong to this distribution.Whereas Vanilla autoencoders try to reconstruct the original data, VAE is also trained to learn the distribution of the data.For that reason, the loss function used to train a VAE is made up of two terms: "reconstruction term", like in the vanilla autoencoder, that tends to make the encoder-decoder work accurately; and a "regularization term" applied over the latent layer that tends to make the distributions created by the encoder close to a standard normal distribution using the Kulback-Leibler divergence (see Equation ( 1)).
where x¯ is the reconstruction of x, and N(µx, σx) a normal distribution with mean µx and standard deviation σx and KL[p, q] is the Kulback-Leilber divergence defined in Equation (2): In Figure 1a,b, respectively, we show the differences between a variational autoencoder and a vanilla one.
Data Classification: Convolutional Neural Networks
A CNN is a Deep Learning algorithm which can take in a bi-dimensional input and be able to differentiate it from another by learning filters which extracts complex features from the inputs automatically.A basic modeling of a CNN is represented in Figure 2.During the training step, each convolution layer learns the filter weights to then produce a feature map.The filter or kernel is sliding over the input and the sum of the convolution generates the feature map.
After a convolution layer, it is common to add a pooling layer.These kinds of layer are use to decrease the number of parameters in the network.This reduces the computational cost and controls overfitting.The most frequent type of pooling is Max-pooling, which takes the maximum value in each window.In order to carry out a classification or a regression problem with the features generated by the convolutional layers, it is necessary to add dense layers at the end of the network.
Dataset
The ICBHI (International Conference on Biomedical and Health Informatics) dataset [2] was created by two research teams (Greece and Portugal), and it includes 920 recordings acquired from 126 subjects.A total of 6898 respiration cycles and 5.5 h of sound was recorded.One thousand, eight hundred and sixty-four of these 6898 respiration cycles were labeled as crackles; 886 contain wheezes and 506 contain both crackles and wheezes.Crackles and wheezes were labeled by experts in the field.Respiratory sounds were recorder from seven different chest locations: trachea, left and right anterior, left and right posterior, and left and right lateral (see Figure 3).High noise levels were included to simulate real situations obtaining a challenging dataset.
where f is the frecuency in hertzs.
There are four steps to be carried out to obtain the Mel spectogram given an audio input: 1.
Sampling the input wave with windows of a fixed size and step.
2.
Compute the Fast Fourier Transform to get the data to the frequency domain.
3.
Generate bins using the Mel scale.
4.
Generate spectogram breaking down the magnitude of the signal into the frequencies of the Mel scale.
After all the spectrograms are built, all the images were resized to have the same number of columns.Each column represents a unit of time, so it is very common to have different sizes throughout all of our datasets.In our case, all the images were resized to the mean number of columns in all the spectrograms (see Equation ( 4)).
) N
where N is the number of spectrograms in the experiment and cols(x) the number of columns of image x.Some of these images can be seen in Figure 4.
Experimental Setup
In this work, a Min-Max feature normalization was carried out to set our data in the range of [0,1] which highly improves the performance of the neural network training.After that, we evaluated the class distribution of the dataset taking into account three different values: Chronic, Non-Chronic, and Healthy.In Table 1, we can see the unbalanced distribution.As we can see, the number of samples of chronic pathologies represents 88.04% of all the dataset.In our experiments, we carried out a classification on the unbalanced dataset with and without using class weights.Furthermore, an augmentation of the less representative classes was done to balance the dataset.This augmentation step was carried out using our proposed VAE.
A convolutional VAE scheme has been implemented in order to generate more samples for the Non-Chronic and healthy classes.In Figure 5, we can see the network configuration.In Table 2, the new size of each class is shown.Some examples of the new images generated can be seen in Figure 6.Once we have our dataset well balanced, we designed a CNN for three class specifications.The scheme of this network can be seen in Figure 4.As we can see, we added some layers such as BatchNormalization and Dropout to avoid the overfitting problem.The output layer consists of three neurons to fit the three class classification.
We used Adam as the optimization algorithm and categorical crossentropy as the loss function.Before training, a train-test split (80-20) was carried out in order to clearly distinguish between the data used for training and that used to evaluate the classifier.
In order to avoid random factor, a 10 cross validation has been carried out in all the experiments showing in all the tables the mean value of the metrics.The intermediate results for the proposal can be shown in Table 3. Table 3.All the iteration results for the 10 cross validation step using the proposal combination of Variational AutoEncoder (VAE) for data augmentation and a CNN for the classification step on chronic diseases detection.As we can see, the standard deviation is very small, which indicates the good generalization of the method using different dataset splits.
Chronic Classification Results
We carried out five different classifications using the CNN scheme shown in Table 4.The first two classifications were made without a data augmentation process, which led to a very unbalanced training.In the first experiment, we trained our data without modifications, while for the second, we calculated the training weights for each class based on their number of elements.The rest of the classification were made by adding the new elements generated with SMOTE, ADASYN, and our convolutional VAE network to the data set.
We used Sensitivity (Recall), Specificity, and Score metrics defined in the same way as the authors did in Reference [11]: where C represents the correctly recognize samples, and N represents the total of the specified class.
In Table 5, we can see the metrics obtained with the five experiments over the chronic classification.Furthermore, well-known metrics, such as precision, recall, and F-Score, have been calculated.The dataset oversampled using VAE achieved the best results with all the metrics.Whereas sensitivity has very high values in all the cases, specificity, precision, and recall show a very poor performance in all the other cases due to the miss-classification of the healthy class.It is also important to notice the high classification of healthy individuals according to the precision score.This is very important due to the high risk of classify a non-chronic or, even worse, a chronic disease as healthy.
In Figure 7, the confusion matrix obtained for the unbalanced classifications and the best oversampling technique are shown.As we can see, in all the experiments, the Chronic class obtains the better results.However, the unbalanced experiments show a very bad performance in the healthy classification, obtaining 0% of Specifity.Our proposal with the balanced dataset demonstrate that by adding new synthetic Mel Spectrogram created with a convolutional VAE yields very good classification for all the classes.Furthermore, in Figure 8, we can see a comparison between our proposal and the methods found in the state-of-the-art of the ICBHI dataset.The results show that our method improves all of the papers in the state-of-the-art.
Experimental Setup
As we did in the chronic classification, the first step we carried out was a normalization using the min-max scaler techinque.A study of the distribution of the pathology classes was done, and it demonstrates that 86.20% of the samples belong to COPD disease (see Table 6).LRTI and asthma have just two and one samples, respectively, so we decided to ignore them for our classification.The same augmentation data algorithm has been carried out to increase the number of samples of all the diseases except that of COPD.In the end, our dataset was made up of a total amount of 4874 spectrograms.We used the same CNN as in Section 4.2.1, except for the output layer which, in this case, has six neurons, one for each class.All of the training parameters were also the same.
In order to avoid random factor, a 10 cross validation has been carried out in all the experiments showing in all the tables the mean value of the metrics.The intermediate results for the proposal can be shown in Table 7.
Table 7.All the iteration results for the 10 cross validation steps using the proposal combination of VAE for data augmentation and a CNN for the classification step on pathologies dataset.As we can see, the standard deviation is also very small on pathologies dataset, which indicates the good generalization of the method using different dataset splits.
Pathology Classification Results
As we did in the chronic classification, we carried out five different classifications using the CNN scheme shown in Table 4 for unbalanced, weighted and balanced datasets.For the classification of most pathologies, the more challenging one, the same metrics were defined in the following way: As we can see in the table, the behavior is exactly the same as in the chronic-non-chronic detection.Dataset augmented using our VAE architecture proposal, outperforms with all the metrics the performance shown by all the other augmentation techniques and even with the raw dataset.In comparison with the ternary classification, on this experiment just VAE augmented dataset achieved optimal results according to Sensitivity.Taking into account the F-Score value, which is one of the most reliable metrics, of our proposal outperforms the second better method (ADASYN augmentation) by more than 72%.
In Figure 9, the three confusion matrix obtained for the two unbalanced and the best balanced dataset are shown.
Conclusions and Future Work
In this article, a new procedure has been proposed to detect respiratory pathologies.In the analysis of medical data, it is very common to have very unbalanced data sets.In our work, we proposed a convolutional variational autoencoder to increase the rare classes.We transformed all respiratory audios into Mel Spectrograms to work with convolutional networks.These types of networks have very fast learning using GPUs and can learn the most relevant characteristics of the images analyzed for themselves without the need for a description step.We carried out two different locations; one for detecting chronic, non-chronic, and healthy pathologies in breathing and the other for identifying these pathologies from each other.In the first experiment, results showed 0.991 of sensitivity and a 0.994 of specifity outperforming all the studies of the state-of-the-art.Furthermore, a new and more challenging experiment with five different (and the healthy one) classes was carried out, with promising results, with the same CNN with a 0.988 score in sensitivity metric and a 0.986 in specificity.
With these results, we can conclude that using Mel Spectrograms and CNNs, pathologies in sounds of breaths can be easily classified even when the training dataset is unbalanced using convolutional variational autoencoders for augmenting the classes with fewer samples.
For future work, we will keep working on the idea of using CNN to deal with variable length audios.The ICBHI dataset samples have similar audio lengths and it would be interesting to be able to train and predict our data without crop or resize the spectrograms no matter how long the audio is.
In addition, it would be nice to be able to detect which parts of the spectrogram emphasizes the disease in order to determine maybe new understandable symptoms by the specialists or even found multiples diseases in the same sample but at different time.
Figure 1 .
Figure 1.In (a), a Variational AutoEncoder (VAE) scheme with the mean and standard deviation layers used to sample the latent vector.In (b), the vanilla autoencoder with a simple latent vector.
Figure 3 .
Figure 3.The sounds were recorded from seven different locations remarked in red.4.1.1.Image Generation In this paper, we are going to deal with audios using their Mel Spectrogram.A Mel Spectogram is a visual representation of the spectrum of a sound on the Mel scale.Mel Scale [28], proposed by Stevens et al. is a perceptual scale of equally-spaced pitches.The conversion of hertzs into Mels is done using Equation (3).
Figure 4 .
Figure 4. Examples of the Mel Spectrograms for the chronic, non-chronic and healthy classes after preprocessing.
Figure 6 .
Figure 6.In (a), the new images generated using the VAE.In (b), the variation between the original and the generated images.
Figure 7 .
Figure 7. (a) Confusion matrix of the unbalanced dataset.(b) Confusion matrix of the unbalanced dataset with weights in the training.(c) Confusion matrix of balanced dataset using our proposal scheme.
Figure 8 .
Figure 8. Comparative between our proposal method and the best results on the state-of-the-art using (International Conference on Biomedical and Health Informatics (ICBHI) dataset.
Figure 9 .
Figure 9. (a) Confusion matrix of the unbalanced dataset.(b) Confusion matrix of the unbalanced dataset with weights in the training.(c) Confusion matrix of the balanced dataset using our proposed scheme with VAE.
Table 1 .
Number of samples for each class.
Table 2 .
Number of samples for each class after data augmentation.
Table 4 .
Scheme of the classification neural network based on convolutional layers.
Table 5 .
Metric results obtained with the five classifications over chronic datasets.
Table 6 .
Number of samples for each class.
Table 8 ,
the aforementioned metrics were calculated for each experiment.
Table 8 .
Metric results obtained with the three classifications over pathologies datasets. | 6,043.8 | 2020-02-01T00:00:00.000 | [
"Medicine",
"Computer Science"
] |
“Comparing riskiness of exchange rate volatility using the Value at Risk and Expected Shortfall methods”
This paper uses theValue at Risk (VaR) and the Expected Shortfall (ES) to compare the riskiness of the two currency exchange rate volatility, namely BitCoin against the US dollar (BTC/USD) and the South African Rand against the US dollar (ZAR/USD). The risks calculated are tail-related measures, so the Extreme Value Theory is used to capture extreme risk more accurately. The Generalized Pareto distribution (GPD) is assumed under Extreme Value Theory (EVT). The family of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models was used to model the volatility-clustering feature. The Maximum Likelihood Estimation (MLE) method was used in parameter estimation. Results obtained from the GPD are compared using two underlying distributions for the errors, namely: the Normal and the Student-t distributions. The findings show that the tail VaR on the BitCoin averaging 1.6 and 2.8 is riskier than on South Africa’s Rand that averages 1.5 and 2.3 at 95% and 99%, respectively. The same conclusion is made about tail ES, the BitCoin average of 2.3 and 3.6 is higher (riskier) than the South African Rand averages at 2.1 and 2.9 at 95% and 99%, respectively. The backtesting results confirm the model adequacy of the GARCH-GPD in the estimation of VaR and ES, since all p-values are above 0.05.
INTRODUCTION
Since its introduction in 2008, BitCoin is the number one traded cryptocurrency in the world in terms of volume. This decentralized currency can transact without the involvement of the central bank or any financial intermediaries. The transactions using BitCoin are done using a BitCoin network where transactions are authenticated on a blockchain. Due to the lack of backing from a central bank or any regulation, BitCoin users and traders are generally exposed or assumed to be at higher risk (volatility). Like all countries in the world, BitCoin trading in South Africa has gained momentum. This means that there are growing movements of people's investments between the South African Rand, which is the currency used to transact in the Republic of South Africa, and the BitCoin, and investors are thus exposed to market risk.
To measure market risk associated with any financial asset, the Basel Committee on Banking Supervision (BCBS) is responsible for developing supervisory guidelines for banks and financial trading desks. BCBS has recommended that Value at Risk (VaR) be computed and reported. VaR is a statistic that measures the riskiness of financial en-
LITERATURE REVIEW
Regardless of the popularity of VaR, its limitations are well documented by many researchers. Rockafellar and Uryasev (2002) showed that VaR is not only incoherent but also fails to precisely estimate the risk of loss when the loss distributions have'fat tails'. "This significantly discreditsthe accuracy of this risk measure" (Chen, 2018). Nonetheless, VaR remains a popular risk measure as it is very simple to calculate and understand. Artzneret al. (1999) not only showed the incoherence of VaR but also introduced the Expected Shortfall, and called it a perfect risk measure. Pflug (2000) showed that ES is a coherent risk measure, based on coherent risk measure theory.ESisarisk measure sensitive to the shape of the tail of the distribution of returns on a portfolio, unlike the more commonly used VaR.
In order for risk practitioners to fully captureextreme or'tail'risk (very big uncertainty or fluctuation in returns)as mentioned in BCBS (2019), Extreme Value Theory (EVT) has been developed. The field of EVT was pioneered by Fisher and Tippett (1928) and Pickands (1975). Fisher and Tippett (1928) obtained three asymptotic limits describing the distributions of extremes assuming variables are independent. The arguments leading to modelling extremes using the generalized Pareto distribution are attributable to Pickands (1975). EVT is the theory of measuring and modeling extreme events (large fluctuations) (tails of statistical distributions), i.e. it is well suited to financial assets with extreme returns (very large fluctuations in returns). The EVT assumes independent and identically distributed (iid) observations. This iid assumption does not always hold for financial time series data. To correct this, McNeil and Frey (2000) proposed a twostage methodology in the form of a GARCH-EVT model using five index returns in his illustrations. The first step is to capture the heteroscedasticity (non-constant variation or fluctuations) features by fitting a GARCH model. The second step is to apply the EVT to residuals extracted from a selected GARCH model using the Generalized Pareto Distribution (GPD) or the Generalized Extreme Value Distribution (GEVD). The second part of this modelling process allows one to capture or describe the large fluctuations in prices and returns. The merits of the GARCH-EVT hybrid model lie in its ability to capture conditional heteroscedasticity (changing variation) in the data through the GARCH framework, while at the same time modelling the extreme tail (large fluctuations) behavior through the EVT method. Byström (2004) applied the GARCH-EVT model to the Swedish and American stock markets and compared different EVT-AMS methods and the Peak over Threshold (POT) method, which in general perform similarly. Murenzi et al.(2015) used the hybrid GARCH models with the EVT model to estimate VaR for the Rwandese currency exchange rate. Their findings indicated that the filtered EVT model performed better than ARMA-GARCH models. Chebbi and Hedhli (2014) applied the GARCH-EVT in managing portfolios with time-varying copula in the Tunisian, American, French, and Moroccan stocks. The copula is able to quantify the interdependence betweenthe different countries' stocks. Koliai (2016) presented a GARCH-EVT model with an R-vine model to manage portfolio risks that consisted of equity, currency indices, and commodities. Chinhamu et al. (2017) investigated the performance of the Generalized Lambda Distribution (GLD), the Generalized Pareto Distribution (GPD), and the Generalized Extreme Value Distribution (GEVD) in modeling daily VaR and ES in platinum, gold, and silver price log-returns. Their findings showed that GPD and GLD generally outperform GEVD for VaR and ES estimation for negative precious metal returns.
This study seeks to apply this hybrid model (GARCH-GPD) in the calculation of the VaR and ES using data from exchange rates BTC/USD and ZAR/USD and to compare their riskiness.
METHODOLOGY
This section describes the three steps that will be taken to fit the model. Secondly, extreme value theory (EVT) is then used to model the tail behavior of the data. The VaR q (X) is then calculated using the Generalized Pareto Distribution (GPD) tail estimation procedure.
Finally, the VaR of the asset is computed using the following formula: where is µ t+1 is the forecasts from the mean equation and σ t+1 is estimated from the volatility prediction model. VaR q (X) and ES q (X) are the VaR and ES of the standardized residuals.
ARMA -GARCH
GARCH models allow one to explain the varying, up and down movements (volatility), in asset prices,e.g. Bitcoin prices, and ZAR/USD exchange rates. The GARCH family volatility models to be considered are GARCH (1,1), EGARCH(1,1), GJRGARCH(1,1), and APARCH(1,1). All four volatility models are to be fitted to the exchange rates and their residuals are used in modelling the tail behavior of the series.
The GARCH(p, q) volatility model is mathematically defined as: where α i and β j are respectively ARCH and GARCH terms, and w is a constant; σ t 2 and σ t-1 2 are respectively the fitted conditional volatility from the model and its previous value. ε t 2 are the squared error terms in the model. The simplest model, the random walk with GARCH(1,1) variance/volatility model, is of the form: Exchange rates are unpredictable, and it makes sense to assume a random walk model.
Exponential GARCH (EGARCH) model
The EGARCH model allows efficient capturing of volatility clustering and asymmetric effects. An EGARCH(1, 1) volatility model can be expressed as: where w, α 1 , β 1 are model coefficients. γ is the leverage effect.
GJR-GARCH model
The GJR-GARCH volatility model was proposed by Glosten et al. (1993). This model takes into account the asymmetry property of financial data in obtaining the conditionals.
EVT -The Generalized Pareto Distribution (GPD)
The peak over threshold (POT) approach in fitting the Generalized Pareto Distribution (GPD) is used to model the standardized residuals from the selected GARCH family model. Balkema and deHaan (1974) and Pickands (1975) showed that for threshold u that is large enough, the POT approach leads to the use of the GPD. The GPD is defined as follows: where x> 0 when ξ ≥ 0 and 0 ≤x≤ -β/ξ. When ξ< 0 and β> 0, G ξ,β (x) is a GPD with the shape parameter or tail index ξ, a scale parameter β and a threshold u The value of ξ shows how heavy the tail is, with a bigger value indicating a heavy tail.
Parameter estimation of GPD
Let u be a sufficiently high threshold, assuming n observations y such that y iu ≥ 0, the subsample {y 1u, ..., y n -u} has an underlying distribution of a GPD, where y iu ≥ 0 for ξ ≥ 0, 0 ≤ y i -u ≤ -β/ξ for ξ< 0, then the logarithm of the probability density function of y iu is: Then the log-likelihood L(ξ, β| y i -u) for the model is the logarithm of the joint density of the n observations, i.e.
The parameters (ξ, β) are obtained by maximizing the log-likelihood function of the subsample under a suitable threshold u.
Conditional VaR
If F is an extreme distribution above some threshold u, then the F u (x) = G ξ,β (x), where 0 ≤ x<x Fu and ξ∈ℝ and β> 0, if x≥u then: Given F̅ (u), F̅ (x) is the formula for survival tail probabilities, it is inverse, gives the highest quantile of the distribution which represent the Value at Risk and is given by: and the Expected Shortfall is given as: . 11
Backtesting
To assess model adequacy and effectiveness in the computation of VaR, two backtesting methodologies are used. The Kupiec unconditional coverage test (Kupiec, 1995) and Christoffersen conditional coverage test (Christoffersen, 1998 (15) where Φ ij is the number of returns in state i who have been in state j previously (state 1 indicates that the VaR estimate is violated and state 0 indicates that it is not) and π i is the probability of having an exception that is conditional on state i the previous day. This statistic follows a chi-square distribution with two degrees of freedom.
RESULTS
Quantitative exchange rates data was collected and modelled so as to achieve the set objectives. Data was obtained from the finance sector website (Investing.com). The currencies considered are the South African Rand (ZAR) against the US dollar (USD) and the BitCoin (BTC) against the US dollar. The data was analyzed in an R-programming environment. The daily exchange rates considered were from 1/1/2015 to 30 /06/2021. The log returns were calculated and used to do the modelling.
The formula used is: whereP t and P t-1 are today and yesterday's closing values of daily prices (exchange rates), respectively.
In Figures 1 and 2, the time series plots reveal several trends in the mean and variance, confirming non-stationarity of the exchange rates prices. The log returns are stationary, around the zero-mean, although volatility is non-constant and clustered, indicating heteroscedasticity, and is common with financial data. Isolated extreme returns are visible and are caused by shocks in the financial markets. Table 1 gives the descriptive statistics of the two exchange rates.
A positive mean for BTC/USD indicates a small increasing trend over time, whereas the opposite is true with a negative mean for the ZAR/USD, indicating a slight decreasing trend over time for the return series.
The Jarque-Bera test rejects the null hypothesis of Normality at the 5% level of significance, suggesting that extreme value theory distributions could be useful in capturing any heavy tails.
Source: Authors' own work. The p-value of the Ljung-Box test for ZAR/USD returns confirms non-rejection of the null hypothesis of no autocorrelation. The fitting of a statistical distribution usually assumes homoscedasticity and no autocorrelation. However, autocorrelation is confirmed for the BTC/USD sincep-value = 0.0006249 < 0.05. The two step approach will therefore be used to help deal with the autocorrelation.
The null hypothesis of no ARCH effects is rejected at the 5% level of significance using the ARCH LM test, suggesting the use of GARCH family models should be considered when analyzing the above-mentioned return series The unit root test and stationary tests show that, at the 5% level of significance, the null hypothesis of a unit root is rejected, and it can be concluded that both exchange rate return series are stationary. The KPSS test results shows that all returns are stationary, since all p-values are greater than 0.05, therefore the null hypothesis of stationarity is accepted
GARCH-EVT models
Based on literature and the financial characteristics presented above, using GARCH-EVT model could lead to a better measure of risk in the tail. As the return series are non-Normal and have a heteroscedasticity feature, as suggested in other research work, using EVT and GARCH model to capture some features of the data is necessary.
All the four GARCH(1,1) models were estimated with both Normal distributed errors and Student's t-distributed errors. Their residuals were extracted, standardized and used to fit the Generalized Pareto distribution models. The aim is to fit a statistical distribution (the GPD) to the extreme residuals and use the estimated parameters and formulas to calculate VaR and ES.
To estimate the GPD model, a thresholdu must be selected. This threshold determines the number of observations above the threshold, N u . As the rule of thumb also suggests that it is ideal to choose the threshold that gives about 100 observations for fitting the Pareto distribution when the data set is large enough (McNeil & Frey, 2000).
The mean excess plots determine a suitable threshold, which is necessary for fitting the GPDmodel.
The choice of a threshold should be depicted by linear increases in the mean excess plot. Figure 3 presents the mean excess function of BTC/USD returns. By observing the meanexcess function in Figure 3, a threshold of between 0.8 and 1.5 seems to be a reasonable choice. The 90th percentile was selected. It provided a reasonable choice as it yielded enough data points for analyses and it falls within the above range.
The parameters of the GPD were estimated using the Maximum Likelihood method and are presented in Table 3.
n and t represent the assumption of Normal and Students't-distributed errors, respectively.Most of the ξ are positive, suggesting the presence of heavy tails, except for the APARCH-GPD-N and eGARCH-GPD-N models.
After observing the mean excess function for ZAR/USD in Figure 4, a threshold of between 0.8 and 1.8 seems to be a reasonable choice for ZAR/USD returns. Again, the threshold at 90th percentile was selected. This is a reasonable choice as it yields enough data points for analyses and it falls within the above range. The pa-Source: Authors' own work. rameters of the GPD were estimated using the Maximum Likelihood method and are presented in Table 4.
Again, n and t represent the assumption of Normal and Student's-distributed errors.
All the ξ are positive suggesting the presence of heavy tails. The ξ for the ZAR/USD are bigger and positive, suggesting that it may be a riskier asset; however, the standard errors of the estimates of ξ are bigger as well. The VaR and ES will give a better picture of the risk.
Value at Risk and Expected Shortfall
The Value at Risk and Expected Shortfall values are calculated at 95% and 99% levels for both exchange rates understudy. Tables 5 and 6 show the estimated values of each VaR and ES.
At both the 95% and 99% levels of significance, daily VaR data suggests that Bit Coin is riskier than the South African rand, as the VaR statistic is higher. The higher VaR statistics mean that one loses more at a specified level of significance.
Source: Authors' own work.
Back testing results
for Value at Risk The estimated VaR are back tested using the Kupiec unconditional coverage test and Christoffersen conditional coverage. The p-values of each test are presented in Table 7.
Based on the p-values from both Kupiec likelihood ratio test and Christoffersen's test likelihood ratio test, the fitted GARCH-GPD models are well suited to the returns series understudy, since the observedp-values are greater than 0.05. Hence, the null hypothesis of model adequacy is accepted.
DISCUSSION
Four GARCH models are applied to the two data sets understudy, namely: the BTC/USD and the ZAR/USD. All four models were considered under two commonly used error distributions, that is normally and Student's t distributed residuals. The residuals were extracted and used to fit Generalized Pareto Distribution, and the estimated parameters were used to estimate risk statistics.
Under the BTC/USD time series, the extreme value index (ξ) seems to be inconclusive as to whether the tails are heavy or short. The GARCH models with Normally distributed errors would mean the tails are short, while the Student's t distributed errors suggest that the tails are heavier. In the case of the ZAR/USD currency series, the EVI suggests that the tails are heavy, hence the use of the EVT model is deemed more appropriate.
The computed values of both VaR and Conditional VaR indicate that there is a higher amount expected to be lost in the BTC/USD than in the ZAR/ USD at both the 95% and 99% confidence levels. This leads to the conclusion that the BTC is riskier than the ZAR. This could be due to the fact that the BTC is not backed by any central bank and is unregulated hence making it highly risky to keep as a savings tool. This information is useful to South African and global investors who need to understand how much risk they take when converting their savings or investments to BitCoin instead of the South African currency, the Rand (ZAR).
The backtest results gave p-values that are way above 0.05. The high p-values indicate that the hybrid model used in the study isgoodand fitsthe currency data set used. The Kupiec test suggests that the GARCH(1,1)-GPD with Normally distributed errors is the best fitting model for BTC/USD, while eGARCH(1,1)-GPD with Normally distributed errors is the best-fitted model for ZAR/USD, as they both have higher p-values at both 95 % and 99% significance levels.
Christoffersen's test likelihood ratio test enables one to ascertain whether the output model violations are independent.A violation is when the actual loss exceeds the VaR estimate. In all the models, the p-values are greater than 0.05, leading to a conclusion that indeed the violations are independent of each other.
CONCLUSION
The purpose of this study is to use VaR and ES to compare the riskiness of the daily returns of the BitCoin (BTC) and South African Rand (ZAR), both currenciesbeingagainst the US Dollar. Both VaR and ES conclude that BTC is riskier than ZAR. This could be of great help to forex market risk managers in South Africa, particularly in choosing whether to keep their savings in the local currency or consider the cryptocurrency, BitCoin.
The hybrid model did capture fat tails and improved the computation of the VaR and ES as shown by the positive EVI (ξ) and backtesting procedures. The high p-values above 0.5 suggest that the GARCH (1,1)-GPD is a very good fit for the two currencies.
These results do not imply that GARCH (1,1)-GPD will always give good fits for every currency data set.
For further research, out-of-sample backtests and comparisons with generalized POT models are recommended, such as DIPOT (Dynamic Intensity Peaks Over Threshold) and PORT (Peak Over Random Threshold). | 4,558.4 | 2022-07-04T00:00:00.000 | [
"Economics"
] |
Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction
Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder – i.e., the local ordering principles – must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction – a method that allows single crystal diffraction measurements on sub-micron sized crystals – and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr0.82Y0.18O1.91) and demonstrate the reliability of the proposed approach.
REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): This manuscript by Schmidt et al demonstrates the use of diffuse electron scattering to probe local structural ordering in yttria-stabilized zirconia.The results are compared to some authors' recent work with diffuse x-ray scattering and diffuse neutron scattering (Schmidt et al, Acta. Cryst. B 79, 2023).Yttria-stabilized zirconia has been extensively studied already (with proper citation in this manuscript), with the previous work in Acta Cryst.demonstrating the value of the newer 3D-ΔPDF approach.The main innovation in this manuscript is the use of electrons to achieve a full reciprocal space volume (as opposed to oriented sections) suitable for 3D-ΔPDF analysis.This is a nice paper, and the proposed application of diffuse electron scattering to smaller crystals may help open up the study of short-range order to a broader community.I have a few comments and questions: 1) The introductory discussion on interpretation of 3D-ΔPDF (lines 59-70), while technically correct, is difficult to follow.It might help to more clearly distinguish between a correlation and its signal in the 3D-ΔPDF (these two can be identified with one another, but it reads as a circular definition).
2) The presented analysis is very much focused on fitting relaxations around vacancies, but the presence or absence of chemical short-range order needs to be mentioned more clearly.Clear statements about ordering or the absence of ordering between Zr/Y atoms and between metal atoms and vacancies would be helpful for those not already familiar with the system; more importantly, the presence of chemical SRO will add additional a peak to the very regions of the 3D-ΔPDF, potentially complicating the fitting analysis done here.The authors do state that vacancyvacancy pairs at <½½½> vectors are more clearly observed with electrons than neutrons, which is a good finding, but it could use a more rigorous statement.Ordering of Zr/Y atoms and expected oxygen vacancies near each type of metal atom should be clearly stated as well.In the absence of such a statemnt, Figure 1 seems to imply that Zr and Y tend towards short-range order, while Figure 4 subtly suggests the distribution of Zr/Y atoms is completely random through its fractional coloring scheme (probably not intentional?).This issue need not take over the paper, but a few clear and well-justified statements on chemical ordering (not just in references) are needed to justify the work on displacements.If chemical ordering can be found directly in the measured electron scattering, all the better! 3) Experimental broadening due to "particular setup" is vague -x-ray and neutron data had a similar resolution to each other (at least in binning); why is the resolution less fine for the electron measurements?I might guess some combination of incident electron energy, detector pixel size, and detector distance for the instrument limited resolution to less than a typical x-ray experiment, but are these truly particular to this setup, or more inherent to electron instruments broadly?Could a currently available electron setup achieve similar resolution to the x-ray and neutron data shown?A long general discussion is not necessary, but a bit more discussion on why this particular setup uses a larger bin size in reciprocal space would be valuable for those not familiar with electron scattering.4) Figure 5 presents the results of quantitative fitting, but these quantities are not quite the same as expected displacements in the system for each kind of intersite pair --the scattering lengths are different for each probe, but the underlying distributions of displacements are the same.Is it possible to infer the expected displacements from the observed shifts?If not, could one make qualitative guesses as to the relative values of the shifts as measured by different probes and show that they match what is fitted?Also, how much does it matter that the positive/negative pairs are not equally displaced from the average position?Part of this might be related to item (2) above.5) A more open-ended question: how much of the observed scattering can be attributed to displacement correlations similar in form to thermal diffuse scattering?Some of the figures (the neutron <½½0> in Fig. 4 is an example) resemble to displacement correlation signatures.This might just need a brief explanation, but this may also affect interpretation of the extracted shifts.
To sum up: I think that the experimental procedure presented here is valuable and interesting, and I think that some clarification on exactly what is being extracted from the data in the analysis could be very helpful to a community that is slowly getting more interested in short-range order.I'd like to make sure that the key points are all being as clearly communicated as possible before the manuscript is published.
Reviewer #2 (Remarks to the Author): In my (not completely unbiased) perception, there have been two topics in the post-pandemic crystallographic conferences that have experienced a particularly strong increase in interest: 3D electron diffraction (3D-ED) and the 3D-DeltaPDF.This is also reflected in a number of papers published in leading scientific journals in recent years.A few of them are cited in this paper.In the present study, the authors show how 3D-ED and 3D-DeltaPDF methods can be successfully combined and open up new possibilities to reliably characterize local structure of disordered structures that have so far eluded detailed investigation: crystallites that have too complex (disorder) structures to be analyzed by powder methods and are too small to be studied by single crystal X-ray methods (or had to be measured at one of the few synchrotron beamlines highly specialized for sub-micro crystals).The authors commendably took the trouble to measure the same structure with X-ray, neutron, and electron diffraction methods and to prepare the data in such a way that 3D-DeltaPDF maps could be successfully calculated in each case.The comparison of the different measurements was complicated by the fact that the respective methods produce different artifacts and have different structural sensitivities.Nevertheless, the authors succeeded in convincingly demonstrating that the analyses for the different methods provide at least semiquantitatively comparable results and that 3D-ED experiments may become a strong complement to X-ray and neutron-based 3D-DeltaPDF investigations.Also, the advantages, disadvantages, and limitations of the different methods are compared and discussed in detail.Below, I will discuss some further limitations of the study, which, however, are not unusual for such an early proof-of-concept study and do not diminish the importance of this paper in any way.On the contrary, I expect that this paper will stimulate further important research.I see no reason why the current limitations cannot be overcome in the near future by more experience and improvement of the available tools, especially since the development of such tools is already in full swing.In the case of 3D-ED, significant progress is currently being made in instrumentation and handling of dynamic scattering effects, while in the 3D-DeltaPDF community a great deal of experience is currently being gained in understanding complex disordered structures and the necessary software is being developed for easier access to the disordered information.The current development of 3D-DeltaPDF tools is focused on X-ray applications, but may straightforwardly be applied to 3D-ED data or easily be adapted.There is no doubt that the 3D-ED / 3D-DeltaPDF combination will benefit greatly from all these developments and will quickly establish itself as an important material characterization tool.I think this paper should therefore definitely be published in nature communication.
My only substantive criticism, which I think requires an adjustment of the manuscript, is the comparison of the measurements of the positions of some 3D-DeltaPDF signals and the conclusion (partly explicit, partly suggested) that the three methods provide quantitatively comparable disorder models.Here I do not fully agree.First, some results show very strong discrepancies, especially in the data shown in the Supplemetary material.There may be good reasons for this due to the different measurement methods, but they had better be rationalized if used as an argument for quantitative comparability of the results from the three measurements.On the other hand, for small displacements, the position of a 3D-DeltaPDF signal is not a good measure of the local displacement correlations.On the contrary, it is almost exclusively the strength of the signal and not the location that is decisive when, for example, two Gaussian functions are subtracted from each other, which is an important feature of 3D-DeltaPDF models.Unfortunately, I am not aware of any literature reference that addresses this, but I have included a plot for demonstration purposes that should be self-explanatory.In other words, a good match in the positions of 3D DeltaPDF signals is not a proof that full quantitative modelling would also give comparable results for displacement correlations.But this would be what we are interested in.Unfortunately, tools for quantitative modelling of 3D-ED / 3D-DeltaPDF models are not available at the moment, so quantitative modelling cannot be required from the authors.However, the text should be worded accordingly a bit more carefully to not suggest wrong conclusions.
The further suggestions for improvement are in the broader sense of linguistic or stylistic nature and I leave it to the authors to accept these or not.
-The term 'correlated disorder' is used several times.I find this somewhat unfortunate, since 'disorder' is more a global descriptor ('disorder model', 'disordered structure', etc., also the term 'disordered atom' is more associated with average structure properties) and less about very localised properties, which are seen in the 3D-DeltaPDF.I would prefer a continuous use the term 'local order' as a more accurate description.
-In the second line of the abstract it is written about 'intentional introduction of disorder'.I think this is a bit unfortunate, since unintentional disorder can be just as interesting.
-line 34ff: It would be good if some non-perovskite examples were also listed.
-line 158: new symbols Delta^-_OO etc. are introduced without defining them.In the course of the text the meaning became clear to me, but without explanation they could be misunderstood.
-Fig.4: I cannot distinguish the colors for Zr and Y.Maybe a better color coding would be helpful.
-line 179: In the context of 3D-DeltaPDF features I would speak of 'densities' instead of 'intensities', because they are derived from scattering densities.
-lines 218 -235: It is repeated several times that ED is more sensitive to light elements than Xray diffraction, which affects the readability of this paragraph.Consider rewriting this paragraph.
-Chapter 'Challenges ...' The challenge of multiple scattering in ED should be included in this paragraph.An additional paragraph discussing the possible influence of multiple scattering on the 3D-DeltaPDF would certainly be interesting, in particular, since some of the authors already have a lot of experience regarding average structure refinements based on 3D-ED diffraction.Would this experience be transferable to diffuse scattering?-Supplement chapter 4: I would write of 'dashed lines' instead of 'dotted lines' and again replace 'intensities' with 'densities'.Also one should write that the crossing points of the lines describe the average interatomic vector.In S4 there are four crossing points which should be listed in the caption.
Dear Authors
The present study describes a successful use of electron diffraction data for conducting 3D local structure analysis on an inorganic material of technological interest, namely yttria stabilized zirconia.The general goal is to demonstrate that the analysis of local structure such as the spatial arrangement of defects and displacive disorder can be determined reliably and in 3D by electron diffraction, thus overcoming crystal size limitations imposed by single crystal X-ray and neutron diffraction.In this respect, this study presents a convincing use of electron diffraction data for conducting 3D-deltaPDF analysis, while conveniently comparing it with analogous results from Xray and neutron 3D-deltaPDFs that have been previously published.
Overall, the study conveys an important message and highlights prominent challenges that need to be solved to make this technique more robust and widely used.As for the "quantitative" aspects of it, particularly standing out in the title and the manuscript itself, I believe that this study should put forward some more caveat and cautionary considerations.In the context of modern crystallography and materials science, this work constitutes an important step beyond the state of the art, which undoubtedly qualifies it for publication.I do have a few points, though, which in my view require attention and I will elaborate in the following.I therefore consider this work valuable as a Nature Communications article after some minor revisions are addressed.
1. Line 41.The Authors mention that the analysis of Bragg diffraction is well established.I would also add that is even "automated", since less and less is left to humans in current crystallographic routines, and crystal structures can be solved by essentially autonomous software (such as the Autochem plugin by Rigaku) when data quality is not particularly problematic.
2. Line 68.The Authors state that the average interatomic vector of neighbouring atoms that vibrate in-phase "is smeared out by the average structure atomic displacement parameters (ADPs)".I understand the intended meaning, but ADPs are used to model electron density distribution, therefore they cannot have any smearing effect themselves.I assume the Authors intended something like "is smeared out in the average structure, as modelled by atomic displacement parameters (ADPs)".For this reason, I think this sentence should be rephrased to make it more accurate.
3. Line 73.I would be more explicit on the crystal size, since "macroscopic" has different meanings depending on the context.Perhaps the Authors can consider using the word "micrometric", and preferably pairing it with "currently" and "in general" to be on the safe side, since sub-microcrystal XRD can be performed in numerous synchrotrons worldwide.
4. The Authors correctly point out that the importance of analyzing nanocrystals is primarily due to the fact that their correlated disorder might be different from their microcrystalline analogues.However, I find this aspect addressed very little when describing the interpretation of the data.For example, at line 130 the Authors describe the broadening of electron diffuse scattering data compared to the X-ray and neutron diffraction one, attributing it to the experimental setup simply based on the fact that both Bragg and diffuse scattering features are affected by broadening at the same time.I believe there are numerous microstructural characteristics that can differ between large microcrystals and nanocrystalline samples, affecting both diffuse scattering and the Bragg peaks' profiles.This is not only a matter of short-ranged correlated disorder, but can also relate to coincidental change in mosaicity and crystallite size.Such effects can also be found in the PDF space, which would potentially invalidate the statement at line 146: "This is a direct consequence of the experimental broadening of the diffuse scattering".I agree that broadening of diffuse scattering relates to correlation lengths in real space, but I am concerned with the use of "experimental" as in 'due to the experimental setup' (meaning in particular all the set of distortions that come with an electron diffraction experiment).I think this is an important aspect to clarify, and personally I would keep the option of having real structure effects impacting patterns and PDFs, which are therefore not due to experimental setup, while having analogous effects.Addressing these aspects could also give the Authors a good chance to comment on the challenge of discriminating the two sources of broadening (structural changes vs. 'experimental' broadening), and the need of quantifying the instrumental sources of distortions in total scattering data from electron diffraction, as well as their effects in the PDF space.This aspect should also be kept in mind when, further in the manuscript, the Authors consider the quantitative differences of correlation lengths.In lines 202 and 205-207, these differences are attributed to the fact that probing matter with electrons and with X-rays or neutrons provides different lengths because of different sensitivity to "structural aspects".However, I would also specify that differences due to the nanocrystalline nature of the sample and its different, unknown microstructure can also be a cause of such varying correlation lengths.
5. The proposed PDF analysis is useful and in line with what previously published based on X-ray and neutron data, but there is an aspect that I did not find addressed explicitly: the impact of vacancy defects on the PDF space.The interpretation appear focused on the consequences of vacancies on structural distortions, leaving the reader with the impression that the only information available from the 3D-deltaPDFs is displacive disorder, and no localisation and quantification of correlation signals due to lack of density (presence of defects) can be distinguished.This might indeed be true, and I believe that, in case, the Authors should state this clearly to better guide the readers.It would be useful to mention qualitatively and briefly what kind of signals can be expected when vacancy defects are present and why they are not interpretable from the available experimental delta-PDFs of nanocrystalline yttria stabilized zirconia.
6.The Authors address the quantitative reliability of the 3D-deltaPDF analysis by comparing correlation lengths in terms of positions of maxima and minima between X-ray, neutron and electron PDFs.I find this a relatively weak part that could be improved, and I will elaborate in the following.
In my view, there are two aspects that can be considered concerning 'quantitative reliability' in the PDF space: the positions of the correlation vectors, and the numerical values (maxima/minima or integrals) of the correlation signals.It appeared to me that the Authors focus selectively on the first aspect.Nonetheless, the second, too, contains important defect structure information, which can be made less reliable due to artefacts from data processing, instrumental broadening, or multiple elastic and inelastic scattering.It is not possible to use comparisons with XPDFs or with neutron PDFs for assessing quantitative reliability, because both shift magnitudes and integrals at specific correlation vectors can be influenced by the fact that nanocrystals can have different local structures, and because, as the Authors pointed out, "different radiations are sensitive to different structural aspects".For this reason, I believe that using such comparisons to evaluate the quantitative reliability does not help much, and indeed this section concludes with the Authors acknowledging that differences are "to be expected".I consider these comparisons nonetheless useful, but I wonder whether the Authors could be more transparent with respect to this ambiguity in quantitative reliability, and formulate how it could be determined more appropriately.This remains an open question that does not stand out enough, in my opinion.It could also become an important point to be presented in the "challenges that need addressing" section: how can we validate our 3D-deltaPDF from electron diffraction data, since we cannot compare it with neutron and X-ray PDF analysis due to the different nature of the beamsample interaction and the possibly different local structure?7. The supplementary material is missing the pristine reciprocal space reconstructions of the main planes of the sample (hk0, h0l, 0kl).Since the production of diffuse scattering reconstructions required not only a reasonable symmetry averaging, but also other steps such as "Karen" filtering, punch-and-fill, and gaussian-dampening, it would be most informative for the readers-especially those who are willing to conduct similar analyses in the future-to have an idea of the pristine reconstruction and possibly some intermediate steps of the data processing.Furthermore, punchand-fill procedures have also an important effect on the features observed in the 3D-deltaPDF, especially the choice of punch radius.Indeed, different punch radii may change the integrals and shift of correlation peaks, as the Patterson function might partly contribute, which is a likely possibility when the diffuse scattering is primarily originating from correlated distortions in the structure.Ideally, the chosen punch radius should be justified, and the effect of different punch radii could be briefly shown to give an idea of how much this process affects the features that are discussed in the manuscript.This would also provide useful insights on the quantitative side of this analysis, since it is a central aspect the Authors aimed at.8.When addressing the challenges of the method, the Authors describe three main points: limited reciprocal space coverage, sample stability to the electron beam, and dynamic range of the detector.However, I think an important aspect is missing: the presence of non-kinematical elastic or inelastic scattering.Kikuchi diffraction and other inelastic scattering events can produce broad band-like intensities that might be problematic to distinguish and separate from the data, adding undesired features to the 3D-deltaPDFs.This is particularly relevant for inorganic samples such as the one addressed in this study, where the Authors took care of preparing it as a thin lamella.The strong influence of sample thickness, ubiquitous presence of undesired multiple and inelastic scattering, and the possibility of using energy-filtered diffraction to at least eliminate most of these intensities, would all be important aspects to be discussed in this last section.
Furthermore, the challenge of validating the electron 3D-deltaPDF analysis with complementary techniques for the reasons described above can also be proposed as an open challenge, since there is no standard practice, as far as I am aware, for this purpose.9.I did not find, in the cited literature, the use of electron diffraction data for 1D PDF analysis, as reported by Gorelik et al. in 2015 (Microscopy andmicroanalysis, 2015, 21(2), 459-471) and later improved towards a quantitatively reliable technique (Gorelik et al. Acta Cryst. 2019, B75, 532-549).This is not only highly relevant to this study, but it might also allow a better quantitative reliability assessment of the electron 3D-deltaPDF analysis by comparing the electron 3D-deltaPDF with its 1D analogue, which, in turn, can be more reliably compared to 1D XPDF.10.Just a couple of writing slips I noticed.Line 44: Since the subject is "powder pair distribution function analysis", I believe the subsequent verb should be "has been".In the caption of Figure 4, line 175 reads "diffraction patterns a simplified model".I imagine "from" should be inserted before "a simplified model".
Finally, I would like to congratulate the Authors on this beautiful work and wish them all the best for the revision process.
Reviewer #1:
This manuscript by Schmidt et al demonstrates the use of diffuse electron scattering to probe local structural ordering in yttria-stabilized zirconia.The results are compared to some authors' recent work with diffuse x-ray scattering and diffuse neutron scattering (Schmidt et al, Acta. Cryst. B 79, 2023).Yttria-stabilized zirconia has been extensively studied already (with proper citation in this manuscript), with the previous work in Acta Cryst.demonstrating the value of the newer 3D-ΔPDF approach.The main innovation in this manuscript is the use of electrons to achieve a full reciprocal space volume (as opposed to oriented sections) suitable for 3D-ΔPDF analysis.This is a nice paper, and the proposed application of diffuse electron scattering to smaller crystals may help open up the study of short-range order to a broader community.I have a few comments and questions: 1.The introductory discussion on interpretation of 3D-ΔPDF (lines 59-70), while technically correct, is difficult to follow.It might help to more clearly distinguish between a correlation and its signal in the 3D-ΔPDF (these two can be identified with one another, but it reads as a circular definition).
The wording was adapted to avoid the term correlation in the description of the PDF signal.The term correlation is now only used with respect to structural correlations causing the observed diffuse scattering.We now use consistently the terms density and intensity to describe the features in the 3D-PDFs.
2. The presented analysis is very much focused on fitting relaxations around vacancies, but the presence or absence of chemical short-range order needs to be mentioned more clearly.Clear statements about ordering or the absence of ordering between Zr/Y atoms and between metal atoms and vacancies would be helpful for those not already familiar with the system; more importantly, the presence of chemical SRO will add additional a peak to the very regions of the 3D-ΔPDF, potentially complicating the fitting analysis done here.The authors do state that vacancy-vacancy pairs at <½½½> vectors are more clearly observed with electrons than neutrons, which is a good finding, but it could use a more rigorous statement.Ordering of Zr/Y atoms and expected oxygen vacancies near each type of metal atom should be clearly stated as well.In the absence of such a statemnt, Figure 1 seems to imply that Zr and Y tend towards short-range order, while Figure 4 subtly suggests the distribution of Zr/Y atoms is completely random through its fractional coloring scheme (probably not intentional?).This issue need not take over the paper, but a few clear and welljustified statements on chemical ordering (not just in references) are needed to justify the work on displacements.If chemical ordering can be found directly in the measured electron scattering, all the better!We agree that in the former version of the manuscript the discussion of potential chemical short-range order was too short.We added clarifications about the dominance of relaxations for YSZ as a model system and commented on potential local order for the evaluated interatomic vectors in the revised version.Specifically, sentences (marked in yellow in the resubmitted manuscript) were added to the Introduction (page 6), Results (page 10, page 12), and the Discussion (page 15).
3. Experimental broadening due to "particular setup" is vague -x-ray and neutron data had a similar resolution to each other (at least in binning); why is the resolution less fine for the electron measurements?I might guess some combination of incident electron energy, detector pixel size, and detector distance for the instrument limited resolution to less than a typical x-ray experiment, but are these truly particular to this setup, or more inherent to electron instruments broadly?Could a currently available electron setup achieve similar resolution to the x-ray and neutron data shown?A long general discussion is not necessary, but a bit more discussion on why this particular setup uses a larger bin size in reciprocal space would be valuable for those not familiar with electron scattering.
We added further information on experimental broadening related to inelastic scattering and sample preparation in the main text (Results, page 8 and 9).
To address the issue of the binning size we added in the SI section 6 the respective fits for the X-ray and neutron data also binned to a grid of 201x201x201 voxels to show that the binning introduces no deviations that are larger than the estimated standard deviations from the shifts for these most local correlations examined here.
4. Figure 5 presents the results of quantitative fitting, but these quantities are not quite the same as expected displacements in the system for each kind of intersite pair -the scattering lengths are different for each probe, but the underlying distributions of displacements are the same.Is it possible to infer the expected displacements from the observed shifts?If not, could one make qualitative guesses as to the relative values of the shifts as measured by different probes and show that they match what is fitted?Also, how much does it matter that the positive/negative pairs are not equally displaced from the average position?Part of this might be related to item (2) above.
As it turns out, the shift magnitudes based on the same model in fact depend on the probe used, i.e., the shift amplitudes differ in 3D-ΔPDF maps for X-rays, electrons, and neutrons.We included a discussion of this aspect in the supporting information in Section 9 on page 19. Figure S15 was added to the same section and demonstrates the discussed effect by extracting the shift magnitudes from simulated model data that was calculated from the identical model crystal.
5
. A more open-ended question: how much of the observed scattering can be attributed to displacement correlations similar in form to thermal diffuse scattering?Some of the figures (the neutron <½½0> in Fig. 4 is an example) resemble to displacement correlation signatures.This might just need a brief explanation, but this may also affect interpretation of the extracted shifts.
We attribute the majority of our observed correlations to displacement correlations of static rather than dynamic origin.Temperature dependent measurements or energy discriminating neutron diffraction measurements could help to resolve the question of how much thermal diffuse scattering contributes to the experimentally observed diffuse scattering.Previous studies showed that diffuse scattering due to oxygen mobility only starts at elevated temperatures and therefore, we do not take this into account here.We clarified this by adding new references 43 and 44 on page 10 (line 192) of the updated manuscript.
To sum up: I think that the experimental procedure presented here is valuable and interesting, and I think that some clarification on exactly what is being extracted from the data in the analysis could be very helpful to a community that is slowly getting more interested in shortrange order.I'd like to make sure that the key points are all being as clearly communicated as possible before the manuscript is published.
In my (not completely unbiased) perception, there have been two topics in the post-pandemic crystallographic conferences that have experienced a particularly strong increase in interest: 3D electron diffraction (3D-ED) and the 3D-DeltaPDF.This is also reflected in a number of papers published in leading scientific journals in recent years.A few of them are cited in this paper.In the present study, the authors show how 3D-ED and 3D-DeltaPDF methods can be successfully combined and open up new possibilities to reliably characterize local structure of disordered structures that have so far eluded detailed investigation: crystallites that have too complex (disorder) structures to be analyzed by powder methods and are too small to be studied by single crystal X-ray methods (or had to be measured at one of the few synchrotron beamlines highly specialized for sub-micro crystals).The authors commendably took the trouble to measure the same structure with X-ray, neutron, and electron diffraction methods and to prepare the data in such a way that 3D-DeltaPDF maps could be successfully calculated in each case.The comparison of the different measurements was complicated by the fact that the respective methods produce different artifacts and have different structural sensitivities.Nevertheless, the authors succeeded in convincingly demonstrating that the analyses for the different methods provide at least semiquantitatively comparable results and that 3D-ED experiments may become a strong complement to X-ray and neutron-based 3D-DeltaPDF investigations.
Also, the advantages, disadvantages, and limitations of the different methods are compared and discussed in detail.Below, I will discuss some further limitations of the study, which, however, are not unusual for such an early proof-of-concept study and do not diminish the importance of this paper in any way.On the contrary, I expect that this paper will stimulate further important research.I see no reason why the current limitations cannot be overcome in the near future by more experience and improvement of the available tools, especially since the development of such tools is already in full swing.In the case of 3D-ED, significant progress is currently being made in instrumentation and handling of dynamic scattering effects, while in the 3D-DeltaPDF community a great deal of experience is currently being gained in understanding complex disordered structures and the necessary software is being developed for easier access to the disordered information.The current development of 3D-DeltaPDF tools is focused on X-ray applications, but may straightforwardly be applied to 3D-ED data or easily be adapted.There is no doubt that the 3D-ED / 3D-DeltaPDF combination will benefit greatly from all these developments and will quickly establish itself as an important material characterization tool.I think this paper should therefore definitely be published in nature communication.
My only substantive criticism, which I think requires an adjustment of the manuscript, is the comparison of the measurements of the positions of some 3D-DeltaPDF signals and the conclusion (partly explicit, partly suggested) that the three methods provide quantitatively comparable disorder models.Here I do not fully agree.First, some results show very strong discrepancies, especially in the data shown in the Supplemetary material.There may be good reasons for this due to the different measurement methods, but they had better be rationalized if used as an argument for quantitative comparability of the results from the three measurements.On the other hand, for small displacements, the position of a 3D-DeltaPDF signal is not a good measure of the local displacement correlations.On the contrary, it is almost exclusively the strength of the signal and not the location that is decisive when, for example, two Gaussian functions are subtracted from each other, which is an important feature of 3D-DeltaPDF models.Unfortunately, I am not aware of any literature reference that addresses this, but I have included a plot for demonstration purposes that should be selfexplanatory.In other words, a good match in the positions of 3D DeltaPDF signals is not a proof that full quantitative modelling would also give comparable results for displacement correlations.But this would be what we are interested in.Unfortunately, tools for quantitative modelling of 3D-ED / 3D-DeltaPDF models are not available at the moment, so quantitative modelling cannot be required from the authors.However, the text should be worded accordingly a bit more carefully to not suggest wrong conclusions.
We acknowledge the concern about the derived shift magnitudes and thank the reviewer for raising this important point.We argue that in the special case of YSZ this procedure is justified.In YSZ we assume static displacements of the oxygen ions towards neighbouring vacancies.With this in mind the "average" oxygen position is not accurately described by a single Gaussian but as the sum of several Gaussians, one for non-displaced and two for each direction of the displaced oxygens.Furthermore, in contrast to the above displayed Gaussians the "average" oxygen position is always centred at the average position, i.e. 0 in the above case.We agree that the discussion of this procedure was not outlined well enough.However, we feel that the main text is not the right place for this discussion.We dedicated a new Section 9 in the supporting information to this issue where we demonstrate that in the case of large static displacements as for YSZ we can directly quantify the shift using a one-dimensional chain as a model system.
To underline the argument that the variability in the shift magnitude is expected for the different probes, we fitted the shift magnitudes to our calculated model PDFs and arrive at a similar degree of variability with similar trends as observed in the experimental PDFs.
We hope that the reviewer agrees that these two points, now outlined in Section 9 of the supporting information and referenced on page 14 in the main text, indeed demonstrate that we can use the derived shift magnitudes to prove that the 3D PDF from electron diffraction can be used for quantitative measures.
The further suggestions for improvement are in the broader sense of linguistic or stylistic nature and I leave it to the authors to accept these or not.
-The term 'correlated disorder' is used several times.I find this somewhat unfortunate, since 'disorder' is more a global descriptor ('disorder model', 'disordered structure', etc., also the term 'disordered atom' is more associated with average structure properties) and less about very localised properties, which are seen in the 3D-DeltaPDF.I would prefer a continuous use the term 'local order' as a more accurate description.
We agree and adapted the text to use local order throughout the text.
-In the second line of the abstract it is written about 'intentional introduction of disorder'.I think this is a bit unfortunate, since unintentional disorder can be just as interesting.
We agree and omitted the word intentional in the abstract.
-line 34ff: It would be good if some non-perovskite examples were also listed.
-line 158: new symbols Delta^-_OO etc. are introduced without defining them.In the course of the text the meaning became clear to me, but without explanation they could be misunderstood.
We added a sentence that explains the subscript and superscript part of the symbols (page 12).
-Fig.4: I cannot distinguish the colors for Zr and Y.Maybe a better color coding would be helpful.
We changed the colours in the figure and adapted the caption.The relevant interatomic vectors in the average structure are now better indicated.
-line 179: In the context of 3D-DeltaPDF features I would speak of 'densities' instead of 'intensities', because they are derived from scattering densities.We adjusted the wording accordingly.
-lines 218 -235: It is repeated several times that ED is more sensitive to light elements than X-ray diffraction, which affects the readability of this paragraph.Consider rewriting this paragraph.
We restructured the paragraph accordingly.
-Chapter 'Challenges ...' The challenge of multiple scattering in ED should be included in this paragraph.An additional paragraph discussing the possible influence of multiple scattering on the 3D-DeltaPDF would certainly be interesting, in particular, since some of the authors already have a lot of experience regarding average structure refinements based on 3D-ED diffraction.Would this experience be transferable to diffuse scattering?
We added multiple scattering and inelastic scattering as a challenge.In principle the formalism behind the multiple scattering is also applicable to large superstructures that are used to calculate diffuse scattering.For a more complete analysis of the effects of multiple scattering and also inelastic scattering we plan to utilize multislice simulations.This is work in progress, but due to the complexity of the problem and the computational efforts needed for such simulations we would strongly prefer to leave this point to future research, where it can be discussed in the length and the thoroughness that we think is necessary and appropriate.
-Supplement chapter 4: I would write of 'dashed lines' instead of 'dotted lines' and again replace 'intensities' with 'densities'.Also one should write that the crossing points of the lines describe the average interatomic vector.In S4 there are four crossing points which should be listed in the caption.
We adapted the captions accordingly.
We would like to thank Reviewer #2 for their detailed insight and hope we could clarify the points raised here in the revised version.
Reviewer #3 (Remarks to the Author):
Dear Authors The present study describes a successful use of electron diffraction data for conducting 3D local structure analysis on an inorganic material of technological interest, namely yttria stabilized zirconia.The general goal is to demonstrate that the analysis of local structure such as the spatial arrangement of defects and displacive disorder can be determined reliably and in 3D by electron diffraction, thus overcoming crystal size limitations imposed by single crystal X-ray and neutron diffraction.In this respect, this study presents a convincing use of electron diffraction data for conducting 3D-deltaPDF analysis, while conveniently comparing it with analogous results from X-ray and neutron 3D-deltaPDFs that have been previously published.
Overall, the study conveys an important message and highlights prominent challenges that need to be solved to make this technique more robust and widely used.As for the "quantitative" aspects of it, particularly standing out in the title and the manuscript itself, I believe that this study should put forward some more caveat and cautionary considerations.In the context of modern crystallography and materials science, this work constitutes an important step beyond the state of the art, which undoubtedly qualifies it for publication.I do have a few points, though, which in my view require attention and I will elaborate in the following.I therefore consider this work valuable as a Nature Communications article after some minor revisions are addressed.
1. Line 41.The Authors mention that the analysis of Bragg diffraction is well established.I would also add that is even "automated", since less and less is left to humans in current crystallographic routines, and crystal structures can be solved by essentially autonomous software (such as the Autochem plugin by Rigaku) when data quality is not particularly problematic.
We included a statement related to automation in routine structure determination.
2. Line 68.The Authors state that the average interatomic vector of neighbouring atoms that vibrate in-phase "is smeared out by the average structure atomic displacement parameters (ADPs)".I understand the intended meaning, but ADPs are used to model electron density distribution, therefore they cannot have any smearing effect themselves.I assume the Authors intended something like "is smeared out in the average structure, as modelled by atomic displacement parameters (ADPs)".For this reason, I think this sentence should be rephrased to make it more accurate.
We rewrote the sentence accordingly.
3. Line 73.I would be more explicit on the crystal size, since "macroscopic" has different meanings depending on the context.Perhaps the Authors can consider using the word "micrometric", and preferably pairing it with "currently" and "in general" to be on the safe side, since sub-microcrystal XRD can be performed in numerous synchrotrons worldwide.
We acknowledge the concern and adapted the sentence as suggested.
4. The Authors correctly point out that the importance of analyzing nanocrystals is primarily due to the fact that their correlated disorder might be different from their microcrystalline analogues.However, I find this aspect addressed very little when describing the interpretation of the data.For example, at line 130 the Authors describe the broadening of electron diffuse scattering data compared to the X-ray and neutron diffraction one, attributing it to the experimental setup simply based on the fact that both Bragg and diffuse scattering features are affected by broadening at the same time.I believe there are numerous microstructural characteristics that can differ between large microcrystals and nanocrystalline samples, affecting both diffuse scattering and the Bragg peaks' profiles.This is not only a matter of short-ranged correlated disorder, but can also relate to coincidental change in mosaicity and crystallite size.Such effects can also be found in the PDF space, which would potentially invalidate the statement at line 146: "This is a direct consequence of the experimental broadening of the diffuse scattering".I agree that broadening of diffuse scattering relates to correlation lengths in real space, but I am concerned with the use of "experimental" as in 'due to the experimental setup' (meaning in particular all the set of distortions that come with an electron diffraction experiment).I think this is an important aspect to clarify, and personally I would keep the option of having real structure effects impacting patterns and PDFs, which are therefore not due to experimental setup, while having analogous effects.Addressing these aspects could also give the Authors a good chance to comment on the challenge of discriminating the two sources of broadening (structural changes vs. 'experimental' broadening), and the need of quantifying the instrumental sources of distortions in total scattering data from electron diffraction, as well as their effects in the PDF space.This aspect should also be kept in mind when, further in the manuscript, the Authors consider the quantitative differences of correlation lengths.In lines 202 and 205-207, these differences are attributed to the fact that probing matter with electrons and with X-rays or neutrons provides different lengths because of different sensitivity to "structural aspects".However, I would also specify that differences due to the nanocrystalline nature of the sample and its different, unknown microstructure can also be a cause of such varying correlation lengths.
We agree that structural origins due to microstructure variations cannot be excluded and indicated so in the revised version of the main text.However, we are convinced that the setup related broadening is the main cause of the reduced observed correlation length.To elucidate this point, we included a section (section 4 in updated SI) in the supporting information that estimates an instrumental resolution function based on the FWHM of an observed Bragg reflection in the reconstruction and henceforth calculate the structural correlation length from the width of the observed diffuse scattering.We attribute the main cause of this observed broadening to inelastically scattered electrons that are responsible for the halo around the primary beam in reciprocal space but at the same time also broaden all features in the diffraction pattern to the same degree.Unfortunately, we currently don't have a setup available with an energy discriminating detector that can still yield the desired reciprocal space coverage to fully quantify this analysis.
5. The proposed PDF analysis is useful and in line with what previously published based on X-ray and neutron data, but there is an aspect that I did not find addressed explicitly: the impact of vacancy defects on the PDF space.The interpretation appear focused on the consequences of vacancies on structural distortions, leaving the reader with the impression that the only information available from the 3D-deltaPDFs is displacive disorder, and no localisation and quantification of correlation signals due to lack of density (presence of defects) can be distinguished.This might indeed be true, and I believe that, in case, the Authors should state this clearly to better guide the readers.It would be useful to mention qualitatively and briefly what kind of signals can be expected when vacancy defects are present and why they are not interpretable from the available experimental delta-PDFs of nanocrystalline yttria stabilized zirconia.
We agree and we added further statements in the results section that describe that in this sample material the displacive local order is dominating here (page 10), commenting on the limited detectability of chemical short-range order in our sample material (page 6, page 10, page 13).
6.The Authors address the quantitative reliability of the 3D-deltaPDF analysis by comparing correlation lengths in terms of positions of maxima and minima between X-ray, neutron and electron PDFs.I find this a relatively weak part that could be improved, and I will elaborate in the following.In my view, there are two aspects that can be considered concerning 'quantitative reliability' in the PDF space: the positions of the correlation vectors, and the numerical values (maxima/minima or integrals) of the correlation signals.It appeared to me that the Authors focus selectively on the first aspect.Nonetheless, the second, too, contains important defect structure information, which can be made less reliable due to artefacts from data processing, instrumental broadening, or multiple elastic and inelastic scattering.It is not possible to use comparisons with XPDFs or with neutron PDFs for assessing quantitative reliability, because both shift magnitudes and integrals at specific correlation vectors can be influenced by the fact that nanocrystals can have different local structures, and because, as the Authors pointed out, "different radiations are sensitive to different structural aspects".For this reason, I believe that using such comparisons to evaluate the quantitative reliability does not help much, and indeed this section concludes with the Authors acknowledging that differences are "to be expected".
The integrals of the 3D-PDFs do indeed give valuable insight on the chemical shortrange order and we added a paragraph in the introduction that explains that in the sample material YSZ displacement disorder is the dominating effect.
To underline that the variations of the determined shift magnitudes can indeed be explained by the different sensitivities of the different radiation types we included a new section 9 in the supporting information: Here, we use our simplistic model crystal and determine the shift magnitudes from the resulting 3D-PDFs calculated from electron, x-ray and neutron diffraction.As the underlying model crystals are identical, Bragg peaks in computational data are exactly one voxel and there are no other sources of background, this comparison enables a quantification of differences in shift magnitudes due to the different probes.We find that the variations we observe here are similar to our experimental observations, where shifts determined from x-ray and electron diffraction experiments are within the uncertainty of each other while due to the larger difference in scattering length the shift as determined from neutron diffraction experiments show larger deviations.The trend of the deviation of the neutron shift is the same in the computational model analysis as observed in the experimental data and so we believe that our quantitative analysis indeed gives reliable results.
I consider these comparisons nonetheless useful, but I wonder whether the Authors could be more transparent with respect to this ambiguity in quantitative reliability, and formulate how it could be determined more appropriately.This remains an open question that does not stand out enough, in my opinion.It could also become an important point to be presented in the "challenges that need addressing" section: how can we validate our 3D-deltaPDF from electron diffraction data, since we cannot compare it with neutron and X-ray PDF analysis due to the different nature of the beam-sample interaction and the possibly different local structure?
We agree that the validation of the derived local order model is a challenge and added an additional paragraph in the discussion section that comments on this issue (page 19).
7. The supplementary material is missing the pristine reciprocal space reconstructions of the main planes of the sample (hk0, h0l, 0kl).Since the production of diffuse scattering reconstructions required not only a reasonable symmetry averaging, but also other steps such as "Karen" filtering, punch-and-fill, and gaussian-dampening, it would be most informative for the readers-especially those who are willing to conduct similar analyses in the future-to have an idea of the pristine reconstruction and possibly some intermediate steps of the data processing.Furthermore, punch-andfill procedures have also an important effect on the features observed in the 3D-deltaPDF, especially the choice of punch radius.Indeed, different punch radii may change the integrals and shift of correlation peaks, as the Patterson function might partly contribute, which is a likely possibility when the diffuse scattering is primarily originating from correlated distortions in the structure.Ideally, the chosen punch radius should be justified, and the effect of different punch radii could be briefly shown to give an idea of how much this process affects the features that are discussed in the manuscript.This would also provide useful insights on the quantitative side of this analysis, since it is a central aspect the Authors aimed at.
We added the unprocessed data sections and a figure showing the effect of the punch radius in the supporting information for reference (Fig. S6).
8. When addressing the challenges of the method, the Authors describe three main points: limited reciprocal space coverage, sample stability to the electron beam, and dynamic range of the detector.However, I think an important aspect is missing: the presence of non-kinematical elastic or inelastic scattering.Kikuchi diffraction and other inelastic scattering events can produce broad band-like intensities that might be problematic to distinguish and separate from the data, adding undesired features to the 3D-deltaPDFs.This is particularly relevant for inorganic samples such as the one addressed in this study, where the Authors took care of preparing it as a thin lamella.
The strong influence of sample thickness, ubiquitous presence of undesired multiple and inelastic scattering, and the possibility of using energy-filtered diffraction to at least eliminate most of these intensities, would all be important aspects to be discussed in this last section.Furthermore, the challenge of validating the electron 3D-deltaPDF analysis with complementary techniques for the reasons described above can also be proposed as an open challenge, since there is no standard practice, as far as I am aware, for this purpose.
We included multiple and inelastic scattering as an open challenge and suggest a detailed quantitative investigation of the effects for the future.e.g., using multislice simulations.
9. I did not find, in the cited literature, the use of electron diffraction data for 1D PDF analysis, as reported by Gorelik et al. in 2015 (Microscopy andmicroanalysis, 2015, 21(2), 459-471) and later improved towards a quantitatively reliable technique (Gorelik et al. Acta Cryst. 2019, B75, 532-549).This is not only highly relevant to this study, but it might also allow a better quantitative reliability assessment of the electron 3D-deltaPDF analysis by comparing the electron 3D-deltaPDF with its 1D analogue, which, in turn, can be more reliably compared to 1D XPDF.
We added the references 15 and 16 when discussing 1D PDF (page 3).
10. Just a couple of writing slips I noticed.Line 44: Since the subject is "powder pair distribution function analysis", I believe the subsequent verb should be "has been".In the caption of Figure 4, line 175 reads "diffraction patterns a simplified model".I imagine "from" should be inserted before "a simplified model".
We corrected the mentioned writing slips.
Finally, I would like to congratulate the Authors on this beautiful work and wish them all the best for the revision process.
We tank Reviewer #3 for their insighfful comments and hope we could address the concerns in the revised version. | 12,118.4 | 2023-05-03T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Hierarchy and dynamics of trace distance correlations
We define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic expressions for the classical and total correlations. The ensuing hierarchy of correlations based on trace distance is compared to the ones based on relative entropy and Hilbert-Schmidt norm. Although some common features can be found, the trace distance measure is shown to differentiate from the others in that the closest uncorrelated state to a given bipartite quantum state is not given by the product of the marginals, and further, the total correlations are strictly smaller than the sum of the quantum and classical correlations. We compare the various correlation measures in two dynamical non-Markovian models, locally applied phase-flip channels and random external fields. It is shown that the freezing behavior, observed across all known valid measures of quantum correlations for Bell diagonal states under local phase-flip channels, occurs for a larger set of starting states for the trace distance than for the other metrics.
Introduction
Quantum entanglement is a central subject in the study of quantum information theory as it is a strikingly non-classical phenomenon and a primary instance of a truly quantum resource in communication and computation tasks [1,2]. However, in mixed states of composite systems, more general quantifiers of quantum correlations exist, most famously the quantum discord [3,4]. Discord is present in most mixed states, even among those with no entanglement [5], and it is of ongoing interest to investigate whether states with discord can be employed as resources for information processing scenarios [6][7][8][9], including those with vanishing entanglement [10].
Some measures of quantum correlations, including the original discord [3] and the one-way quantum deficit (alias relative entropy of discord) [11,12], are based on entropic quantities. Another method, the 'geometric' approach for quantifying quantum correlations, consists in choosing a metric over the space of quantum states, and using this to find the distance to the nearest zero-discord (classical) state. Several measures have been defined in this way, including the Hilbert-Schmidt measure of discord [13,14] and its modifications [15][16][17]. The trace distance measure of quantum correlations [18,19] falls into the latter category.
The trace distance between two quantum states ρ and σ is defined as where Ô 1 ≡ Tr|Ô| = Tr Ô †Ô is the Schatten-1 norm, or trace norm, withÔ being an arbitrary operator. The trace distance metric arises naturally in quantum mechanics and admits an intuitive operational interpretation related to the probability of successfully distinguishing between two quantum states in a hypothesis testing scenario [20]. An important feature of the trace distance in dynamical contexts is its contractivity under trace preserving and completely positive maps [21]. A closed expression for the trace distance discord has been obtained for Bell Given a state ρ living in a bipartite Hilbert space H, the trace distance between ρ and its closest classical state χ ρ ∈ P defines the quantum correlations (discord) D TD of ρ. The trace distance between χ ρ and its closest product state π χ ρ ∈ P defines the classical correlations C TD of ρ. The trace distance between ρ and its closest product state π ρ ∈ P defines the total correlations T TD of ρ. See equations (6), (12) and (13) in the main text for rigorous definitions.
diagonal states of two qubits [18,19] and more generally for X -shaped states of two qubits [22]. The trace distance discord has been theoretically studied in dynamical conditions in [23,24], and experimentally investigated in a nuclear magnetic resonance two-qubit system under phase and amplitude damping channels [25]. These findings naturally encourage one to exploit the trace distance to introduce total and classical correlations as well, in order to construct a unified view of the correlations present in a composite quantum system and investigate their hierarchies and dynamical properties.
In this paper, we construct a unified hierarchy of quantum, classical and total correlations in bipartite quantum states based on the trace distance (see figure 1). Unlike similar hierarchies based on relative entropy [11] or Hilbert-Schmidt norm [26], the trace distance measures of correlations present surprising features. For Bell diagonal states of two qubits, we complement the study of Nakano et al [18] and Paula et al [19] by deriving closed expressions for the classical and total correlations defined via trace distance. Counterintuitively, classical and quantum correlations do not add up to the total ones, not even for simple Bell diagonal states. In particular, the closest product state to a generic bipartite state, according to trace distance, is not in general the product of its marginals, which is instead the case e.g. for relative entropy. We further investigate the dynamical evolution of quantum, classical and total correlations in typical non-Markovian environments by highlighting peculiar aspects and differences with the dynamics of relative entropy-based correlations.
This paper is organized as follows. In section 2, we recall the expression, in the case of Bell diagonal states, for the trace distance measure of discord and we provide the explicit form of the associated closest classical states. In section 3, we obtain expressions for the classical and total correlations of Bell diagonal states and discuss their features. In section 4, we examine the behavior of quantum, classical and total trace distance correlations in simple dynamical models. We conclude in section 5.
Quantum trace distance correlations and closest classical state
We consider the class of two-qubit Bell diagonal states (or states with maximally mixed marginals [27]) expressed in the Bloch representation as where the coefficients R ii are the nonzero correlation matrix elements and σ i are the Pauli matrices. In the basis of Bell states, a Bell diagonal state is instead written as where j = 1, 2, r = ±, j,r λ r j = 1 and where we have indicated with |1 ± ≡ (|01 ± |10 )/ √ 2 the one-excitation Bell states and with |2 ± ≡ (|00 ± |11 )/ √ 2 the two-excitation Bell states. The relations among the eigenvalues λ r j and the correlation matrix elements R ii are from which one obtains the inverse relations . The trace distance discord quantifying quantum correlations of an arbitrary state ρ AB ≡ ρ of a bipartite system AB, as revealed on subsystem A, can be defined as [18,19] where C the set of classical states χ. By classical states we mean states with zero discord on subsystem A, also known as classical quantum states, which can be written in general as being a probability distribution, |i A an orthonormal basis for subsystem A and τ i B an ensemble of arbitrary states for subsystem B. We have denoted by χ ρ the classical state closest to ρ in trace distance, which achieves the infimum in equation (6). Due to the hermiticity of the density matrices, the previous equation is equal to where λ D i are the eigenvalues of the matrix (ρ − χ ρ ). In [18], it has been proven that when A is a qubit, the trace distance discord is equivalent to the so-called negativity of quantumness, which quantifies the minimum negativity of entanglement [2] created with an apparatus during a local projective measurement of subsystem A, according to the formalism of Streltsov et al [7], Piani et al [8] and Adesso et al [28].
The same measure also coincides with the minimum trace distance between ρ and the state decohered after a minimally disturbing local measurement where A is a projective measurement on subsystem A [18]. A closed expression for the trace distance discord D TD (ρ B ) for arbitrary Bell diagonal states ρ B of two qubits was obtained in [18,19]. One simply has where R int represents the intermediate value among the moduli |R ii | (i = 1, 2, 3). In the following, for completeness, we construct the explicit form of the closest classical state χ ρ B to an arbitrary Bell diagonal state ρ B , which attains the minimum in equation (6) resulting in the expression given by equation (9) for the trace distance discord.
Closest classical state
It is known in the literature that the classical state closest to ρ B according to both the relative entropy distance and the Hilbert-Schmidt distance is still a Bell diagonal state and has the form [11,15] where R kk is the one among the elements R 11 , R 22 , R 33 such that |R kk | ≡ R max = max{|R 11 |, |R 22 |, |R 33 |}. Notice that the closest classical state χ ρ B above is symmetric under exchange of subsystems A, B, thus it has vanishing discord when detected either on subsystem A or on subsystem B according to any distance measure [13]. We now show that this state is also the closest classical state to ρ B in the trace distance. Using the relations of equation (4) among the eigenvalues of a Bell diagonal state and the coefficients R ii , one can distinguish different cases in the ordering of the |R ii | and one can correspondingly obtain the expression of the trace distance discord D TD (ρ B ) for the class of Bell diagonal states. Let us select indices i, j and k as an ordering of 1, 2 and 3 such that |R ii | |R j j | |R kk |. In this case we postulate that the closest classical state assumes the form as in equation (10), from which one gets Notice that flipping the sign of R j j or R ii in the above expression simply swaps the two absolute value terms, thus leaving the entire expression invariant. Therefore, no matter the signs, we obtain for this choice D TD (ρ B ) = 1 2 R int , where R int = |R j j |, which matches the expression announced in equation (9) and computed independently in [18,19]. The above calculation shows that the state χ ρ B of equation (10) is indeed the classical state closest to an arbitrary Bell diagonal state ρ B in the trace distance. Interestingly, the state of equation (10) is thus the closest classical state to a Bell diagonal state for all the three distances, namely relative entropy, Hilbert-Schmidt and trace distance. In the following section, we see that this similarity among the different metrics is not preserved when classical and total correlations are concerned.
Total and classical trace distance correlations
The definition of quantifiers of total and classical correlations for a bipartite state ρ in geometric terms [11,26] requires finding the closest product state to ρ and to χ ρ , respectively, where χ ρ is the classical state closest to ρ as defined in equation (6); see figure 1 for a schematic picture. We define by P the set of product states π = γ A ⊗ τ B , where γ A and τ B are arbitrary states defined on the marginal Hilbert spaces of subsystems A and B, respectively. Note that P ⊂ C ⊂ H in general, where H represents the Hilbert space of the composite system AB and C contains classical states as defined earlier. Adopting trace distance in the present framework, we can introduce quantifiers of total and classical correlations for a bipartite state ρ as follows: where π ρ and π χ ρ indicate, respectively, the product state closest to ρ and the product state closest to χ ρ in trace distance, while λ T i and λ C i are the eigenvalues of the matrices (ρ − π ρ ) and (χ ρ − π χ ρ ), respectively.
In the next subsections, we derive explicit expressions for equations (12) and (13) for Bell diagonal states.
Classical correlations
We now find a closed form for π χ ρ B and the analytical value of C TD for Bell diagonal ρ B . Defining two arbitrary states of single qubits A and B with corresponding Bloch vectors For a given product state, we consider a corresponding state π − given by vectors . We have seen that the state of equation (10) is the closest classical state ρ B to a Bell diagonal state ρ B for the trace norm. By comparison of characteristic polynomials, it can be verified that if k = 1, then χ ρ B − π + has the same eigenvalues as χ ρ B − π − , where as before k is the index such that |R kk | ≡ R max . This gives us Trace distance also satisfies the convexity property Equivalent results can be found when flipping the sign of any other single vector element a i or b j for i, j = k. This means that for the closest product state π χ ρ , only the Bloch vector elements a k and b k can be nonzero. Optimizing over these two remaining elements gives the form with the specific solution found at Finally, plugging this state in equation (13) gives Remarkably, there is a nice division of roles between the intermediate and the maximum correlation matrix element of an arbitrary Bell diagonal state of two qubits: the former entirely characterizes the trace distance discord, while the latter entirely characterizes the trace distance classical correlations. We notice that the product state π χ ρ B closest to the classical state χ ρ B is not the product of its marginals, and is not even a Bell diagonal state in general. This already reveals how minimizing trace distances from the set P of product states is a nontrivial problem which can have counterintuitive solutions. This marks a significant difference between the trace distance and the relative entropy and Hilbert-Schmidt distances.
Total correlations
For most metrics, finding the distance between a given composite state and the closest product state is an easier problem compared to, e.g. minimizing the distance from the set of separable or classical states. Adopting the relative entropy, for instance, the distance between a bipartite state ρ and the set of product states returns the mutual information of ρ, which is exactly computable, while the relative entropy of entanglement and the relative entropy of discord are generally hard to obtain. It is in this respect quite surprising that the situation is radically different using the trace distance. Notwithstanding its privileged role in quantum statistics [20,21], it seems that the trace distance does not induce an intuitive characterization of total correlations in bipartite states. In other words, if we are facing the task of distinguishing between a bipartite state ρ and the closest product state in trace distance, the answer is not trivial. In general, the closest product state is not the product of the marginals of ρ. This makes the optimization of the distance in equation (12) over P already complicated for simple classes of two-qubit states. Here we focus on ρ being an arbitrary Bell diagonal state ρ B .
We base our analytical analysis on an ansatz which is verified numerically. The ansatz is that the closest product state π ρ B to ρ B can be found once more among the states of the form given by equation (17) Plot of T TD obtained by numerically optimizing the product state closest to a Bell diagonal state ρ B against the analytic expression of the trace distance total correlations corresponding to a product state given by equation (17) for the same ρ B . Dark blue crosses show each point (constituting a sample of 10 3 random states ρ B ), while a solid red line shows equality between the two. of the nonzero Bloch vector element and the relative sign of a k and b k depend only on R kk , we anticipate that the actual optimal value of a k determining T TD depends on R ii and R j j as well, which means that in general π ρ B = π χ ρ B , as schematically depicted in figure 1. Under the ansatz of equation (17), the total trace distance correlations of a Bell diagonal state ρ B can be written as follows: where s = R kk /|R kk | is the sign of R kk and a k is the product state parameter from equation (17). Note that this expression is invariant under interchange of R ii and R j j . The remaining optimization in equation (20) can be solved in closed form. It turns out that the optimum a k is either 0 (meaning that the closest product state is the identity, i.e. the product of the marginals of ρ B ), or it has to be found among those values which nullify each of the absolute value terms in equation (20). However, the resulting explicit expression for T TD (ρ B ) is too long and cumbersome to be reported here.
It is important to comment on the validity of the ansatz behind equation (20). We have ran an extensive numerical test where we compared the conjectured expression for T TD (ρ B ) obtained under the assumption of equation (17), with a numerical minimization of equation (12) over arbitrary product states π of two qubits. The result for a sample of 10 3 Bell diagonal states ρ B (out of a total of 10 6 tested ones) is shown in figure 2: the numerically optimized trace distance for all tested states falls on or above the straight line representing equality with the analytical formula resulting from equation (20), which means that no product state could be found numerically closer-in trace distance-to a generic Bell diagonal state, than the one analytically given by equations (17) and (20).
For the majority of states ρ B , the optimal a k = sb k = 0, which means that the closest product state is not the product of the marginals, in contrast to the total correlation measures obtained by using the relative entropy or Hilbert-Schmidt norms [11,15]. Additionally, the triangle inequality for trace distance implies in general but unlike the other norms the inequality is typically sharp for the trace distance case. In this respect, we wish to point out that this is not a byproduct of the ansatz used to derive equation (20). Even though a closer product state to ρ B might be found (which appears extremely unlikely based on our numerical analysis), the expression in equation (20) would remain an upper bound to the true trace distance total correlations, therefore not altering the sharpness of the inequality (21). Hereby we will confidently regard the value of T TD (ρ B ) given by equation (20) as the exact value of the trace distance total correlations for arbitrary Bell diagonal states ρ B .
Examples
Here we present some explicit examples where we compute quantum, classical and total correlations in particular families of two-qubit Bell diagonal states and comment on their properties.
One simple class of Bell diagonal states is Werner states [29], for which R 11 = −R 22 = R 33 = r , for 0 r 1. For these states, the values of the correlations are: T TD (ρ) = This is shown in figure 3 (left). It is notable that, while quantum and classical correlations increase smoothly, the total correlations have a sudden change point at r = 4 5 . This point marks the transition from the region for which the closest product state is the product of the marginals, 0 r 4 5 , to the region where it is instead a product state of the form as in equation (17) with a k = √ r . A second simple class of states, also displayed in figure 3 (Right), are the rank-2 Bell diagonal states, for which R 11 = −R 22 = c, R 33 = 1, for 0 c 1. The values of trace distance correlations for these are Here we see that while again quantum correlations increase smoothly, for total correlations there are actually three regions, with two sudden changes. In this case it is the middle region, with 1 2 c 3 4 , for which the closest product state is the product of the marginals. In the final region, 3 4 c 1, the closest product state is pure. We can additionally note that for both Werner and rank-2 Bell diagonal states, it is always the case that T TD = D TD + C TD except for the trivial cases where one of them vanishes. Notably, classical correlations are constant for rank-2 Bell diagonal states.
Dynamics of trace distance quantifiers of correlations
In this section we analyze the dynamics of the trace distance quantifiers of correlations in two specific models exhibiting non-Markovian evolutions and compare them to the dynamics of the correlations measured by relative entropy S(ρ σ ) ≡ −Tr(ρ log σ ) − S(ρ) [11], where S(ρ) ≡ −Tr(ρ log ρ) is the von Neumann entropy. This analysis will serve the purpose to highlight possible peculiarities in the dynamical behaviors of the trace distance quantifiers of correlations and to show possible qualitative differences with the dynamics of the entropic ones. The choice of the entropic quantifiers of correlations for the dynamical comparison is due to the fact that both relative entropy and trace distance measures are contractive for any trace-preserving completely positive map , that is S( ρ σ ) S(ρ σ ), δ TD ( ρ, σ ) δ TD (ρ, σ ): that is a required property for any bona fide distance-based measure of correlations [24]. For instance this property is not exhibited by the Hilbert-Schmidt distance, used to define the geometric discord [13] which was as such revealed to be an unsuitable measure of quantum correlations [16,30]. It is also worth to mention that the relative entropy is adopted as a measure of distance between two states ρ, σ even if it is asymmetric with respect to the exchange ρ ↔ σ and is thus a pseudo-distance: moreover, S(ρ σ ) diverges when σ is a pure state [31]. Differently, the trace distance is symmetric to the exchange ρ ↔ σ and it does not present singularities when σ or ρ are pure states.
Total correlations T , discord D and classical correlations C based on relative entropy are defined as [11] whereπ ρ ∈ P andχ ρ ∈ C are, respectively, the product state and the classical state closest to ρ, whileπχ ρ ∈ P is the product state closest toχ ρ . These states are such that they minimize the corresponding relative entropies, and do not in general coincide with the ones minimizing the trace distance measures of correlations in equations (6), (12) and (13). It is worth to notice here that, for the class of Bell diagonal states ρ B , D(ρ B ) coincides with the original definition of quantum discord [3,4] and the relative entropy correlation quantifiers satisfy the additivity relation: T = D + C (an analogous relation also holds when using geometric quantifiers defined via the Hilbert-Schmidt distance [15]). The explicit expressions of the entropic correlation quantifiers for Bell diagonal states are [27] where λ r j and R max are defined, respectively, in equation (4) and after equation (10). We shall take into account two different models, a dynamics under local phase-flip channels and an environment of random external fields.
First model: phase-flip channels
We take two noninteracting qubits under local identical phase-flip channels [15]. Phase-flip noise, i.e. pure dephasing, is an emblematic type of nondissipative decoherence [1] which arises naturally in typical solid state implementations, such as the case of superconducting qubits interacting with impurities under random telegraph noise [32]. In our setting, each qubit is subject to a time-dependent phenomenological Hamiltonian [33] H (t) =h (t)σ z , where σ z is a Pauli operator and (t) = αn(t) where α is a coin-flip random variable taking the values ±|α| while n(t) is a random variable having a Poisson distribution with mean value equal to the dimensionless time ν = t/2τ . This two-qubit system is characterized by a non-Markovian dynamics that maintains the system inside the class of Bell-diagonal states with the three coefficients R ii (t) of equation (2) evolving as where i = 1, 2 and f (ν) = e −ν [cos(µν) + sin(µν)/µ] with µ = (4ατ ) 2 − 1. Using equations (26) and (25) the quantum correlations can be analytically computed. We notice that the closest classical state χ ρ B (t) of equation (10) is frozen during the time intervals when |R 33 (t)| > R max , being R kk (t) = R 33 (t) = R 33 (0). In figure 4 entropic discord D and trace distance discord D TD are plotted as a function of the dimensionless time ν for two different initial Bell diagonal states. It is displayed that the [34]. Notice also that the two discords display different qualitative behaviors in the Right panel of figure 4: while D TD is constant, D has sudden changes but no freezing regions. This demonstrates that the freezing property occurs for a wider range of initial conditions for trace distance discord than for entropic discord. This phenomenon has also been pointed out in [23], where a richer phenomenology of trace distance discord compared to other measures of discord was uncovered, including the possibility of double sudden changes when phase-flip is combined with amplitude damping. In general, our recent geometric analysis in [24] shows that, within the space of Bell diagonal states, the trace distance discord D TD has broader subregions in which it remains constant compared to any other bona fide measure of discord. This clearly results in the possibility of larger freezing intervals under various dynamical trajectories compared to other measures. We will now investigate whether this is the case for the second dynamical model studied in this work.
Second model: random external fields
We consider a pair of noninteracting qubits each locally coupled to a random external field, whose characteristics are unaffected by the qubit it is coupled to. This implies that back-action on the dynamics of the qubits is absent [35,36]. Each environment is a classical field mode with amplitude fixed and equal for both qubits. The phase of each mode is not determined, and is equal either to zero or to π with probability p = 1/2. This model describes a special case of two qubits each subject to a phase noisy laser [37] but where the phase can take only two values and with the diffusion coefficient in the master equation equal to zero. It has been considered to study revivals of entanglement without back-action [6,35,36]. In this model, the dynamical map for the single qubit S = A, B is of the random external fields type [38] and can be written as where U S i (t) = e −iH i t/h is the time evolution operator, with H i = ihg(σ + e −iφ i − σ − e iφ i ), and the factor 1/2 arises from the equal field phase probabilities (there is a probability p S i = 1/2 associated to each U S i ). Each Hamiltonian H i is expressed in the rotating frame at the qubitfield resonant frequency ω. In the basis {|1 , |0 }, the time evolution operator U S i (t) has the matrix form where i = 1, 2 with φ 1 = 0 and φ 2 = π. The single-qubit map S t generates a nondissipative non-Markovian evolution described by a master equation in a generalized Lindblad form [39]. The overall dynamical map t applied to an initial state ρ(0) of the two-qubit system, ρ(t) ≡ This map moves inside the class of Bell diagonal states [36]. The three coefficients R ii (t) of equation (2) evolve as where j = 1, 3.
In figure 5 we plot entropic discord and trace distance discord for two different initial conditions. Even in this case, as occurred in the above phase-flip channels, the entropic discord changes its qualitative time behavior for the two different initial conditions (time regions of freezing in the left panel, increase and decrease in the right panel), while the trace distance discord maintains the same qualitative dynamics. This is a further confirmation of the fact that the freezing property for trace distance discord occurs for a wider range of initial conditions than for entropic discord.
Once again, it is possible to show that the freezing for both D and D TD (left panel of figure 5) occurs when the initial coefficients R ii (0) of the Bell diagonal state satisfy the general condition of freezing for quantum correlations under nondissipative evolutions [24]. Notice that the sudden changes in the slope of the two discords occur at the same times; these times can be analytically found for given initial conditions [24,34].
Dynamics of total and classical correlations measured by trace distance
We can now analyze the time behavior of the total and classical trace distance correlations described in section 3, for the two models studied above. Figures 6 and 7 show the dynamics of total T TD , classical C TD and quantum D TD correlations quantified by the trace distance for the local phase-flip channels and for the random external fields, respectively. There are several features of note, both in commonality and contrast with the relative entropy distance measure of discord.
Similarly to the case of relative entropy distance, the trace distance classical correlations switch between being frozen and varying at exactly the same points in time as the trace distance discord. This behavior, known as sudden transition between classical and quantum decoherence [34], can be understood from the analytic expressions of equations (9) and (19), from which we can see that, for trace distance, quantum correlations depend only on R int for Bell diagonal states, whereas classical correlations depend only on R max . While this is not true in general for the relative entropy distance (see equations (24)), this turns out to be the case for trajectories which experience frozen entropic discord [32]. Similarly, for both measures, the total correlations do not appear to experience freezing or sudden change, indicating their dependence on more than one R ii value.
In contrast to the relative entropy distance, however, where C(t ) = D(t ) at any threshold time t at which there is a sudden change, for trace distance C TD (t ) < D TD (t ). This too can be understood by reference to the analytic expressions, which show that C TD < D TD whenever R max = R int .
Scaling of the freezing regions of quantum correlations
We now show a general scaling property of the freezing region for quantifiers of quantum correlations as a function of the initial conditions. This property, which is found for local Markovian nondissipative channels [24], can be generalized to any local channel maintaining the Bell diagonal structure of the two-qubit density matrix with R ii (t) = R ii (0) f 2 (t), R j j (t) = R j j (0) f 2 (t) and R kk (t) = R kk (0) (i, j, k = 1, 2, 3, i, j = k), where f (t) is a characteristic timedependent function of the channel with the properties f (0) = 1 and | f (t)| 1. In fact, the initial conditions for general freezing are R ii (0) = ±1, R j j (0) = ±R kk (0) [24]. Assuming that |R ii (t)|, |R kk (t)| |R j j (t)| for any t, the freezing occurs when |R ii (t)| |R kk (t)| = |R kk (0), that is when f 2 (t) |R kk (0)|. If the function f (t) is analytically invertible, the threshold times t when there is a sudden change can be explicitly determined from the equation f 2 (t ) = |R kk (0)|. Due to the properties of f (t), the general result under these conditions is thus that the smaller is |R kk (0)|, the longer is the freezing region of quantum correlations whose amount however correspondingly decreases.
For example, in the case of local random external fields considered above we find that the general freezing of quantum correlations occurs when cos 2 (2gt) |R 22 (0)| and the first sudden change time is at gt = 1 2 arccos √ |R 22 (0)|. In figure 8 we display the scaling of freezing by plotting the trace distance discord as a function of the dimensionless time gt for different values of the initial coefficients, fixing λ ± 2 (0) = 0 (i.e. R 33 = −1). We notice that by decreasing the value of λ + 1 (therefore of |R 22 (0)|), the regions of freezing become longer and the amount of preserved quantum correlations smaller. This phenomenon is universal among all bona fide measures of quantum correlations as a consequence of the analysis in [24]. discord this scaling of the freezing regions can furthermore occur also with initial conditions outside those for general freezing (for instance, for |R 33 | = 1, see right panel of figure 5).
Conclusion
Bell diagonal states of two qubits are often the simplest yet highly relevant class of states for which one is able to analytically calculate measures of correlations. Investigations of different types of correlations in Bell diagonal states can reveal insights into remarkable dynamical features such as frozen quantum correlations [24,34], and can lead to a deep understanding of the structure and interplay of different forms of (non)classical correlations.
In this paper, we adopted the trace distance as a metric to define correlations in bipartite quantum states. Extending the analysis of Nakano et al [18] and Paula et al [19] in which a discord measure based on trace distance was defined, we completed a unified approach to bipartite correlations by defining classical and total correlations based on the trace distance metric. For Bell diagonal states, we obtained analytical expressions for classical and total trace distance correlations, in addition to the known one for quantum correlations [18,19]. Interestingly, trace distance discord is entirely specified by the intermediate Bloch correlation element of Bell diagonal states, while trace distance classical correlations only depend on the maximum Bloch correlation element for the same states. The total correlations have a nontrivial expression which depends on all the Bloch elements, and are obtained for a state ρ by taking the trace distance from a product state which is not, in general, equal to the product of the marginals of ρ.
This is an interesting fact in its own right, which did not seem to be noticed before: the product state π minimizing the trace distance, i.e. the probability of error in discriminating π from the correlated state ρ, is not the product of the marginals of ρ in general. We presented explicit examples including Werner states and rank-2 Bell diagonal states, where this fact became manifest. Unlike relative entropy-based approaches to correlations [11], for trace distance the total correlations are almost never equal to the sum of classical and quantum ones, but stay strictly smaller than that.
We have examined the behavior of quantum, classical and total trace distance correlations in two simple non-Markovian dynamical models: qubits under local phase-flip channels, and under the action of a random external field. The sudden transition between classical and quantum decoherence, first demonstrated for entropic quantifiers of correlations [34], occurs as well for trace distance correlations. However, the trace distance measures exhibit unique qualitative features, including the presence of frozen discord [24] under a greater range of starting states compared to other measures of quantum correlations.
The simple expressions obtained in this paper for trace distance correlations of Bell diagonal states make them amenable to precise experimental verification in highly controllable dynamical implementations realized either with photons [28,40] or with nuclear magnetic resonance techniques [25]. It might be intriguing to investigate in the future whether the gap between the trace distance total correlations and the sum of trace distance classical correlations plus discord can be of any operational significance in some information processing task. To our knowledge, one operational interpretation for a trace distance based quantifier of correlations was reported for the trace distance discord in the context of remote state preparation fidelity for noisy one-way quantum computations [41]. More generally, we reiterate that the trace distance discord also quantifies operationally the minimum entanglement (negativity) activated between a two-qubit system and an apparatus during a local premeasurement [7,8], as very recently observed experimentally [28].
Another interesting direction for future investigation would be to add one more layer to the hierarchy of trace distance correlations by computing the minimum distance from the set of separable states, which would define a measure of entanglement [2] based on trace distance. Finally, we can expect that some of the results presented here can be extended to more general classes of two-qubit states such as the X -shaped density matrices, adopting the methods of Ciccarello et al [22]. | 8,688.4 | 2013-07-15T00:00:00.000 | [
"Physics"
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Bogoliubov corner excitations in a conventional s-wave superfluid
Higher-order topological superconductors and superfluids have triggered a great deal of interest in recent years. While Majorana zero-energy corner or hinge states have been studied intensively, whether superconductors and superfluids host higher-order topological Bogoliubov excitations with finite energies remain elusive. In this work, we propose that Bogoliubov corner excitations with finite energies can be induced through only mirror-symmetric local potentials from a trivial conventional s-wave superfluid. The topological Bogoliubov excited modes originate from the nontrivial Bogoliubov excitation bands. These modes are protected by the mirror symmetry and are robust against mirror-symmetric perturbations as long as the Bogoliubov energy gap remains open. Our work provides a new insight into higher-order topological excitation states in superfluids and superconductors.
Introduction and motivation
Topological phases have ignited intensive research interests in the past two decades.Intrinsic topological states with n-th order in d dimension exhibit d − n dimensional gapless boundary states.Due to the bulk-boundary correspondence, the nontrivial bulk topology for the higher-order topological states (n > 1) is different from the conventional (n = 1) topological states [1][2][3][4].The celebrated tenfold way can characterize the first-order topological insulators and superconductors in a unified way in terms of three nonspatial symmetries, i.e. time-reversal, particle-hole, and chiral symmetries [5][6][7].However, higher-order topological states are usually related to crystalline symmetries, and comprehensive topological classifications have been made recently with point group symmetries [8][9][10][11][12].
In this paper, we show that Bogoliubov corner excited modes could emerge in a conventional s-wave superfluid on a honeycomb lattice with the mirror-symmetric onsite potential.To gain more intuitive insight, we first showcase an s-wave superconductor on a one-dimensional (1D) lattice with inversion-symmetric potential hosting topologically nontrivial edge excitation modes, despite the ground state for the superconductor is in a trivial phase.These topological modes could extend to a defect chain with non-zero mirror symmetric onsite potentials on a two-dimensional (2D) square lattice.Furthermore, the higher-order topological Bogoliubov corner excitation modes are present in an s-wave superfluid on a 2D honeycomb lattice.These Bogoliubov excitation modes are protected by the nontrivial topology for the Bogoliubov excitation bands, and are robust against mirror-symmetric perturbations.
The remainder of this paper is organized as follows.In section 2, we take a simple 1D s-wave superconductor as an example to show that the inversion-symmetric onsite potential could induce localized edge excitation modes.The topological origin of edge modes is explored and demonstrated.In section 3, we consider a defect chain on a 2D square lattice exhibiting robust edge modes.In section 4, we consider an s-wave superfluid on a honeycomb lattice with the mirror-symmetric potential, and show the Bogoliubov corner excitation modes.In section 5, we discuss relevant topics including experiment realizations, and draw a conclusion.
Bogoliubov edge excitations in 1D s-wave superconductors
We first consider a simple model, i.e. 1D s-wave superconductor, to present topologically protected Bogoliubov edge excitations induced by the inversion-symmetric potentials, as shown in figure 1(a).Its physics is described by the Hamiltonian Ĥ = Ĥ0 + ĤV .The first part reads where t denotes the tunneling strength between nearest neighbor sites, ⟨. ..⟩ represents the summation over all nearest-neighbor sites, σ = (↑, ↓) is the spin index, and ∆ 0 is an s-wave superconductor order parameter.
The second term ĤV = ∑ i V i ĉ † i,σ ĉi,σ describes onsite potentials with inversion symmetry.In the following, we consider each unit cell consisting of four sublattices with the potentials V i = V a if mod (i, 4) = 0 or 1 and V i = V b if mod (i, 4) = 2 or 3.For simplicity, we set V a = −V b = V throughout the paper if not otherwise specified.We set nearest-neighbor hopping as the unit of energy.
Through the Fourier transformation, the Hamiltonian Ĥ for the system with periodic boundary conditions can be written as 2 (1 ± cos k), and ξ 0 = t 2 sin k.The Pauli matrices s, σ, τ act on sublattice space, spin space and particle-hole space, respectively, while the nought subscripts represent identity matrices.
The system preserves time-reversal (T ), particle-hole (P) and chiral symmetries (C).The energy spectra for the system are given by Each energy level is four-fold degenerate.The energy gap for the two excitation bands E +,+ and The system preserves inversion symmetry with I = s x s x σ 0 τ 0 .In the absence of inversion-symmetric potentials, namely V = 0, the two Bogoliubov excitation bands are degenerate at inversion-symmetric k = π with ∆E = 0, as illustrated in figure 1(b).When V ̸ = 0, an energy gap ∆E ̸ = 0 is opened, as shown in figure 1(c).Therefore, the introduction of inversion-symmetric potentials opens the gap for excitation bands, which implies a topological phase transition as discussed in the following.
To demonstrate the topological properties of the system, the eigenenergies for a chain with open boundaries are computed and plotted in figure 2(a).We observe four degenerate states emerge at the gap between the excitation bands.Two states localize at the left end and the other two localize at the right end of the chain, as illustrated in figure 2(c).So far, we have focused on the special cases V a = −V b = V for simplicity.We would like to remark that if V a ̸ = −V b , the system also preserve the inversion symmetry, and the Bogoliubov edge states could also be driven from a the conventional s-wave superconductor.In We also note that the energy gap ∆E between the two excitation bands above zero energy is determined by ∆ 0 and the onsite mirror-symmetric potential.The topological corner modes remain isolated from the bulk excitations in the energy gap even if ∆ 0 decreases an infinitesimal quantity when We would use the Wilson loop approach to characterize the bulk topology of the system with inversion symmetry.The base momentum point is set to be k .The corresponding Bloch wave functions are denoted by |u m (k)⟩ with m representing the band index.We construct a matrix where n stands for the number for occupied bands.The Wilson loop operator then is defined as where ∆k = 2π /N, and N is the number of unit cells.The effective Hamiltonian is defined by H = −i ln W/π .The eigenvalues for H are denoted by v s with s = 1, 2, . .., n.The bulk topological invariant is then given by ξ = ∑ n s=1 v s .Through numerical calculations, the topological invariant is given by ξ = ±2 in superconductor phase if V ̸ = 0, suggesting two localized Bogoliubov edge excitations would appear at each one edge of the 1D lattice, as demonstrated in figure 2. The localized Bogoliubov edge excitations are topologically protected and robust against inversion-symmetric perturbations as long as the bulk energy gap remains open.See appendix for detailed discussions.
The above simple toy model exhibits interesting topological properties induced by inversion-symmetric potentials.However, the long-range superconductor order in a 1D realistic system is forbidden due to the strong quantum fluctuations.In the following, we would propose a realistic platform to manifest intrinsic first-order and higher-order topology, whose topology can be explicitly understood from the above 1D model.
Bogoliubov corner excitations in an s-wave superfluid on a square lattice
Here we consider ultracold Fermionic atoms with pseudo spin loaded in a 2D square lattice.The physics for the system is described by a tight-binding Hamiltonian as where U is the strength of an onsite attractive SU(2)-invariant interaction, and µ denotes the chemical potential.Given a local dip potential with mirror symmetry applied to a one-dimensional line as shown in figure 3(a), the one-dimensional defect chain also enjoys the mirror symmetry along x.The total Hamiltonian then becomes where 3 on sites on the defect chain "Def".
As the interaction U becomes stronger, the fermions would be paired and enter a superfluid phase when U exceeds a critical value.The superfluid order at the lattice site i is assumed as Through the Bogoliubov-Valatin transformation, the creation operators ĉ † i,↑ and ĉ † i,↓ are written as where N u is the number of unit-cells, and ψ † n and ψn are creation and annihilation operators for Bogoliubov quasi-particles such that the Hamiltonian Ĥsqu can be diagonalized.The coefficients u n i,σ and υ n i,σ can be derived from the following equations where Ĥ0,ij,σ denotes the element of the Hamiltonian matrix Ĥsqu with U = 0 under the basis Ψ = ( Ĉ1 , . .., Ĉm , . .., Ĉ2Nu ) T with Ĉm = (ĉ m,↑ ,ĉ m,↓ ).
Through the numeric calculations, we compute the superfluid order parameter at each lattice site on a square optical lattice under open boundary conditions, as shown in figure 3(c).The superfluid order on the defect chain is weaker than that in other regions due to the non-zero mirror symmetric potentials.In addition, we observe that the superfluid order on the boundary is stronger than that in the bulk, and the superfluid order in the bulk is nearly uniform.This is consistent to the intuition that the lattice sites in the bulk are less affected by the boundary.The eigenenergy distributions versus potential V have been shown in figure 3(b), indicating isolated states (denoted by red lines) emerge in the energy gap for Bogoliubov quasiparticles.The particle density distributions for the isolated states, as plotted in figure 3(d), showcase these in-gap states are localized at the end of the defect chain.
We would like to remark that the above defect chain can be considered as a one-dimensional s-wave superfluid imprinted on the 2D lattice.While the defect chain couples with other chains, it also exhibits topological nontrivial properties as long as the energy gap remains open.
Bogoliubov corner excitations in an s-wave superfluid on a honeycomb lattice
Consider a two-component Fermi gas loaded in a 2D honeycomb optical lattice with a uniform chemical potential.Turning on the onsite attractive interaction for fermionic atoms, the fermions would be paired and enter the s-wave superfluid phase from the semimetal phase when the interaction exceeds a critical value [41].Its Bogoliubov excitations are gapless and show trivial properties.Hereafter, we would consider there exists onsite potential with mirror symmetry as shown in figure 4(a), and showcase Bogoliubov corner excitations could be induced from the excitation bands.
At the mean-field level, the physics of a system with a mirror-symmetric potential is described by the Hamiltonian as under the basis vector 2,3,4 denotes the superfluid order parameter on the sublattice site m as indexed in figure 4(a).The Hamiltonian preserves mirror symmetries, M x = (s x s x .D) σ 0 τ z and M y = (s 0 s 0 .D) σ 0 τ 0 , where D is a diagonal unitary matrix [42].The self-consistent equations for the superfluid order and particle filling ratio are given by Through numerical self-consistent calculations for equations ( 11) and ( 12), we find ∆ m ≡ ∆ and n m ≡ n for all m at zero temperature.The rich phase diagram, which has been shown in figure 4(b), exhibits a range of interesting and physically distinctive phases including semimetal (SM), second-order topological insulator (STI), and superfluid phases with a non-zero superfluid order (normal superfluid and superfluid with Bogoliubov corner excitations).Here the chemical potential µ is set to be zero, so the filling ratio is not fixed.Figure 4(b) showcases that at fixed interaction, for example U = 4, as V becomes larger, the system would enter STI since it is hard to form pairing when V exceeds a critical value.We compute the energy spectra for the superfluid under periodic boundary conditions and the numerical results are presented in figure 5. We observe the s-wave superfluid order opens the energy gap for the Dirac semimetal, as shown in figures 5(a) and (b).However, the Bogoliubov excitation band remains gapless.After turning on the onsite potential with mirror symmetry, a direct energy gap emerges, as depicted in figure 5(c).As the potential strength increases, the energy gap becomes larger and a full gap exists when the potential exceeds a critical value, as illustrated in figure 5(d).
To explore the nontrivial properties of Bogoliubov excitation bands, we calculate the eigenenergies for the superfluid versus V with fixed interaction U under open boundary conditions.Four degenerate states emerge in the energy gap for Bogoliubov excitations, as shown by the red lines with four-fold degenerates in figure 6(a).They are localized at two corners of the sample as shown in figure 6(c).Through the numeric calculations, we compute the superfluid order parameters at each lattice site on a honeycomb optical lattice under open boundary conditions, as shown in figure 6(b), we can observe that the bulk superfluid order is uniform.Through comparing figure 6(c) with (d), it is also clear that with increasing potential V, the Bogoliubov corner modes become more localized.In summary, there are two different Bogoliubov excitations in the superfluid phase, one with gapless Bogoliubov excitation bands dubbed NSF, and the other with gapped Bogoliubov excitation bands called CSF, as shown in figure 4(b).We would like to emphasize that figure 4(b) combines the quantum phase diagram (consisting of semimetal, second topological insulator and superfluid) and the state diagram (consisting of supefluid with and without Bogoliubov corner excitations).The transition between STI and CSF is a second-order phase transition from a band insulator to an s-wave superfluid.For example, at a fixed interaction U = 6, the superfluid phase gradually evolves as V decreases.The energy gaps for the Bogoliubov excitation bands in CSF and single-particle excitation bands in The emergence of Bogoliubov corner excitations is the exhibition of the bulk topology, characterized by the topological invariant protected by mirror symmetry.Taking a similar procedure as in the one-dimensional case above, the topological invariant at each k y is defined by where the Wilson loop operator reads W x,k = F x,k+Nx∆kx . ..F x,k+∆kx F x,k , ∆k x = 2π /N x , and N x is the number of unit cells in the x direction.The entry of matrix with N y the number of unit cells in the y direction, and ξ ′ y takes similar form as ξ ′ x .Through numeric calculations, we obtain the topological invariant (ξ ′ x , ξ ′ y ) = (2, 0) in the CSF regime and (0, 0) in NSF regime, as shown in figure 4(b).In summary, the s-wave superfluid phase have two different types of Bogoliubov excitations: trivial Bogoliubov excitations in NSF regime, and higher-order Bogoliubov corner excitations in CSF regime.We emphasize that the ground state of the s-wave superfluid in both regimes is topologically trivial.The topological property of excited corner modes originates from the Bogoliubov excitation bands.
Discussions and conclusions
The s-wave superfluid with a uniform chemical potential exhibits trivial Bogoliubov excitation on a 1D lattice, and 2D square or honeycomb lattice.Intriguingly, we find the onsite potential with mirror symmetry could open the energy gap in Bogoliubov excitation spectrums.The Bogoliubov excitation bands exhibit topological nontrivial properties and the edge modes manifest themselves as zero-dimensional (0D) Bogliubov excitations localized at the end of a 1D lattice and the corners of a 2D honeycomb lattice, although the ground states for the systems remains in a trivial phase.Since the systems preserve inversion or mirror symmetry, the winding number can characterize the nontrivial excitation band.
We would like to remark that our model in this work can be implemented in ultracold atoms.The 2D square and honeycomb optical lattices have been implemented in experiments [43][44][45][46][47].The mirror symmetric potential could be realized by tuning the laser beams.For example, the mirror-symmetric potential on 2D square lattice can be achieved through a pair of coherent counterpropagating laser beams with wave length 2a and 8a along x [48].The onsite attractive interaction could be finely tuned through Feshbach Resonance technique [49][50][51][52].The Bogoliubov excitation band could be detected through the momentum-resolved spectroscopy based on two-photon process that transfers energy and momentum to the New J. Phys.26 (2024) 033050 W Tu et al ensemble of atoms [53].The localization character of topological corner modes can be determined by looking at their localization length detected by a spectroscopy setup [54].
In summary, we propose that topological Bogoliubov excitations can be induced solely by onsite potentials in a topologically trivial conventional s-wave superfluid.The edge excitations manifest themselves as 0D modes localized at edges or corners of the system.These modes are robust against inversion or mirror symmetric perturbations as it preserves the degeneracy.Our work provides new insights for understanding higher-order topological excited states in conventional superconductors and superfluids, and also provides realistic platforms for engineering nontrivial Bogoliubov corner excitations in real experiments.
Appendix. Robustness of edge and corner modes against perturbations
We consider two cases to show the robustness of edge and corner modes against mirror-symmetric random perturbations on onsite potentials.We first impose the perturbations on a 1D lattice with edge modes.It takes the form Ĥper = ∑ i,σ Γ i ĉ † i,σ ĉi,σ , where the random potential Γ i = κγ i , κ represents the amplitude, γ i = γ N−i+1 ∈ [0, 1] is a random quantity with i ⩽ N/2 and N the number of lattice sites.We take a 1D lattice with N = 40 and compute the energies of the system for different onsite perturbations, as shown figure 7(a).Figure 7(b) showcases the particle density distribution of the corner modes for κ = 0.1.The above results indicate that four degenerate in-gap corner modes are robust against mirror-symmetric perturbations while they may acquire a finite energy shift.Next we consider the mirror-symmetric perturbations on the honeycomb lattice with corner modes.Similar results are obtained as shown in figures 7(c) and (d).In summary, the degenerate edge and corner modes are robust against the mirror-symmetric perturbations on onsite potentials as long as the energy gap remains open.We would like to remark that the degeneracy of edge and corner excitations is protected by the inversion or mirror symmetry.If the inversion or mirror symmetry is broken by the random local disorder, the degeneracy would be lifted and the edge and corner modes may disappear.
Figure 1 .
Figure 1.(a) Illustration of a 1D lattice with inversion-symmetric onsite potentials Va and V b .Each unit cell consists of four sublattice sites indexed by 1-4 (from left to right).(b) and (c) Energy spectra for 1D superconductor with onsite potentials Va = −V b = 0 and Va = −V b = 0.2, respectively.The superconductor order parameter is set to be ∆0 = 0.6 in (b) and (c).Common parameter is set to be t = 1.
Figure 2 .
Figure 2. (a) and (b) Eigenspectrum versus inversion-symmetric onsite potential V for a 1D lattice with 40 sites.The in-gap red lines denote four-degenerate Bogoliubov edge excitation modes, where each edge of 1D lattice hosts two localized modes.In panel (a), we set Va = −V b = V while in (b), we choose Va = V, V b = −0.8V.(c) and (d) The particle density distribution versus the site index, corresponding to the colored dish in panels (a) and (b) respectively.To be specific, in panel (c) Va = −V b = V = 1 and in panel (d) Va = 1, V b = −0.8.Common parameters are set to be ∆0 = 2, t = 1.
Figure 3 .
Figure 3. (a) Illustration of a square lattice with a defect chain respecting the mirror symmetry.(b) Eigenspectrum for the s-wave superfluid versus mirror-symmetric onsite potential V on the 20 × 19 square lattice.The in-gap red lines indicate four-degenerate Bogoliubov corner excitation modes.(c) Distributions of s-wave superfluid order parameters on the square lattice with a defect chain.(d) Particle density distributions of the in-gap states.The blue dashed line denotes the defect chain.The Bogoliubov excited states shown in (c) and (d) have been indicated by the blue dot in (b) with the mirror-symmetric onsite potential V = 5.Common parameters in (b)-(d) are set to be t = 1, U = 10, µ = 0.05.
Figure 4 .
Figure 4. (a) Illustration of a honeycomb lattice with a mirror-symmetric onsite potential.Each unit-cell consists of four sublattice sites indexed by 1-4 with onsite potential configuration (V1, V2, V3, V4) = (Va, V b , V b , Va).(b) A rich global phase (state) diagram plotted against the potential and interaction strength including second-order topological insulators (STI), semimetal (SM), normal superfluid (NSF) and superfluid with Bogoliubov corner excitations (CSF).The parameters are set to be t = 1 and µ = 0.
Figure 6 .
Figure 6.(a) Eigenspectrum versus mirror-symmetric onsite potential V for the honeycomb lattice.The in-gap red lines denote four-degenerate Bogoliubov corner excitation modes.(b) Distributions of s-wave superfluid order parameters on the honeycomb lattice.(c) and (d) Particle density distributions of the in-gap states.These chosen parameters in sub-figures also have been indicated by colored dots in (a).In (b) and (c), Va = −V b = V = 2.2.In (d), Va = −V b = V = 4.5.Common parameters are set to be t = 1, U = 10.
Figure 7 .
Figure 7. (a) Eigenenergies E vs the state index in the presence of mirror-symmetric perturbations with different amplitude k = κ on a 1D lattice.The parameters are ∆0 = 2, V = 1 (b) The particle distribution of the in-gap modes denoted by stars in (a).(c) and (d) Similar to (a) and (b) but with U = 6 and V = 2 on a honeycomb lattice.Common parameter is set to be t = 1.
⟨u m,k+∆kx |u m,k ⟩ with |u m,k ⟩ being the Bloch wave function of the energy bands E m (k), i.e. h h (k) u m,k = E m (k) while ξ x | 5,007.8 | 2024-03-20T00:00:00.000 | [
"Physics"
] |
Microscopic Electron Dynamics in Metal Nanoparticles for Photovoltaic Systems
Nanoparticles—regularly patterned or randomly dispersed—are a key ingredient for emerging technologies in photonics. Of particular interest are scattering and field enhancement effects of metal nanoparticles for energy harvesting and converting systems. An often neglected aspect in the modeling of nanoparticles are light interaction effects at the ultimate nanoscale beyond classical electrodynamics. Those arise from microscopic electron dynamics in confined systems, the accelerated motion in the plasmon oscillation and the quantum nature of the free electron gas in metals, such as Coulomb repulsion and electron diffusion. We give a detailed account on free electron phenomena in metal nanoparticles and discuss analytic expressions stemming from microscopic (Random Phase Approximation—RPA) and semi-classical (hydrodynamic) theories. These can be incorporated into standard computational schemes to produce more reliable results on the optical properties of metal nanoparticles. We combine these solutions into a single framework and study systematically their joint impact on isolated Au, Ag, and Al nanoparticles as well as dimer structures. The spectral position of the plasmon resonance and its broadening as well as local field enhancement show an intriguing dependence on the particle size due to the relevance of additional damping channels.
Introduction
An accurate description of microscopic properties of metal nanoparticles (metal NPs-MNPs) is important to predict the optical response of e.g., molecules in close proximity to metal surfaces and resulting field enhancement and quenching effects. Nanoparticles as part of functionalized layers in sensing, spectroscopy [1] and light harvesting applications, photovoltaics [2][3][4][5][6][7] and photocatalysis [8][9][10][11][12], can improve the performance of such devices. They are efficient subwavelength scatterers improving the light trapping effect and MNPs provide, in particular, large local fields enhancing charge carrier generation, absorption, and light-induced effects from other nanostructures such as spectral conversion [13] or photoluminescence [14].
For over a hundred years, modeling of the optical properties of MNPs relies on classical electrodynamics. In highly symmetric cases (spherical and cylindrical NPs) analytic solutions are obtained within Mie scattering theory [15] using corresponding basis functions. The electric part E of the electromagnetic field creates a polarization field P = α( 0 , )E in solid matter, expressed in terms of the permittivities 0 (ω) and (ω) of the environment and the bulk material, respectively. This polarizability α, depending only on the optical response at a frequency ω, neglects microscopic electron interaction effects at the ultimate nanoscale arising not only from the quantum nature of the free electron gas in metals, but also from accelerated motion in the plasmon oscillation. produce scattering and interference effects of electrons which mutually interact with incoming light, see Figure 1a. Hereby, h is Planck's constant, m is the (effective) electron mass which depends on the bulk material, and E is the energy of the electron wave. Typically, this wavelength is about 7.5 nm in solids at room temperature T = 300 K, where E = k B T with the Boltzmann constant k B . For MNPs, the main source of electron scattering is the particle surface, see Figure 1b, where the surface-to-volume ratio indicates the relevance of such scattering events. Microscopic interaction effects of electrons in metals are accurately described using first-principle methods, e.g., Density Functional Theory (DFT) [16][17][18]. These solve Schrödinger's equation for a large, but finite number of electron wave functions from all atoms in the considered system. Unfortunately, even with strong approximations such as the Time Dependent Local Density Approximation (TDLDA), time-consuming algorithms limit their applicability to particles of a few nanometers in size [19][20][21]. Moreover, advances in fabrication of nanostructures along with experimental access to particle sizes and interparticle spacings below 10 nm led to the possibility of direct or indirect observation of such effects [22][23][24][25][26][27][28][29]. The situation described above resulted in increased interest in semi-classical approaches towards the incorporation of damping and interaction effects stemming from the quantum nature of charge carriers, illustrated in Figure 1. In this article, we present two such semi-classical approaches, the Random Phase Approximation (RPA) and Generalized Nonlocal Optical Response (GNOR), and ultimately combine them into a single framework to study their joint impact on MNPs of different materials, sizes and in different environments.
The original formulation of light scattering by a sphere by Gustav Mie [15] excludes microscopic dynamics of the conduction band electrons in bulk and surface effects. However, efforts to extend have been made since the 1970s [30][31][32][33][34][35][36][37][38][39]. Advanced semi-classical material models can be derived from perturbative theories [40,41], by separating the free electron dynamics from the core electron polarization via the hydrodynamic equation for an electron plasma [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], and from microscopic theories [60][61][62][63][64]. It should be noted that a major advantage of ab initio methods lies in their capability to account for the electron spill-out (evanescent tail of the electron wave functions) of the electron density into the surrounding dielectric medium. It was shown within the hydrodynamic framework that the electron spill-out can be adequately incorporated [57,65] and a current-dependent potential can be accounted for [66], which is, however, out of scope of the present study. In this article, we combine two semi-classical approaches towards microscopic electron dynamics into a single feasible framework to address quantum corrections in MNPs allowing the description of isolated particles, clusters and large-scale (two-or three-dimensional) devices via the integration of analytical expressions into standard procedures. We hereby focus on results on damping in MNPs derived from the microscopic Random Phase Approximation (RPA), stemming from Lorentz friction, and spatial dispersion (nonlocal) effects obtained with the hydrodynamic approach. We discuss briefly the separate ingredients of these approaches in the next sections and give more details in the methods section. Moreover, we compare and combine the different processes of mesoscale electron dynamics stemming from scattering, Figure 1a,b, irradiation (Lorentz friction), Figure 1c, and nonlocal interaction, Figure 1d, and study their impact on the optical response of isolated MNPs and dimers. An emphasis is put on the size regimes where these effects are dominant for the materials silver, Figure 2, as well as for aluminum and gold, Figure 3.
Results
We briefly discuss classical electrodynamics and mesoscopic electron dynamics obtained from the RPA and GNOR theories. In summary, we compare quantum correction models stemming from microscopic RPA derivations with the following, semi-classical damping expressions and nonlocal interaction effects. Both approaches are described in more detail in the next sections and the methods section. The advantage in the analytic formulation is the straightforward integration with existing computational tools for nanospheres using modified Mie simulations and multiple scattering techniques [67] for clusters thereof or commercial software such as COMSOL (http://www.comsol.com).
Classical and Phenomenological Approaches
Typically, the optical response of a metal is described with the Drude model via the frequencydependent permittivity where b is the background permittivity given by bound (valence band) electrons, ω 2 p = 4πn 0 e 2 /m is the plasmon frequency, determined by the material dependent electron density n 0 and mass m, and γ p is the inherent (bulk) damping rate. This widely used Drude model applies only to bulk material and should be modified for nanostructures to include effects due to the finite size of the system. One of the corrections considered by Kreibig and von Fragstein [68] is the inclusion of an additional damping due to the scattering on the physical particle boundaries, depicted in Figure 1b. This is in particular important in particles of sizes equal or smaller than the mean free path λ b of electrons in bulk metal. In such a case, the electrons will experience (in the classical picture) additional scattering from the boundary of the system. Mathematically, it is described as γ K = v F/L e f f , where v F is the Fermi velocity of the electron gas and L e f f is the effective mean free path of electrons resulting from collisions with the particle surface [38,68,69]. The common feature is that L e f f reflects the volume (proportional to the number of electrons inside the nanoparticle) to surface ratio of the particle. According to this, we get the γ K (a) = Cv F/a, where a is the radius of the nanoparticle and C is a constant of the order of unity which depends on the scattering type and particle radius. Similarly, collision effects in the bulk, depicted in Figure 1a, can be described via the damping term γ p = v F/2λ b .
Random Phase Approximation
Nevertheless, this phenomenological approach neglects the microscopic dynamics of electrons inside the MNP. Their accelerated movement (plasmon oscillation) leads to energy loss via irradiation of the electromagnetic field, see Figure 1c. In case of nanoparticles much smaller than the incident wavelength, this effect can be expressed by the Lorentz friction, an effective field stemming from the plasmon induced dipole field D(t) as E L = 2 /3c 3 ∂ 3 D(t) /∂t 3 , with c being the speed of light [70]. The dynamics of the electron density can be described using a driven, damped oscillator, with the incident electromagnetic wave being the driving force and the damping arising form electron scattering (bulk γ p and Kreibig damping γ K ) and electromagnetic field irradiation (Lorentz friction).
An analytical form of the exact solution for the damping γ and self-frequency ω L (the exponents Ω i of solution ∼e iΩ i t for self-modes i) including Lorentz friction exists [61], which is discussed in more detail in the methods section. They can be summarized as follows 3 and 1/τ 0 = γ p . Exact inclusion of the Lorentz friction indicates that the radiative losses and the self-frequencies are a complicated function of particle radius as given by Equation (3), see the methods section for a detailed discussion.
Direct comparison to experimental work for this framework is available within Refs. [61][62][63][64] and good agreement has been found.
Nonlocal Optical Response
Aside from electron irradiation due to Lorentz friction, we discuss spatial dispersion (nonlocality) which denominates the effects of electron coupling over a short distance, see Figure 1d [40]. Such interactions are inherent to the solution for the displacement field D of the Coulomb equation In homogeneous media, we can assume a dependence on the distance |r − r | rather than on the specific position of electrons, which allows solving Maxwell's equations in Fourier space D(ω, k) = (ω, k)E(ω, k).
The dependence on the wave vector k enables us to describe nonlocal electron-electron interaction (Coulombic force) and electron diffusion effects. It is important to note that the large-k response that originates in the subwavelength oscillations of plasmonic excitations is not only an inherent prerequisite for many intriguing wave phenomena, but also particularly sensitive to nonlocality. However, the common Mie result has no upper wavelength cut-off and does suppress short-range electron interactions which can strongly dampen the response beyond ω/v F . We show in the corresponding section below that accounting for nonlocal response leads to longitudinal pressure waves as additional solutions to the combined system of differential equations of the electromagnetic wave equation and (linearized) Navier-Stokes equation. This is in contrast to the damping expressions derived by Kreibig and for Lorentz friction. Such additional waves offer further damping channels, however, they can also support resonant enhancement effects [12,51,59,71].
Remarks on Retardation, Multipolar Response and Computational Feasibility
Both of the presented semi-classical approaches towards microscopic corrections in the mesoscale electron dynamics in metal nanoparticles have the advantage of analytic expressions fully compatible with existing computational procedures. For the quantum confinement picture of Kreibig and the mesoscopic RPA result for the Lorentz friction, modified damping terms were derived, see Equations (1a)-(1d), which can be used to directly replace the damping in the Drude expression for the permittivity given in Equation (2) and subsequently be used in standard Mie calculations and procedures to calculate optical properties of complex structures, e.g., with a multiple scattering approach [67] or within commercial software such as COMSOL.
It is important to note that although all electrons participate in plasmon oscillations, part of their irradiation is absorbed by other electrons in the system. This is in analogy with the skin-effect [72] in metals and introduces an effective radiation active electron layer of the depth h ∼ 1 /σω (σ is the conductivity) underneath the particle surface. Therefore, the effective energy transfer outside of the nanoparticle will be reduced by the factor 4π 3 (a 3 −(a−h) 3 )/ 4πa 3 3 . According to this, we expect a decrease of radiative damping, especially for larger particles.
The nonlocal theory introduces a novel type of electron motion, longitudinal pressure waves, in addition to the transversal modes stemming from the classical electromagnetic wave equation. This additional electronic excitation offers further damping channels due to the energy lost in dampened motion. Here, the Mie coefficients are derived from the coupled system of optical and electronic excitation yielding modified scattering matrices that can again be implemented in existing methods. The properties of the longitudinal wave are given by analytic expressions such as their wave vector and their importance with respect to the common Mie solution is entirely captured in a single additional term, see the methods section for details.
Retardation is important when either the particle radius or the overall system size becomes large, i.e., for particle dimers, clusters and arrays. Although the presented microscopic effects are highly localized, they can have a strong impact on a larger particle or system in the interplay with long-range retardation effects. In addition, particle layer modes can couple to nonlocal modes within particle arrays and thus increase their impact on a larger scale [59,71]. It is thus noteworthy that the hydrodynamic theory and the damping terms stemming from microscopic analysis within the RPA allow fully retarded calculations; equally for planar geometries (nonlocal Fresnel coefficients) [51] and regular, two-dimensional particle arrays [41,59,71] and even charge carriers in electrolytes (Nonlocal Soft Plasmonics) [12].
Single Metal Nanoparticles
We compare the quantum correction models introduced in the previous section, see Figure 1, as well as the combined effect of Kreibig damping Equation (1b), Lorentz friction Equation (1d) and spatial dispersion to classical Mie calculations for the materials gold, aluminum and silver in Figures 2 and 3. Hereby, we show the effect on the Localized Surface Plasmon Resonance (LSPR) for all materials in Figure 2a, confirming that the modified damping rates do not alter the resonance position predicted by the classical calculations, whereas nonlocal response-and in combination with any damping model-does predict an increasing blueshift of the nanoparticle resonance with decreasing particle size. Looking at the extinction cross section as a function of particle radius in Figure 2b for silver and Figure 3 for gold and aluminum, we find that all correction models result in a reduction of the optical response in dependence of both the material and particle size, typically yielding a different optimized particle size. Hereby, Kreibig damping with a ∼1/a dependence drastically attenuates the optical response for the smaller size regime below the maxima (15 nm for Ag, 20 nm for Au, and 10 nm for Al), while the complex size dependence of Lorentz friction results in a greater effect above this particle size. The diffusion coefficient in the hydrodynamic (GNOR) model (imaginary part of the nonlocal parameter β GNOR ) is chosen thus that its dampening effect captures the Kreibig result [56]. This is best seen in Figure 3a for Au. The hydrodynamic pressure (real part of the nonlocal parameter β GNOR ) describes Coulomb interaction between electrons and results in the blueshift observed in Figure 2a at very small particle sizes below 5 nm. We can further incorporate the analytical expressions for Lorentz friction. This combined result shows the strongest attenuation since all different damping channels are included. At a larger particle size (60 nm for Ag, 80 nm for Au, and 40 nm for Al) all material models converge with classical Mie theory where the mesoscale electron dynamics cease to have an impact.
The damping associated with the Lorentz friction can be approximated to the simpler perturbative expression Equation (1c) in a narrow size window, see the methods section for a detailed discussion. Since the exact solution can be obtained with analytical expressions which can be incorporated into standard calculation schemes, we discuss exclusively exact Lorentz friction results. Figure 4. Maximum enhancement factor EF= |E| 2 /|E 0 | 2 at the particle surface for gold. Dependence of (a) the maximum EF and (b) its wavelength position for the different quantum corrections on the particle radius in water. (c), (d) The same as a function of the permittivity 0 of the surrounding medium for nanospheres of (c) R = 10 nm and (d) R = 50 nm.
We study the (maximum) field enhancement factor EF= |E| 2 /|E 0 | 2 just outside of the NP (r → a+) for the different damping models in Figure 4 for gold nanospheres. Hereby, Figure 4a shows the spectral position of the field maximum. The local field enhancement reveals the size dependence of the field resonance with the damping rates. It should be emphasized that Kreibig damping shows a strong redshift for small particle sizes of the spectral position of local field enhancement maxima in contrast to experimental findings [25][26][27] and approaches the Mie result for larger sizes. Nonlocal optical response agrees with the blueshift of the plasmon resonance found experimentally for noble metals, as already seen in the extinction cross section, Figure 2a. However, in order to correctly describe simple metals, the inclusion the electron spill-out region [52,57,65] is crucial. Furthermore, advances towards the spatial dispersion found in (doped) semiconductors were made recently [73,74], which is of further interest when using dielectric nanoparticles to enhance the performance of photovoltaic devices.
Lorentz friction is closest to the classical calculation for smaller sizes and deviates stronger at larger sizes. This is in agreement with the findings of Figures 2 and 3. The corresponding field enhancement, shown in Figure 4b for gold MNPs in water, is strongly suppressed for the considered particle size range when including the damping models while spatial dispersion by itself reduces the predicted field enhancement mostly for smaller particle sizes and converges with the classical Mie result rapidly with increasing particle size. This behavior is corrected by incorporating Lorentz friction into the GNOR result. Figure 4c,d shows the (maximum) field enhancement of gold nanoparticles in dependence of the refractive index (RI) of the surrounding medium (from air n = 1 to Si n = 3.4) for two particle sizes. This is accompanied with a linear (in case of the nonlocal theory approximately linear) shift in the resonance wavelength towards longer wavelengths (not shown). With increasing RI of the host medium, the enhancement factor reaches a saturation value which for increasing particle size converges for all material models discussed. The discrepancy between the local field enhancement values predicted remains similar for small MNPs in different host media spanning several orders of magnitude. The complexity of the Lorentz friction makes it necessary to restrict ourselves to the dipolar response of the plasmon oscillation. It is therefore important to consider the material, particle size and wavelength regime in order to assess whether the dipolar response model is adequate for the system under study. We show in Figure 5 for Au NPs the dipolar and the converged result of local field enhancement obtained from classical Mie calculations at a fixed frequency close to the respective plasmon resonance. Here, the dipolar approximation is valid up to ca. 100 nm in particle radius which in general covers the discussed microscopic effects well. The inset in Figure 5 compares this for the combined theories showing small differences already for particles above 25 nm radius.
Dimers
For particle dimers, in addition to their size, the particle distance becomes important and retardation effects cannot be neglected for larger particles in close proximity. This can transfer the impact of localized microscopic electron dynamics onto a larger structure. Figure 6 shows the (maximum) field enhancement at the center of a gold dimer in water as a function of both particle size and distance for the different theories considered. The impact of nonlocal response, Figure 6b, on the classical Mie theory, Figure 6a, is visible as strong quenching of the local fields. It is worth remembering that one main effect is a blueshift in the position of the maximum enhancement factor, see again Figure 4a and Ref. [41]. In addition, the maximum field enhancement within the parametric area of particle and gap size is EF ≈ 9000 for the Mie calculations and EF ≈ 3000 for the nonlocal theory, showing that indeed there is an impact of the longitudinal waves found. The damping observed within Kreibig theory, Figure 6c, is dramatic for the dimer setup and the dominant contribution in the combined theory as seen in Figure 6d. This is also evidenced by comparing the Lorentz friction with and without nonlocal damping, see Figure 6e,f, respectively. The Lorentz friction has a strong impact on the optical response for larger particle sizes, but also dampens the dimer setup for increasing gap size, which points towards retardation and the increasing structural size as the main source for this damping effect. This leads to slightly stronger damping when combined with the additional plasmon quenching within GNOR in Figure 6f.
The strong field quenching poses limitations to the photovoltaic effect in solar cells. However, considering different materials for MNPs and their environment, the size regimes where local field quenching is dominant can be avoided with the presented theory of combined damping.
Summary
In conclusion, we have presented a number of semi-classical corrections to incorporate electron dynamics and non-classical interaction effects into optical response calculations for nanoparticles. Hereby, pure damping models, such as the Kreibig damping and Lorentz friction, derived from microscopic RPA theory, show an intriguing dependence on the particle size, where the material influences relevant size regimes. On the other hand, semi-classical nonlocal theories allow evoking additional modes in the system by explicitly considering mesoscopic dynamics of free electrons. This results in a correction of the spectral position of resonant phenomena and introduces additional, implicit damping channels. The phenomenological Kreibig damping does yield a plasmon broadening that agrees with experiments [38], however, it also introduces a redshift of the resonance with respect to the classical Mie result contrary to measurements on nanoparticles [25][26][27]29]. This is addressed by using the hydrodynamic GNOR (generalized nonlocal optical response) approach, i.e., by introducing a diffusion parameter, able to reproduce the Kreibig damping while fully capturing the observed plasmon broadening.
An important aspect is that the resulting analytical expressions can be implemented into existing computational procedures in a straightforward manner, as isolated theories or combined, allowing the comparison to experiments with little added numerical effort. We have studied the combined effect of these mesoscopic electron interaction effects for single nanospheres and gold dimers and have evidenced the importance of retardation as a way to communicate localized quantum effects and impact a larger structure.
The straightforward inclusion of electro-optical effects at the nanoscale into (metal) nanoparticle systems is of importance in nanostructures employed for photovoltaics and catalysis as well as in spectroscopy and sensing applications.
Electron Dynamics within the RPA
The model of electron dynamics inside MNPs [60][61][62] presented here is an extension to the RPA theory developed by Pines and Bohm [75] for bulk metals. In our model, a finite, rigid jellium defines the shape of a nanoparticle. The plasmon oscillations are described as local electron density fluctuationŝ ρ(r, t) obtained from the Heisenberg equation with a corresponding HamiltonianĤ e for electrons inside the MNP in the jellium model taking the following formĤ The operator of the local electron density is defined as where Ψ e is the electron wave function, N e is the number of collective electrons, r j and m are their positions and mass. The ion field is approximated as averaged background charge density and described as n e (r)|e| = n e Θ(a − r)|e|, where Θ is the Heaviside step function, a is the radius of the MNP and n e = N e/V. The first term in the Hamiltonian stands for the kinetic energy of electrons, the second for interaction between electrons and positive background charges (approximating the ion lattice potential) and the last for electron-electron Coulomb interaction.
Taking into account the sharp form of the positive charge density n e (r), one can decompose Equation (5) into two parts corresponding to the inside and outside of the NP, which leads to two separate solutions describing the surface and bulk plasmons. This description is valid for NPs larger than ca. 5 nm for which the surface is well defined and the spill-out effect is negligible. δρ(r, t) = δρ 1 (r, t), for r < a, δρ 2 (r, t), for r ≥ a,(r → a+) .
The electron density fluctuations are then described with the formulas and where F is the Fermi energy.
The structure of the above equations is of an harmonic oscillator, which allows including a damping term in phenomenological manner by adding to the right hand side − 2 /τ 0 ∂ρ 1(2) (r,t) /∂t. The damping 2 /τ 0 = γ p + γ K includes collision effects and Kreibig damping due to the particle boundary.
Assuming homogeneity of the external electric field E(t) inside the NP (dipole approximation), the solution for surface modes reduces to a single dipole mode and for bulk modes δρ(r, t) = 0 where r < a.
The function Q 1m (t) (m = −1, 0, 1) represents dipole modes, Y lm (Ω) is the spherical function. The former can be related to the vector q(t) via Then the plasmon dipole can be defined as Knowing this, the damping caused by electric field irradiation can be simply added to the right hand side of Equation (12) as additional field E L = 2 /3c 3 ∂ 3 D(t) /∂t 3 hampering charge oscillations and can be rewritten in the form The above equation is a third order linear differential equation and the exponents ∼e iΩ i t of its solutions are given in Equation (3). A perturbation approach can be applied to Equation (14) for small particles using ∂ 2 D(t) /∂t 2 = −ω 2 1 D(t). Then the resulting damping term takes the form 3 . The comparison of both damping terms is shown in Figure 7 justifying the usage of the perturbation formulation for (gold) particles with radii up to ca. 30 nm, where the second term proportional to ∼a 3 still fulfills the perturbation constrain. For larger radii, the discrepancy between both solutions grows rapidly since the irradiation losses within the perturbation approach scale as a 3 . Therefore, the radiative losses dominate plasmon damping for large nanospheres. On the other hand, scattering is more important for smaller nanospheres scaling as 1 a . One can observe thus the size-dependent crossover in Figure 3a of the damping at ca. 12 nm for gold.
Electron Dynamics with the Hydrodynamic Model
In recent years, a great effort to theoretically [41,43,44,[46][47][48][49][50][51][53][54][55][56]59] describe and subsequently to experimentally [25][26][27]29] verify the effect of spatial dispersion in metals was made. In the hydrodynamic approach, coupling the electromagnetic wave equation to the (linearized) Navier-Stokes equation allows treating the conduction band electrons as a plasma subject to short-ranged interaction such as the Coulomb force included in the pressure term p = β 2 ρ ind and electron diffusion via the diffusion coefficient D. It is convenient to abbreviate β 2 GNOR = β 2 + D(γ p − iω) (where GNOR refers to the Generalized Nonlocal Optical Response model [55,56]). With this, we can write the wave equation in a compact form where and ⊥ = b − ω 2 p/ω(ω+iγp ). Together with the continuity equation ∇j ind = iωρ ind , we readily obtain a separate wave equation for the induced charges where ∇E = 4π / b ρ ind was used. This yields the wave vector of the longitudinal field and motion of electrons Nonlocal theories predict finite distributions of induced charges at an illuminated metal surface-in contrast to classical electrodynamics-with a characteristic penetration depth Im(1/q) comparable to the electron spill-out [41,76]. Thus, this system of coupled equations yields an additional wave solution, longitudinal in character, and can be solved for different geometries leading to nonlocal extensions of Mie [41,48] and Fresnel coefficients [51], including for charge carriers in electrolytes [12]. Typically, hard-wall boundary conditions are assumed for the additional boundary conditionnj ind ≡ 0 prohibiting electrons to trespass through the particle surface into the dielectric surrounding, using a uniform electron density n 0 = ω 2 p m /4πe 2 inside the material and neglecting the electron spill-out. However, it was shown that a smooth surface distribution of electrons can be taken into account accurately [57,65] and that the hydrodynamic model is capable of dealing with the spill-out by solving the above equations with position-dependent material parameters ω p (z) 2 = 4πn 0 (z) e 2 /m. The main observations of nonlocal theories are a blueshift of the plasmon resonance with respect to the common local approximation and plasmon broadening, in particular tied to the diffusion coefficient which can be set to fully capture the broadening found with Kreibig damping [55,56]. In the present work, we have adopted the diffusion coefficients as deduced in Ref. [56] for the different materials, reflected, for instance, in the correspondence between the Kreibig and GNOR result for gold in Figure 3a. Moreover, we add the Lorentz friction result from the RPA technique summarized in Equation (1d) to our GNOR calculations.
Next, we present the derivation of nonlocal Mie scattering coefficients of individual spheres and nanoshells described with the hydrodynamic model [41] starting from Equation (17) which describes the evolution of the electric field, together with Equation (18) which is the wave equation for the induced charge. The resulting scattering matrices can be used to investigate interacting spheres with a multiple scattering method [67]. The hydrodynamic model has no free parameters which makes the resultant nonlocal response for the short distances involved in the interaction (Coulomb force, diffusion) between the charges of MNPs the sole source of these effects, in contrast to the quantum-confinement picture for plasmon broadening presented by Kreibig. It is convenient to use an expansion of the electric field into scalar functions [77] as where L = −ir × ∇ is the angular momentum operator, and the superscripts E, M, and L indicate electric, magnetic, and longitudinal components, respectively. The additional boundary condition, Equation (16), becomes withrj = 0 in terms of the scalar functions and the angular momentum number l using the identity −r · (∇ × L) = (−ir × ∇) · L = L 2 = l(l + 1). The boundary conditions for the electric and magnetic field components result in the continuity of ψ M , (1 + r ∂ ∂r )ψ M , ψ L + (1 + r ∂ ∂r )ψ E , and ψ E for the scalar functions.
The magnetic and electric scalar functions ψ ν (ν = {E, M}) obey a Helmholtz equation of the form (∇ 2 + k 2 ⊥ )ψ ν = 0 and can therefore be expanded in terms of spherical Bessel functions ψ ν = ∑ L ψ ν L j L (k ⊥ r). Similarly, the electron density is expanded into ρ ind (r, ω) = ∑ L ρ L j L (qr), with the longitudinal wave vector q given by Equation (19). The longitudinal scalar function satisfies a different wave equation, namely ∇ 2 ψ L = 4πk/ b , which we find from the Coulomb law ∇ b E = 4πρ ind .
Note that the above analysis is needed for the metal region, where the electric (ν = E) and magnetic (ν = M) field are given by A ν l j L , with j L = j lm (k ⊥ r). Outside the particle, the longitudinal scalar function vanishes since there are no induced charges in the dielectric surrounding. Therefore, the electric scalar field is given by j lm (k 0 r) + t ν l h + lm (k 0 r) with unknown parameters A ν l and scattering matrix t ν l . Exploiting the boundary conditions stated above, we find a set of linear equations for the magnetic and electric scattering matrices. Interestingly, the magnetic scattering matrix is unchanged with respect to the local theory, indicating that magnetic modes are not sensitive to the induced longitudinal modes. The scattering matrix for the electric scalar function is more complicated than in the local approximation due to the appearance of ψ L in the metal region that contains information on the nonlocal response. The additional boundary condition yields a prescription to calculate ρ L .
The local scattering matrix can then be extended by a single parameter describing nonlocal behavior of the electron motion in the conduction band g l = l(l + 1)j l (θ ⊥ )j l (qa) qaj l (qa) and becomes with θ 0 = ka √ 0 and θ ⊥ = ka √ ⊥ .
t E l = − ⊥ j l (θ ⊥ )[θ 0 j l (θ 0 )] + 0 j l (θ 0 )([θ ⊥ j l (θ ⊥ )] + g l ) where the primes indicate differentiation with respect to the θ variables. The scattering coefficients t ν l fully contain the optical response of the particle for an external observer. Note that the nonlocal parameter g vanishes under the assumption of local response (β GNOR → 0 ⇒ g l → 0) fully recovering the original Mie coefficients [15,78]. This allows us to study the electro-optical properties of NPs with only a small correction in available numerical procedures, see for instance Figure 5.
Likewise, for a nonlocal metal nanoshell, the magnetic response is insensitive to the nonlocal properties of the material. The electric part, however, mixes with the longitudinal components from the two interfaces of the metal intermediate layer. For the electric scalar functions, we obtain a linear system of six equations and analytical solutions exist for the metal nanoshell [41,79].
Simulations
The modeling presented in this article was obtained by both using the commercial software COMSOL Multiphysics (http://www.comsol.com) and in-house numerical code to evaluate Mie coefficients, from Equation (23).
To make predictions that can be compared to experiments, the expressions obtained are used to calculate e.g., the extinction cross section of an individual sphere via σ ext = 2π Note that only the electric scattering matrix is sensitive to nonlocal contributions. The scalar electric field is obtained from j lm (k 0 r) + t E l h + lm (k 0 r) outside the particle, with the corresponding spherical Bessel and Hankel functions and the related vector field from Equation (20).
The analytic damping expressions Equations (1a)-(1d) are directly introduced as damping terms in the permittivity of the different material permittivities, Equation (2).
For dimers, we use a multiple elastic scattering approach [67]. | 8,170.4 | 2018-05-31T00:00:00.000 | [
"Physics"
] |
Adaptive Fuzzy Fault-Tolerant Control against Time-Varying Faults via a New Sliding Mode Observer Method
: In this study, the problem of observer-based adaptive sliding mode control is discussed for nonlinear systems with sensor and actuator faults. The time-varying actuator degradation factor and external disturbance are considered in the system simultaneously. In this study, the original system is described as a new normal system by combining the state vector, sensor faults, and external disturbance into a new state vector. For the augmented system, a new sliding mode observer is designed, where a discontinuous term is introduced such that the effects of sensor and actuator faults and external disturbance will be eliminated. In addition, based on a tricky design of the observer, the time-varying actuator degradation factor term is developed in the error system. On the basis of the state estimation, an integral-type adaptive fuzzy sliding mode controller is constructed to ensure the stability of the closed-loop system. Finally, the effectiveness of the proposed control methods can be illustrated with a numerical example.
Introduction
In industrial processes, actuator and/or sensor always occur with various components faults due to unexpected physical constraints and reasons [1][2][3][4]. In order to maintain the reliability of the overall control systems, fault detection and isolation (FDI) and fault-tolerant control (FTC) have received increasing research attention during the past decade [5][6][7][8]. The design scheme of FDI is to generate a residual signal to judge whether the faults occur and provide a solution to determine the location of the faults [9][10][11]. However, in practice, it is difficult to obtain the exact information of the fault. In this sense, the fault estimate has been developed and has become an ideal design basis of FTC [12,13]. In recent years, a great number of fault estimation methods have been reported in the existing literature, for instance, nonlinear observer method, adaptive learning observer method, filter-based estimation method and differential geometry methods, etc. [14][15][16].
Consequent to the in-depth study of SMO by researchers, combined with fuzzy and adaptive technologies [17][18][19], sliding mode observers have been widely used in motors, aerial vehicle, and other fields [20][21][22][23][24]. Among these existing fault estimation approaches, sliding mode observer (SMO) [25][26][27] refers to one of the most popular nonlinear observer methods, where the fault is reconstructed by the so-called equivalent output error injection principle [14]. In this research forefront, a few fault estimation SMO results have been developed for various systems by the researchers [11,28]. In [29], a fault estimation SMO was developed for mismatched nonlinear systems with unknown disturbances, where an adaptive law was designed to update the sliding mode gain online. In [30], the authors proposed a cascaded SMO method to cope with the fault estimation problem for the case in which the first Markov matrix of the system is not a full rank. In [31,32], based on a descriptor system augmentation strategy, the authors proposed a new type of extended SMO approach, which was applied to Ito stochastic systems and Markovian jump systems, respectively.
Sliding mode control is a very effective control method, and some new ideas have been put forward recently by researchers [33,34]. Hou et al. [35] solved the chattering problem common in the sliding mode control for the servo motor system by designing a new continuous terminal sliding mode control algorithm. In [36], an optimization problem based on non-negative constraints was defined for time-varying delay systems, to obtain sliding mode surface parameters and simplify the stability analysis process. In [37], the nonlinear function with sliding variable was introduced by the approach law, which alleviates the chattering phenomenon and improves the tracking performance.
However, it should be pointed out that most existing fault estimation results are concerned only about actuator faults or sensor faults. Moreover, most of the reported work has been focused on only additive actuator fault, while multiplicative type actuator fault (also called fault degradation factor) has received little research attention. In fact, in many practical control systems such as satellite systems, the multiplicative actuator faults may always occur with a time-varying characterization. However, the existing SMO methods in the aforementioned literature cannot be applied directly to solve this design problem due to technical constraints, and only additive actuator faults are therefore considered. It is thus desirable to develop a new effective SMO approach to investigate this problem.
In this paper, we aimed to research the fault estimation and FTC design problem for the continuous-time nonlinear system, where sensor fault, external disturbance, time-varying multiplicative actuator faults, and unknown nonlinearity are considered simultaneously in a unified framework. A new type of SMO based on a system augmentation scheme is developed for the investigated plant. The designed observer can estimate state vector, sensor faults, and external disturbance, which thus possesses a more extensive estimation performance, compared to the traditional SMO method. Moreover, due to the tricky structure of the observer, the time-varying actuator degradation factor in the derived error system can be eliminated. Based on the state estimation of the SMO, an adaptive integraltype sliding control law is designed to ensure the asymptotic stability of the overall fault control systems, where an adaptive fuzzy updating law is involved with the controller gain to approximate the unknown nonlinearity of the plant. Finally, a simulation example is given to verify the effectiveness of the proposed FTC methods. The structure of this article is as follows: Section 2 gives the system model, hypothesis, and related theory. Section 3 designs the observer and controller and analyzes the stability and the accessibility of sliding mode motion. Section 4 provides a simulation example. Section 5 summarizes the whole paper.
Notation: The n-dimensional Euclidean space is defined by R n . The set of all m × n real matrices is represented as R m×n . Positive-definite (negative-definite) matrix A is defined by A > 0 (< 0). An identity matrix is defined by I n (n is the dimension of matrix I); diag{...} denotes a block diagonal matrix.
Problem Statement
Consider the following uncertainty nonlinear system subject to time-varying actuator fault, sensor fault, and external disturbance: where the hth actuator has no fault; Case 2 : ρ h (t) = 0, the hth actuator is outage; Case 3 : ρ h (t) ∈ (0, 1), the hth actuator is partial loss of effectiveness; Case 4 : f ah (t) = 0, the hth actuator undergoes stuck fault.
For the given system matrices A, B, C, D s , D x , D y , E, the matrix E is supposed to satisfy that E = BB f in this paper. Without loss of generality, we suppose that the pair (A, B) is controllable, and the pair (A, C) is observable. In order to study the problem of the redundancy actuator fault, we assume that rank(B) = l ≤ m. Thus, we have B = B 1 B 2 , where B 1 ∈ R n×l and B 2 ∈ R l×m . Then, the state equation of the original system (1) can be rewritten asẋ (2) Remark 1. Different from the existing results of the simultaneous actuator fault and sensor fault in [38], the fault problem in this paper is more complex. The time-varying actuator faults including loss of effectiveness fault, outage fault, and stuck fault, combined with bias sensor fault, are first studied simultaneously. Due to the more general character of actuator fault, the traditional observerbased controllers are unable to provide the desired estimation and control performance; this is also the difficulty in FTC design.
In this paper, we give the following assumptions: The stuck actuator fault f a (t), bias sensor fault f s (t) and external disturbance d(t) are supposed to satisfy that where f a1 , f s1 , f s2 , d 1 , d 2 are unknown scalars.
Assumption 2 ([32]
). It is assumed that the actuators satisfy the redundancy condition: rank( Assumption 3. The system matrix dimensions satisfy: rank(B 1 ) = rank(CB 1 ) = l, and a scalar σ can be found such that Remark 2. Assumption 1 is proposed for proofing the stability of closed-loop systems and the accessibility of sliding mode motion in Section 3, which is an important condition for scaling. Compared to the traditional methods in [39], Assumption 2 will relax the restriction that the norm bound of the external disturbance, stuck actuator fault, and bias sensor fault, which will be applicable to a larger class of practical systems. Assumption 3 is a necessary condition in the process of designing a controller.
Fuzzy Logic Systems
The fuzzy IF-THEN rules of fuzzy logic systems (FLSs) are given as follows [40]: T andȳ(t) represent the input and output of the FLS, respectively. F ιi and G ιi are fuzzy sets (ι = 1, 2, ..., n). i = 1, 2, · · · , N (N is the number of the fuzzy rules). Obviously, the FLS can be represented as follows: and it is assumed that µ G i (ȳ i ) = 1. Define the following fuzzy basis functions: Denoting Lemma 1 ([41]). For any continuous function, f (x) defined over a compact set Ω and any given positive constant δ 0 , there exists θ such that Since x(t) is not measurable, the function f (x) can be represented by the following FLSs: where δ f (t) is the approximation error. Then, the reconstruction error δ(t) can be obtained In general, δ(t) is assumed to be bounded with whereδ > 0 is an unknown constant.
To design the adaptive law for the unknown vector θ, we supposed that θ > 0 throughout the paper, which is not to lose the generality and also used in the FTC problems of fuzzy logical systems ( [41]).
Observer Design
Consider the following augmented system:x From Assumption 3, we have Hence,CB 1 is fully column rank. Then, we define that where ζ ∈ Rn ×p is a free matrix to be selected. Before the design of fault-tolerant observer, we define the following matrices: where L 1 ∈ Rn ×p is the gain matrix to be designed later. Now, we introduce the following lemma for the existence of L 1 , which will be used in the observer design. Proof. Since (I − HC) can be invertible through selecting an appropriate matrix ζ, the matrix I − HC sH 0 I p is of full column rank for ∀ s ∈ R + . Then, it can be obtained that Since the pair (A, C) is detectable, when s = −σ, it is obvious that When s = −σ, the following equation holds from Assumption 3 Summarizing the analysis above, we have Consequently, the pair (A 0 ,C) is detectable. It completes the proof.
Then, the following sliding mode observer for system (12) is developed: where z(t) ∈ Rn;x(t) = [x(t),d(t), D sfs (t)] T is the estimation ofx(t); u s (t)Rn is the discontinue input to be designed; the matrices A 0 , L 1 , L, L s , H are defined in (16). Then, we have˙x The augment system (12) can be rewritten aṡx Define thatē(t) =x(t) −x(t), we havėē Remark 3. It can be seen that the effect of the time-varying actuator degradation has been removed in the error dynamics (24) by using an interesting matrix parameter design of H. This will help us to employ the sliding mode observer (SMO) technology to obtain the estimation of the system statex(t).
Since the constants f a1 , f s1 , f s2 , d 1 , d 2 are unknown in Assumption 1, we introduce a positive constant ψ such that where σ is given in (13). It can be seen that ψ is also unknown in (25), so we will substitute the estimationψ(t) for ψ in the observer design, and the adaptive law for ψ is presented,ψ (t) = c e s e (t) ,ψ(0) ≥ 0 where s e (t) is defined in (27), and c e is the adaptive gain parameter. Now, the sliding mode is defined as follows: where s e (t) ∈ Rn, and P > 0 is the Lyapunov matrix such that where the parameter matrix R ∈ R (m+n d +q)×p is to be determined. Then, we design the discontinuous input u s (t) as follows: where ε is a positive constant designed later.
Controller Design
Let u(t) = B T 2ũ (t), we havė In the following part a Lemma is presented.
Lemma 3.
For the nonsingular matrix B 2 ρ(t)B T 2 in (30), a positive scalar µ can be found such that B 2 ρ(t)B T 2 ≥ µI l .
Proof. Based on Assumption 3, we have that is, m(m ≥ l) actuators do not surfer outage. Without loss of generality, the first l actuators are assumed to kept from outage, and ρ o (t), ρ a (t) ∈ R m×m are defined as follows where 0 < ρ h (t) ≤ 1 with h = 1, 2, ..., l. So we have Obviously, Consequently, the matrix B 2 ρ(t)B T 2 is invertible. Then, we have where µ = λ min (B 2 ρB T 2 ). Hence, we have It completes the proof.
Then, the following integral sliding surface is constructed where and K ∈ R l×n is designed later. D sfs (t) andd(t) can obtained in the observer (21) that Denoting It can be seen that B 2 ρ(t)B T 2 is invertible according to Lemma 1. Therefore, the equivalent control law in the sliding mode can be obtained fromṡ(t) = 0 that Substituting (41) into (30), the sliding mode dynamics can be obtained as follows: where A a = A − B 1 FCA, I e = I n 0 , According to Assumption 2, it can be shown thatė f s (t),ė d (t) are bounded, and they will both converge to 0. In addition, the disturbance d(t) has also been assumed in the sense of L 2 norm in (1). Therefore, we assume Φ(t) ∈ L 2 [0, ∞].
In the following theorem, the stability condition for the overall closed-loop system is given. Theorem 1. Given a positive scalar γ, the closed-loop system (24) and (42) is robust stable with an H ∞ performance γ, that is x(t) 2 + ē(t) 2 ≤ γ 2 Φ(t) 2 , if there exist symmetric positive definite matrices P ∈ Rn ×n , Q ∈ R n×n , matrices X ∈ R n×n , Y ∈ Rn ×p , R ∈ R (m+q)×p such that where The proportional gain L 1 in (24) and K in (42) can be calculated as Proof. First, we define the error variableψ(t) =ψ(t) − ψ, where ψ andψ(t) are defined in (25) and (26), respectively. Choose the following Lyapunov function: where Then, we haveV Sinceψ(t) =ψ(t), it can be derived from the adaptive law (26) and (27) that Let QB 1 K = X and PL 1 = Y, when Φ(t) = 0, after some algebraic manipulation, it can be obtained from (49) and (50) thaṫ If we can obtain the feasible solutions to (43), then it can be concluded thatV(t) < 0 in (51). Therefore, system (24) and (42) is asymptotically stable when Φ(t) = 0. Now we will consider the H ∞ performance under zero initial conditions that From (49) and (50), we have where Ω is defined in (43). From (52) and (53), it can be obtained that J < 0, and the H ∞ performance has been established. Since B 1 is of full column rank, B T 1 B 1 is nonsingular. Hence, we have K = (B T 1 B 1 ) −1 B T 1 Q −1 X. It completes the proof.
Remark 4.
It is evident that there is linear matrix equality in Theorem 1, and the LMI toolbox can not be used directly. According to the algorithm in [41], (44) can be taken as Thus, the following inequality can be obtained: where η i is a parameter to be designed. By the Schur complement, it is derived that Then, the following minimization problem is equivalent to Theorem 1: subject to (43) and (55) which can be solved by the LMI toolbox in MATLAB directly. Using pseudo-inverse can be, in some cases, not trivial. Ref. [42] encountered the same problem as solving (46) in solving the pole assignment problem, which divided the problem into two stages to solve and simplified the calculation process. This method can be considered to solve the case in which it is difficult to calculate the pseudo-inverse matrix. Ref. [43] proposes a new control specification for solving pole assignment based on LMI, and we will consider using this method to solve the LMI problem in this paper in a subsequent work.
Reachability Analysis of Sliding Motion
In the following section, the reachability of the sliding surfaces s(t) in (37) is analyzed. Before designing the sliding mode control law u(t), we present the following adaptive laws:˙θ where c θh , c δ , c ξ are the positive adaptive gains to be designed, andξ(t) is the estimation of ξ such that Obviously, we haveθ h (t),δ(t),ξ(t) ≥ 0. The sliding mode lawũ(t) is designed as +δ(t))sgn(s(t)), where η > 0 will be designed later.
Remark 5. In order to illustrate the computational effort of solving the LMI, we proposed the following through MATLAB LMI Toolbox: 1. Select a suitable free matrix ς and a scalar σ, which satisfies Equation (4), such that (I − HC) is invertible; 2. Design an appropriate Equation (29), define suitable matrices H, A 0 , L s , L 2 , L, and solve the minimization problem Equation (56); 3. Design adaptive law Equation (57), Equation (65), and sliding mode law Equation (59).
By analyzing the reachability of sliding motion, we have the following theorem: Theorem 2. If there exist matrices 0 < P T = P ∈ Rn ×n , 0 < Q T = Q ∈ R n×n , and matrices R ∈ R (m+n d +q)×p , X ∈ R n×n , Y ∈ Rn ×p , such that (43) and (44) hold. Based on the input u(t) defined in (59), the system state of (42) can be driven onto the sliding surface s(t) = 0 in finite time.
Proof. First, denoting thatθ
Then, we define that We haveV The proof is completed.
Remark 6.
Specifically, when the unknown actuator efficiency factor is constant as ρ(t) = ρ, the estimation of the ρ can be given in the proposed methods, and the stabilization of the closed-loop system can be also guaranteed simultaneously.
Now, the adaptive law for ρ h is given bẏρ
where B h 2 is the hth column of B 2 . The SMC lawũ(t) is designed in (59).
Theorem 3.
If there exist symmetric positive definite matrices P ∈ Rn ×n , Q ∈ R n×n , matrices R ∈ R (m+q)×p , X ∈ R n×n , Y ∈ Rn ×p , such that (43) and (44) hold. Under the control input u(t) in (59), the trajectory x(t) of the closed-loop system (42) will be driven onto the sliding surface s(t) = 0 in finite time.
Proof. Define thatρ
Then, we havė The proof is completed.
Simulation Example
In this section, a numerical example is given and the correctness of the theorem is verified. Consider an uncertain nonlinear system subject to time-varying actuator fault, sensor fault, and external disturbance as form (1), where with n = 2, m = 2, p = 2, l = 2, q = 1, n d = 2, σ = 0.2,n = n + n d = 4. It can be checked that (A, B) is controllable, and (A, C) is observable. Let f (x) = sin(x 1 (t)), σ = 0.2, f a (t) = 1 1 denote the stuck actuator fault.
1. Observer Design: In the first step, the fault-tolerant observer is designed given the following matrices: The simulation results for system (2) are shown in Figures 1-6 below. The trajectory of error vectorē(t) is shown in Figure 1. Figure 1 illustrates a comparison between the actual state of the system and the state estimated by the observer, and the error is asymptotically stable. The trajectories of output error sliding surface s e (t) and discontinuous term u s (t) are shown in Figures 2 and 3, respectively. As shown in Figure 4, the state of the system is asymptotically stable, thus verifying that the sliding surface and controller are effective. It can be seen from Figure 3 that the system can reach the sliding surface in a short time, which is basically consistent with the theoretical analysis. The sliding variables (40) and the sliding mode controllers (59) are very close to zero after 8s. The comparisons of state vector x(t), external disturbance d(t), and sensor fault f s (t) and their estimations are illustrated in Figures 4-6, respectively. It can be seen that the proposed FTC approach can ensure the asymptotical stability of the closed-loop fault system. The study in [44] investigates an adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems. The comparison of the performance of the two controllers is given in Table 1 using the same data of Example. By comparison, it can be found that our method is better than the adaptive fuzzy sliding-mode controller (59) in terms of convergence time and steady-state error.
Performance Indexes Convergence Time (s) Steady-State Error
Our method 8 0.002 The controller in [8] 14 0.04
Conclusions
In this study, the adaptive fuzzy FTC problem was addressed for a class of nonlinear systems with actuator fault, sensor fault, and external disturbance. By augmenting the original plant into a normal system, a new SMO was designed to obtain the estimation of the state vectors and faults information. Based on the state estimation, an integral-type SMC strategy was developed to stabilize the closed-loop fault system. The advantage of this study is providing an observer that can simultaneously estimate state vectors, sensor faults, and external disturbances and has a wider estimation range than the traditional SMO. In addition, the effect of the time-varying actuator degradation in the error system can be eliminated because of the structure of the observer. However, there are some limitations in this article. For example, the proposed method is complicated in practical application and cannot be directly applied to descriptor systems. Future work will focus on extending the designed methods (small-gain theorem [44,45]) to more complicated systems such as switched systems and stochastic systems.
Data Availability Statement:
The data used to support the findings of this study are obtained directly from the simulation by the authors. | 5,300.4 | 2021-07-21T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Gateway-Assisted Retransmission for Lightweight and Reliable IoT Communications
Message Queuing Telemetry Transport for Sensor Networks (MQTT-SN) and Constrained Application Protocol (CoAP) are two protocols supporting publish/subscribe models for IoT devices to publish messages to interested subscribers. Retransmission mechanisms are introduced to compensate for the lack of data reliability. If the device does not receive the acknowledgement (ACK) before retransmission timeout (RTO) expires, the device will retransmit data. Setting an appropriate RTO is important because the delay may be large or retransmission may be too frequent when the RTO is inappropriate. We propose a Gateway-assisted CoAP (GaCoAP) to dynamically compute RTO for devices. Simulation models are proposed to investigate the performance of GaCoAP compared with four other methods. The experiment results show that GaCoAP is more suitable for IoT devices.
Introduction
The Internet of Things (IoT) is a network linking physical objects that generally have embedded sensors/actuators (SA) to sense events and interact with the environment. Those physical objects usually called devices communicate with each other with limited human interaction. When the devices detect some event happening, they generate data and send it to relative receivers. For example, the implantable medical devices are introduced to collect patients' data (e.g., blood pressure or body temperature) [1]. Once the devices sense the change of patients' status, the devices notify relevant medical units immediately.
There are two major messaging patterns: request/response and publish/subscribe. Request/response pattern is widely used in the Internet where data are stored in servers. The data transmission occurs because of users' requests. This pattern is suitable for user-centric applications such as web browsing, since the data retrieval is passive. However, IoT applications are data-centric applications. Publish/subscribe patterns are widely used in IoT since IoT devices can sleep most of the time and wake up to publish data occasionally [2]. Figure 1 shows the simple publish/subscribe model.
The interested party called a subscriber registers their interest to the server. This registration process is called subscription (see step 1 in Figure 1). The publisher produces information and the server forwards the information from the publisher to the subscribers (see step 2 in Figure 1) [3].
This publish/subscribe model for IoT is supported by protocols such as Message Queuing Telemetry Transport for Sensor Networks (MQTT-SN) [4] and the Constrained Application Protocol (CoAP) [5]. For the purpose of staying lightweight, the transport layer of these two protocols are both User Datagram Protocols (UDPs). However, reliability of data transmission is one of the most important issues in some IoT applications with sensors, such as environmental condition monitoring [6]. In these applications, sensors have diverse reliability requirements. For example, temperature information in normal range can tolerate loss up to a certain percentage. On the other hand, the sensor data reflecting a high temperature should be reliably delivered to the control center. As a result, both MQTT-SN and CoAP provide retransmission mechanisms. There is a timer called retransmission timeout (RTO). If the device does not receive the acknowledgement (ACK) before the RTO expires, the device will retransmit the data. RTO setting can be fixed or dynamic. For dynamic settings, the Round Trip Times (RTTs, from the devices to the server) measured from previous messages by the devices are used for computing RTO. In unstable wireless environments, the performance of fixed RTO is poor. If the fixed RTO is too small, unnecessary retransmission occurs. While the fixed RTO is too large, the latency becomes quite large since the duration of each retransmission becomes long. Note that MQTT-SN and CoAP both apply fixed RTO. Thus, dynamic RTO can adapt to the wireless network and overcome the two problems above.
The network of IoT devices is usually connected using wireless with high data loss rate and unstable RTT. The existing protocols need to be modified to adapt to the network conditions. Moreover, the characteristics of IoT devices have to be considered. Our aim is to propose a gateway-assisted retransmission mechanism suitable for IoT devices to obtain dynamic RTO.
Related Works
In this section, we first introduce two popular lightweight publish/subscribe protocols that can be used in IoT. To minimize power consumption, both protocols adopt fixed RTO as retransmission criteria. We then describe two mechanisms using dynamic RTO.
Message Queuing Telemetry Transport (MQTT) is a machine-to-machine connectivity protocol that runs over Transmission Control Protocol (TCP) [7]. It is designed for short length packets. MQTT-SN is a modified version of MQTT for sensor networks. Instead of TCP, MQTT-SN runs over UDP for lightweight purposes [4]. Figure 2 shows the architecture of MQTT-SN. Although IoT devices use the MQTT-SN protocol, they need a gateway to connect to the MQTT server while the connection between the gateway and the server is still the MQTT protocol. There are two types of MQTT-SN gateways: transparent gateways and aggregating gateways. Transparent gateways maintain each connection from the devices to the server but aggregating gateways only maintain one MQTT connection to each server. There are three levels of Quality of Service (QoS) that can be used when the data are delivered. Level 0 is called at-most-once delivery. This is best-effort delivery without any retransmission service so the data are always transmitted at most once. Level 1 is called at-least-once delivery. The data are delivered at least once. The device stores the data until it receives an ACK (called PUBACK) from the receiver. Level 2 is called exactly-once delivery, which guarantees that the data are received only once [4]. For QoS levels 1 and 2, a retransmission mechanism is required. MQTT-SN specification provides two parameters for retransmission: T retry and N retry . The first one indicates a fixed RTO value recommended between 10 and 15 s. The second one represents the maximum number of retransmissions recommended from three to five times. CoAP is proposed by the Internet Engineering Task Force (IETF) for constrained devices to connect to the Internet. Based on UDP, CoAP supports both reliable (called Confirmable or CON) and unreliable (called Non-Confirmable or NON) transmission. By using NON, there is no need to return ACK and no retransmissions occur. On the other hand, when the RTO of a device expires, the publication data will be retransmitted by using CON. Initial RTO is defined as the RTO used for the first transmission of a message. In CoAP, the default maximum number of retransmissions is four, and the initial RTO is randomly chosen from 2 to 3 s. Once the RTO expires before ACK reception, the next RTO is updated with exponential back-off mechanism. (i.e., if the initial RTO is two, the next RTO is updated to four and the third time will be to eight.) [5] Note that configuration of these parameters is application-specific. Without loss of generality, we only consider the default values proposed by RFC 7252 in this paper.
MQTT-SN and CoAP use fixed RTO, which is simple but may not work well in wireless networks. The dynamic RTO in TCP is defined in RFC 6298 [8]. The notations used in calculating dynamic RTO are shown in Table 1. The following five rules of RTO are defined in RFC 6298: 1. When there is no RTT sample, the RTO is set to 1 (i.e., Ω = 1); otherwise, the RTO is set based on smoothed round-trip time (SRTT, denoted as γ * ) and RTT variation (RTTVAR, denoted as V γ ). 2. When the first RTT sample γ is obtained, 3. When a new RTT is sampled, then where α = 1/4 and β = 1/8.
The RTO Ω is calculated by SRTT and RTTVAR as follows
: 5. When retransmission is triggered, exponential back-off is performed. Note that the specification suggests that RTO value is bounded within 1 and 60 s.
Note that RFC 6298 ignores the RTT samples of the retransmitted data, which follows Karn's algorithm [9].
CoCoA, which is introduced as an Internet-Draft [10], enhances the congestion control mechanism for CoAP. Based on the calculation in RFC 6298, it defines two extra RTOs. One is called strong RTO (denoted as Ω strong ) and Ω strong = γ * + 4V γ . The other is weak RTO (denoted as Ω weak ) and Ω weak = γ * + V γ . When there is no RTT sample, the RTO is set to 2 (i.e., Ω = 2). The subsequent update of RTO occurs when an RTT is sampled. If the RTT is sampled from the first transmission of a message, the RTO is updated as On the other hand, if the RTT is sampled from the retransmission of a message, the RTO is updated as If the RTO is not updated over 30 s, the RTO is updated by Another improvement is the back-off mechanism. In CoCoA, variable back-off factor (VBF, denoted as ∆) is decided based on the initial RTO as follows: Note that ∆ is always equal to 2 in exponential back-off used by CoAP and RFC 6298. When a message is sent, one of the two policies, persistent policy or Replacing-Retransmitted-Publication (RRP) policy, is chosen. In persistent policy, when a message is sent, the device drops following messages until it receives the corresponding ACK. While the number of retransmissions matches the maximum retransmissions number, the device does not wait anymore. RRP policy is like persistent policy except that if the message is retransmitted due to RTO timeout, the message can be replaced by a newly generated message. In previously described protocols, MQTT-SN uses persistent policy while CoAP, RFC 6298, and CoCoA use RRP.
We observe that neighboring devices would observe similar RTT (with the same server), and thus most dynamic RTO computation could be reduced by sharing the computed RTO values between devices. Based on those previous works, we propose a gateway-assisted mechanism to help devices get RTO earlier. Consequently, the number of retransmissions is reduced, which results in considerable power savings.
Gateway-Assisted CoAP (GaCoAP)
In this section, we introduce our main idea with the procedure of our scheme. Then, we briefly describe the RTO computation applied in our mechanism.
In our architecture, we consider a star topology, which means that each device connects to the gateway directly. The gateway is a transparent gateway between IoT devices and the server. In order to apply dynamic RTO, we consider that the gateway computes the RTO for the devices, connecting to it instead of computing by the devices themselves. Moreover, the devices can overhear the RTO values of other devices when they need to monitor the channel to ensure that the channel is idle before transmitting a packet.
The devices overhearing from this method may consume only a little extra power. However, the devices can obtain an appropriate RTO earlier by overhearing. Since the network status is similar for every device in the same wireless sensor network (WSN), the RTO value calculated by the gateway reveals the latest RTO of the WSN. If a device does not transmit data for a while, it can still update its RTO by overhearing. Having the latest RTO value reduces the data retransmission, which causes considerable power consumption. Note that, when no data is to be transmitted, repetitive overhearing may cause significant extra power consumption. Therefore, in our design, the devices overhear the RTO values only before they transmit packets.
When the device publishes the first message, the default RTO is set to 2. Once an RTT is measured by the device, RTO is recalculated for the next message. GaCoAP also adopts RRP policy when sending a message. Figure 3 shows the procedure of our scheme with the following steps: 1. The RTT is updated upon the receipt of the previous ACK and stored in the device for further use.
2. When the device publishes a new message, the RTT information is contained in the message and delivered to the gateway. 3. The gateway retrieves the RTT information to compute the RTO for the device and stores the RTO value in itself. After that, the gateway removes the RTT information from the message. 4. The gateway forwards the message to the server. 5. If some subscribers have registered the corresponding interest, the server forwards the message to them. 6. The server sends an ACK as a response to the device. 7. Before the gateway forwards the ACK to the device, it puts the RTO information into the ACK. 8. The gateway returns the ACK to the device. At the same time, the gateway broadcasts this RTO to other devices. While some devices are monitoring the downlink channel right at that time, they can receive the RTO information. If the coming RTO is larger than the one kept in it, it updates the RTO by the new one. If the devices are not monitoring, they just omit this information. 9. The device configures the RTO value and updates the RTT.
Finally, based on CoCoA, the RTOs are classified into strong RTOs and weak RTOs. The gateway retrieves the RTT information that contains the RTT value and the retransmission flag. If the retransmission flag is set up, the gateway adopts the weak RTO. Setting up the flag means that the RTT is obtained after at least one retransmission. On the other hand, the strong RTT is adopted if the ACK is received after the first transmission (i.e., there is no retransmission).
The variables SRTT and RTTVAR are calculated as Equations (1) and (2) if the RTT is measured during the first time, or Equations (3) and (4) are applied. Then, the RTO is updated by Equations (6) and (7), and the VBF in the back-off mechanism is as Equation (9). If the RTO value is not updated for 30 s, we use Equation (8) as the aging function.
In our design, we only have one GaCoAP relation, which is between the device and the server. In other words, there is no GaCoAP relation neither between the device and the gateway nor between the gateway and the server. The gateway is only in charge of RTO calculation and forwarding the messages between the device and the server. The RTT and the RTO occupy two extra bytes of the PUBLISH message and the ACK, respectively. Note that the RTT and the RTO are only delivered between the device and the gateway (and are thus unknown to the server).
Simulation Model
In this section, we describe our simulation model. Our simulation model for each method is implemented as an OMNet++ module [11]. IoT devices, gateways, and servers are three entities in our simulation. In the following experiments, the gateway connects to 30 IoT devices. For illustration purposes, we describe the simulation flow chart for IoT devices in GaCoAP. The simulation flow charts for gateways and servers are simpler, and are thus ignored in this paper. Figure 4 is the simulation flow chart for IoT devices in GaCoAP. There are several variables used in the simulation. num_retrans is the current number of retransmissions. max_retrans is the maximum number of retransmissions. numMessage is the number of messages published from the device. numThrow is the number of messages thrown out. numFailed is the number of messages that cannot be sent successfully. totalRetry is the total number of retransmissions. numACK is the number of ACKs successfully received by the device. PUBLISH_serialNum is the serial number of current PUBLISH messages. RECEACK_serialNum is the serial number of each received ACK message. BUSY parameter is used to indicate whether the device is waiting for ACK or not. If it is waiting for the ACK of the first transmitted message, BUSY is set to 1. If it is waiting for the ACK of the retransmitted message, BUSY is set to 2. Otherwise, BUSY is set to 0; RETRANSMISSION parameter is used to indicate whether this message is the retransmitted message or a newly generated message. If the message is a retransmitted message, RETRANSMISSION is set to true. Steps in the simulation model are described as follows: Step 1. Devices initialize the setting. For example, numMessage is set to 0.
Step 2. Generate the first PUBLISH message, which is treated as an event. Then, insert this event into the event list.
Step 3. Delete the first event e from the event list. This event now needs to be processed.
Step 4. Extract e.type to see what type this event is. If the type is PUBLISH, go to Step 5.
If the type is TIMEOUT, go to Step 9. If the type is RECEACK, to to Step 13.
Step 5. Parameters numMessage and PUBLISH_serialNum is increased by 1. Generate the next PUBLISH message and insert it to event list.
Steps 6-8. Check BUSY status. If BUSY is 0, the device sends the message at Step 7. The condition BUSY = 2 means that the device is waiting for an ACK of retransmitted message. By applying RRP policy, the device stops waiting and sends the newly generated message. When the device sends the message, BUSY is set to 1. Set the initial RTO to the default value or the value calculated before. Generate the TIMEOUT event based on RTO and insert it into the event list, and also generate the RECEACK event and insert it into the event list. Set the RECEACK_serialNum of the RECEACK event to PUBLISH_serialNum. If BUSY is 1, numThrow is increased by 1, which means that this message is thrown out. Go to Step 18.
Step 9. If the type is TIMEOUT, check whether the corresponding RECEACK event occurs or not. If the ACK is received, go to Step 18; otherwise, go to Step 10.
Step 10. Check whether the device can retransmit the message. If num_retrans < max_retrans, go to Step 12 for retransmission; otherwise, go to Step 11. Step 11. The device has no quota to retransmit the message, so this message is not sent successfully. numFailed is increased by 1 and num_retrans is set to 0. Go to Step 18. If the RECEACK_serialNum is less than PUBLISH_serialNum, just go to Step 18 because this ACK is not the one the device is waiting for now. Otherwise, go to Step 17.
Step 17. The device receives the ACK message. Therefore, numACK is increased by 1, BUSY is set to 0, and the device calculates the RTT according to the received time of the ACK message. Finally, update RTO computed by the gateway and then go to Step 18.
Step 18. This step checks the ending criterion. The criterion we use is whether the simulation is more than 1200 s or not. If the ending criterion is matched, end the program. Otherwise, go back to Step 3.
In our simulation, MQTT-SN [4], CoAP [5], CoCoA [10] and RFC 6298 [8] are also implemented based on relevant documents, and the details are ignored. Note that MQTT-SN uses persistent policy, and the other methods use RRP. In our experiments, we suppose that the fixed RTO value in MQTT-SN is set to 10 s. In CoAP, IoT devices choose a random number from 2 to 3 s as their initial RTO. Additionally, we suppose that the message generation intervals follow exponential distribution with a mean of five seconds. The maximum number of retransmissions in all methods is set to three.
Results
This section compares GaCoAP with MQTT-SN, CoAP, dynamic RTO in TCP (i.e., RFC 6298), and CoCoA under two different message loss rates (MLR): 0% and 10%. We introduce three output measures to investigate the performance. The first one is the average number of retransmissions in the device (denoted as δ). The second is the average message delivery ratio of the device (denoted as ρ). The last one is the average latency (denoted as λ), which means the round-trip time between the device and the server. We also investigate the impact of the number of devices connected to a gateway on δ. Finally, we discuss the power consumption in our method.
First of all, we introduce two functions to generate latency in our simulation. The latency is divided into two parts: one is the latency from device to gateway, and the other is the latency from the gateway to the server. The connection of the former is wireless while the latter is backbone. The latency varies with time, and the current one is related to the previous one. Based on the observation of RTT samples in [12,13], we use a saw-like function to formulate the latency in our simulation, and the slope of RTT model is 0.12. We assume that the saw-like function of the latency between the device and the gateway is as follows: where µ is the average value of the saw-like function and t denotes time. In our experiments, we consider four different values of µ, which are 1, 2.5, 5, and 10. On the other hand, we assume the saw-like function of the latency between gateway and server is as follows: Figure 5 compares the average number δ of retransmissions. As we know, if the RTO configuration is appropriate, the number of retransmissions should be small. MQTT-SN and CoAP use fixed RTO, which results in worse performance than the other three methods using dynamic RTO in many cases. This figure shows that δ in MQTT-SN significantly increases as µ increases, while δ in CoAP is insensitive to µ. This phenomenon is explained as follows. RTO in MQTT-SN is set to 10 s, so δ is small when µ is small. While µ becomes large, δ is getting worse. Take µ = 5, for example, where the average one-way latency between device and gateway is 5.05 s. Obviously, RTO as 10 s is too small to be suitable for this situation. On the other hand, devices in CoAP choose RTO randomly from 2 to 3 s as their initial RTO. This RTO value is too small even though µ is set to 1. However, RTO is updated with an exponential back-off mechanism, such that δ becomes insensitive to µ in the observed range.
Compared to CoCoA and GaCoAP, RFC 6298 only takes RTT of first transmission into account and ignores the RTTs of retransmissions. This RTT information cannot reflect the entire network situation in real-time. As a result, the δ performance in RFC 6298 is worse than that in CoCoA and GaCoAP. In GaCoAP, RTO is not only based on the calculation in CoCoA but also updated by shared ACK message. Device in GaCoAP can obtain an appropriate RTO earlier so GaCoAP outperforms other methods, especially in bad network conditions. In the case that MLR = 10% and µ = 10, the devices adopting GaCoAP can save at most (1.902 − 0.507)/1.902 = 97.3% in terms of the number of retransmissions and (0.998 − 0.507)/0.998 = 49.1% at least. Figure 6 shows the effects of µ and MLR on the average message delivery ratio ρ (which means the ratio of the messages received by the server and the messages sent by the device). In this figure, MQTT-SN has the best performance because it uses the persistent policy (while others adopt RRP policy). Messages published by a device in MQTT-SN is not replaced by newly coming messages and the device always waits for the ACK of the current message it sends. Unfortunately, although ρ in MQTT-SN is large, the messages may be out-of-date. Since CoAP uses fixed RTO and adopts RRP policy, retransmission is triggered with higher probability, and then the current message is more likely to be replaced by a new message. On the other hand, the number of retransmissions in GaCoAP is small, so the message is hardly replaced. Even though working in the worst network conditions (i.e., MLR = 10% and µ = 10), GaCoAP still has a 99.8% message delivery ratio, thus it improves the message delivery ratio to at most 0.998 − 0.774 = 22.4% among methods with RRP policy. Figure 7 compares the average latency λ in each method. Overall, the latency in CoAP is the lowest because of frequent retransmissions. Once a message is lost, the device does not take a long time to wait for an ACK. Adopting an appropriate RTO can reduce the number of retransmissions, but this encounters larger latency. If the message is lost, the device may wait for more than a round-trip time and then trigger the message retransmission. Because RTO in GaCoAP is more suitable than other dynamic RTO methods, the latency in GaCoAP is a little bit larger. In the case that MLR = 10 % and µ = 10, the devices adopting GaCoAP sacrifice at most 21 s − 11 s = 10 s latency. Note that 10 s latency is acceptible in most IoT applications. Finally, the latency in MQTT-SN is the largest due to its large and fixed RTO (i.e., 10 s). Figure 7 compares the average latency λ in each method. Overall, the latency in CoAP is the lowest because of frequent retransmissions. Once a message is lost, the device does not take a long time to wait for an ACK. Adopting an appropriate RTO can reduce the number of retransmissions but this encounters larger latency. If the message is lost, the device may wait for more than a round-trip time and then trigger the message retransmission. Because RTO in GaCoAP is more suitable than other dynamic RTO methods, the latency in GaCoAP is a little bit larger. In the case that MLR = 10 % and µ = 10, the devices adopting GaCoAP sacrifice at most 21 s − 11 s = 10 s latency. Note that 10 s latency is acceptible in most IoT applications. Finally, the latency in MQTT-SN is the largest due to its large and fixed RTO (i.e., 10 s).
To investigate the effect of moving RTO calculation from device to gateway, Figure 8 compares the average number δ of retransmissions in CoCoA and GaCoAP under different numbers of devices (connected to a gateway). Note that GaCoAP uses the same dynamic RTO calculation rules as that in CoCoA. After RTO calculation, the gateway in GaCoAP shares the RTO to other devices. The figure shows that, as long as there are more than five devices connected to gateway, δ in GaCoAP is always smaller than that in CoCoA. When the number of devices is few, the effect of overhearing cannot play a role and device has to wait for RTO calculation by gateway. In this situation, device in CoCoA obtains suitable RTO more quickly than that in GaCoAP. Nevertheless, a gateway certainly connects to more than five devices in practice. In fact, we extend our experiment up to 100 devices connected to a gateway, and the results are consistent. Figure 7 compares the average latency λ in each method. Overall, the latency in CoAP is the lowest because of frequent retransmissions. Once a message is lost, the device does not take a long time to wait for an ACK. Adopting an appropriate RTO can reduce the number of retransmissions but this encounters larger latency. If the message is lost, the device may wait for more than a round-trip time and then trigger the message retransmission. Because RTO in GaCoAP is more suitable than other dynamic RTO methods, the latency in GaCoAP is a little bit larger. In the case that MLR = 10 % and µ = 10, the devices adopting GaCoAP sacrifice at most 21 s − 11 s = 10 s latency. Note that 10 s latency is acceptible in most IoT applications. Finally, the latency in MQTT-SN is the largest due to its large and fixed RTO (i.e., 10 s).
To investigate the effect of moving RTO calculation from device to gateway, Figure 8 compares the average number δ of retransmissions in CoCoA and GaCoAP under different numbers of devices (connected to a gateway). Note that GaCoAP uses the same dynamic RTO calculation rules as that in CoCoA. After RTO calculation, the gateway in GaCoAP shares the RTO to other devices. The figure shows that, as long as there are more than five devices connected to gateway, δ in GaCoAP is always smaller than that in CoCoA. When the number of devices is few, the effect of overhearing cannot play a role and device has to wait for RTO calculation by gateway. In this situation, device in CoCoA obtains suitable RTO more quickly than that in GaCoAP. Nevertheless, a gateway certainly connects to more than five devices in practice. In fact, we extend our experiment up to 100 devices connected to a gateway, and the results are consistent. To investigate the effect of moving RTO calculation from device to gateway, Figure 8 compares the average number δ of retransmissions in CoCoA and GaCoAP under different numbers of devices (connected to a gateway). Note that GaCoAP uses the same dynamic RTO calculation rules as that in CoCoA. After RTO calculation, the gateway in GaCoAP shares the RTO to other devices. The figure shows that, as long as there are more than five devices connected to a gateway, δ in GaCoAP is always smaller than that in CoCoA. When the number of devices is small, the effect of overhearing cannot play a role, and the device has to wait for RTO calculation by the gateway. In this situation, a device in CoCoA obtains suitable RTO quicker than that in GaCoAP. Nevertheless, a gateway certainly connects to more than five devices in practice. In fact, we extend our experiment up to 100 devices connected to a gateway, and the results are consistent.
Finally, we discuss the power consumption issue. Compared to other methods, devices in GaCoAP can save power owing to the reduction of retransmissions. If a device often triggers retransmission, it encounters higher transfer power consumption. In our experiments, the number of retransmissions in GaCoAP is the smallest, with only one exception (i.e., µ = 1 and MLR = 0%). Assume that the packet size is 31 bytes, the size of Medium Access Control (MAC) ACK is 5 bytes, and the size of the application ACK is 12 bytes (this assumption follows the experiment setting in [14]). Based on Table 4 in [14], a device consumes 1182 ms·mA (summation of Id 3, Id 4, and Id 5) power when it transmits a packet. If the device needs to retransmit the packet, an extra 951 ms · mA (summation of Id 3 and Id 4) is required. For example, if the average number of retransmission is 0.1, the actual power consumption is 1182 + 951 × 0.1 = 1277.1 ms·mA. From Figure 5, the device in GaCoAP saves 1.902 − 0.507 = 1.395 retransmission times compared to MQTT-SN in the case that MLR = 10% and µ = 10. As a result, each device can save 1840.185 ms·mA (951 ms·mA ×1.395) power for a packet at most. Even compared to CoCoA, the device in GaCoAP can still save 0.998 − 0.507 = 0.491 retransmission times. Each device saves at least 466.941 ms·mA (951 ms·mA ×0.491) power for a packet. Finally, we discuss power consumption issue. Compared to other methods, device in GaCoAP can save power owing to the reduction of retransmissions. If a device often triggers retransmission, it encounters higher transfer power consumption. In our experiments, the number of retransmissions in GaCoAP is the smallest with only one exception (i.e., µ = 1 and MLR = 0%). Assume that the packet size is 31 bytes, the size of Medium Access Control (MAC) ACK is 5 bytes, and the size of the application ACK is 12 bytes (This assumption follows the experiment setting in [14]). Based on Table 4 in [14], Indeed, compared to calculating the RTO by the device itself, sending extra two bytes for the Finally, we discuss power consumption issue. Compared to other methods, device in GaCoAP can save power owing to the reduction of retransmissions. If a device often triggers retransmission, it encounters higher transfer power consumption. In our experiments, the number of retransmissions in GaCoAP is the smallest with only one exception (i.e., µ = 1 and MLR = 0%). Assume that the packet size is 31 bytes, the size of Medium Access Control (MAC) ACK is 5 bytes, and the size of the application ACK is 12 bytes (This assumption follows the experiment setting in [14]). Based on Table 4 in [14], a device consumes 1182 ms·mA (summation of Id 3, Id 4, and Id 5) power when it transmits a packet. If the device needs to retransmit the packet, extra 951 ms · mA (summation of Id 3 and Id 4) is required. For example, if the average number of retransmission is 0.1, the actual power consumption is 1182 + 951 × 0.1 = 1277.1 ms·mA. From Figure 5, the device in GaCoAP saves 1.902 − 0.507 = 1.395 retransmission times compared to MQTT-SN in the case that MLR = 10% and µ = 10. As a result, each device can save 1840.185 ms·mA (951 × 1.395) power for a packet at most. Even compared to CoCoA, the device in GaCoAP can still save 0.998 − 0.507 = 0.491 retransmission times. Each device at least saves 466.941 ms·mA (951 × 0.491) power for a packet. Indeed, compared to calculating the RTO by the device itself, sending two extra bytes for the RTT and receiving the RTO result in more power consumption. Compared to this consumption, the power savings of calculating the RTO is ignorable. According to [14], sending a packet over the air costs 31.5 ms·mA (see event 8). In our design, sending a packet that contains the RTT information occupies two extra bytes, which means that the device has to spend an additional 0.0645 ms (2 bytes/31 bytes). Therefore, the additional power consumption is 2.0318 ms·mA (0.0645 ms × 31.5 mA). On the other hand, the device updates the RTO in two ways. One is receiving its ACK with two extra bytes to carry the RTO. The other is receiving the ACK to get the RTO by overhearing. In [14], the required current for receiving MAC ACK or application ACK is 26.5 mA (see event 16). With the first way, the device has to receive two extra bytes, which costs an additional 1.70925 ms·mA (0.0645 ms ×26.5 mA). Using the second method, the device receives a whole 14 byte application ACK, which costs an additional 11.9677 ms·mA (0.4516 ms ×26.5 mA). Note that performing CSMA/CA observation also consumes energy, but it is common for all mechanisms (performing one observation consumes 1.325 ms·mA).
To put it briefly, a device adopting GaCoAP spends at most 13.677 ms·mA (per packet) to send the RTT and receive the RTO. However, this device can save at least 466.941 ms·mA per packet from reducing retransmissions. The power consumption mentioned above can be converted to other units for easy understanding. For example, a normal AAA battery (with capacity 1200 mAh) can be used to transmit 3, 654, 822 packets (1200 × 3, 600, 000/1182) if no retransmission occurs. If the average number of retransmission is 0.1, then only 3, 382, 664 packets (1200 × 3, 600, 000/1277.1) can be transmitted. In Figure 5, when MLR = 10% and µ = 10, the energy required for a packet in GaCoAP is 1182 + 951 × 0.507 + 13.677 = 1677.834 ms·mA, while the energy required for a packet in MQTT-SN is 1182 + 951 × 1.902 = 2990.802 ms·mA. In this case, 2,574,748 packets can be transmitted in GaCoAP, while only 1,444,428 packets can be transmitted using a single AAA battery.
As a final remark, the network environment is simple in our experiment (a gateway connects to 30 devices), but it is more complex in the real sensor networks. From our simulation results, the GaCoAP mechanism outperforms the others, especially in worse conditions (i.e., large latency and high message loss rate).
Conclusions
In this paper, we proposed a gateway-assisted method for IoT devices to determine the RTO value of their wireless link. The main concept is transferring the calculation from devices to a gateway. The gateway dynamically calculates the RTO and then broadcasts the result to the devices connected to it. Using this method, the devices can save more power because they are able to obtain an appropriate RTO value earlier by overhearing. Then, we conducted experiments from four aspects to investigate the performance.
Compared to the other methods, the devices in GaCoAP can get dynamic RTO earlier, which results in much smaller retransmission times and larger message delivery ratio with some latency sacrifice. In the case that MLR = 10% and µ = 10, the devices adopting GaCoAP can save at most 73.3% in terms of the number of retransmissions, and improve the message delivery ratio to at most 19% among methods with RRP policy. The devices only sacrifice up to 10 s (21 s−11 s) latency. Note that 10 s latency is ignorable in most IoT applications. The message delivery ratio in MQTT-SN is the best due to persistent policy; however, the number of retransmissions in MQTT-SN is the largest and the delivered message may be out-of-date. As long as the gateway connects to more than five devices, the GaCoAP mechanism outperforms all other mechanisms in terms of the number of retransmissions. Therefore, GaCoAP is better than other methods for IoT applications concerning energy usage.
Recently, several works have discussed applying Information Centric Networking (ICN) to IoT [15][16][17]. The IoT devices can benefit from this network paradigm in terms of power consumption, especially in multi-hop networks. Although we only consider the star topology in this paper, it is worth discussing how GaCoAP performs in ICN in the future. Another interesting work is applying lightweight application protocols on smartphones to improve performance of transmission. Since smartphones are embedded with various sensors and are widely used in modern society, it is important to involve smartphones in sensor networks. In [18], the performance of applying MQTT and CoAP to smartphones has been studied. Applying GaCoAP to smartphones brings more benefits (e.g., multiple sensors) as well as more challenges (e.g., mobility). We will also consider adopting GaCoAP on smartphones in future work. | 8,842.4 | 2016-09-22T00:00:00.000 | [
"Computer Science"
] |
The see-saw portal at future Higgs factories: the role of dimension six operators
We study an extension of the Standard Model with electroweak scale right-handed singlet fermions $N$ that induces neutrino masses, plus a generic new physics sector at a higher scale $\Lambda$. The latter is parametrized in terms of effective operators in the language of the $\nu$SMEFT. We study its phenomenology considering operators up to $d=6$, where additional production and decay modes for $N$ are present in addition to those arising from the mixing with the active neutrinos. We focus on the production with four-Fermi operators and we identify the most relevant additional decay modes to be $N\to \nu \gamma$ and $N\to 3f$. We assess the sensitivity of future Higgs factories on the $\nu$SMEFT in regions of the parameter space where the new states decay promptly, displaced or are stable on detector lengths. We show that new physics scale up to $5-60\;$TeV can be explored, depending on the collider considered.
Introduction
Neutrino masses and mixing can be explained by adding to the Standard Model (SM) a new Weyl fermion N , total singlet under the SM gauge group, which acts as the right-handed (RH) counterpart of the left-handed (LH) SM neutrino. The lightness of the neutrino masses can be explained by the see-saw mechanism [1][2][3][4] where v is the Higgs vacuum expectation value (VEV), y the strength of the Dirac type interaction and M N the Majorana mass of the RH neutrino. While there is no indications on the energy scale at which this mechanism takes place, there is nowadays a strong interest in models where RH neutrinos have a mass at the EW scale. From one side they are in fact an interesting alternative, in that they can generate the observed matter-antimatter asymmetry via neutrino oscillations [5,6], while they can be searched for at colliders and at beam-dump experiments [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, if lighter than O(100) MeV, they can be relevant for the solution of longstanding anomalies reported in the neutral-current [26][27][28] and charged-current [29][30][31][32][33][34][35][36][37] semileptonic decay of B mesons [38][39][40]. Their phenomenology is driven by the mixing θ with the active neutrinos which drives their production rates and and their decay width and hence their lifetime.
The naive see-saw scaling of Eq. (1.2) can be modified if multiple RH neutrinos are present with specific Yukawa and Majorana mass textures that ensure an approximate lepton number symmetry [41,42]. Consequently scenarios with a much larger mixing angles can be realized, thus altering the RH neutrinos phenomenology. It's also interesting to speculate on the possibile presence of additional NP states at a scale Λ v, M N , whose effects can be parametrized in the language of effective field theories in the so called νSMEFT, where a tower of higher-dimensional operators O d Λ 4−d built out with the SM fields and the RH neutrinos is added to the renormalizable lagrangian. At the lowest possible dimension, d = 5, there are two genuine, i.e. that contains at least a RH neutrino field, νSMEFT operators: one that triggers the decay of the SM Higgs boson into a pair of RH neutrinos and a dipole operator with the hypercharge gauge boson [43,44]. Already at d = 6 many more operators are present [9,45,46] with interesting phenomenological consequences, since they also can induce new production and decay channels.
Many of these operators have been subject of theoretical studies, especially for what concerns their phenomenology at the Large Hadron Collider (LHC), see e.g. [9,21,43,44,[47][48][49][50][51][52][53]. However, RH neutrinos with a mass at the EW scale are one of the primary goals of future lepton colliders, since the generally small production cross section proper of EW singlet states can be overcome, thanks to the clean detector environments and the typically lower SM backgrounds with respect to hadronic machines. For the post LHC era many future lepton colliders have been proposed. These includes e + e − facilities, both circular ones as the Future Circular Collider [54][55][56][57] (FCC-ee) and the Compact electron-positron collider [58,59] (CEPC), and linear ones as the International Linear Collider [60][61][62] (ILC) and the Compact Linear Collider [63,64] (CLIC). Finally, a great attention has recently arose for multi TeV µ + µ − colliders [65], which could provide a great handle to test higherdimensional operators whose effect grows with energy.
In a recent paper [66], we have investigated the prospects of these machines, commonly denoted as Higgs factories, in testing the two genuine d = 5 operators of the νSMEFT through Higgs and Z boson physics and focusing on RH neutrinos with masses in the [1 GeV − m h,Z ] range. There we have shown that future lepton colliders can test exotic branching ratios (BRs) for the Higgs and Z boson down to ∼ 10 −3 and 10 −9 respectively, greatly surpassing the reach of future indirect measurements of the Higgs and Z boson width. In this paper we extend our previous work by studying the phenomenology of the νSMEFT operators that arise at d = 6. Since these are typically generated by different ultraviolet (UV) completions than the d = 5 ones, the bounds on the cut off-scale Λ derived in [66] do not necessarily direct apply 1 .
We focus on EW scale RH neutrinos with masses in the [1 GeV − m W ] range and study the additional production and decay channels induced by the d = 6 operators. We distinguish two main decay channels: a two body decay into a SM neutrino and a photon, N → νγ, and a three body decay into a SM leptons and a fermion pair which can proceed either as N → νff or N → ff , where = e, µ, τ . In the three body decay cases the final state fermions could involve either a pair of quarks or leptons. For what concerns the production, we identify the most relevant channels as single-production and pair-production of RH neutrinos induced by four-Fermi d = 6 operators, since they induce amplitudes that grow with the energy of the process.
The paper is organized as follows. In Sec. 2 we set our notation and review the νSMEFT framework, while in Sec. 3 we present the properties of the future colliders which are under analysis. Then in Sec. 4 we study the main decay channels induced by the d = 6 operators and present the expressions for the various partial widths. We then show under which conditions these additional decay modes can dominate with respect to the one already present at renormalizable level and induced by the active-sterile mixing. We further quantify the lifetime of the RH neutrinos once these operators are switched on. In Sec. 5 we discuss the additional production modes relevant for studies at future Higgs factories. We present our results in Sec. 6, Sec. 7 and Sec. 8 for prompt, displaced and detector stable RH neutrinos. We finally conclude in Sec. 9. We then report in App. A the expressions for the spin averaged matrix elements squared relevant for the N three-body decay via an off-shell SM boson induced by d > 4 operators.
Theoretical framework
The νSMEFT is described by the following Lagrangian Here N is a vector describing N flavors of RH neutrino fields, singlet under the SM gauge group, and N c = CN T , with C = iγ 2 γ 0 . Furthermore L L is the SM lepton doublet, Y ν is the 3×N Yukawa matrix of the neutrino sector withH = iσ 2 H * , M N is a N ×N Majorana mass matrix for the RH neutrinos and O n the Lorentz and gauge invariant operators with dimension n built out from the SM and the RH neutrino fields, with Λ indicating the EFT cut-off. In [9,[43][44][45][46] the νSMEFT has been built up to d = 7 and at d = 5 only three operators exists. The first is the well-know Weinberg operator [69] while the two
four-Fermi scalar operators
Other four-Fermi operators where B µν is the SM hypercharge field strength tensor and 2σ µν = i[γ µ , γ ν ], which have been recently investigated in [66]. At d = 6 many more operators are present. They are reported in Tab. 1, where we split them between operators that involve the Higgs boson and four-Fermi operators which do not 2 .
Neutrino mixing formalism
We summarize here the properties of the neutrino sector of the νSMEFT, and we refer the reader to [66] for a more detailed discussion. Under the approximation in which the contribution to the active neutrino masses dominates over the ones induced by the effective operators the active neutrino mass matrix takes the standard form where U is the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [70,71] and m d ν is the diagonal matrix of neutrino masses. Eq. (2.2) can be solved for the Yukawa matrix of the neutrino sector. In the Casa-Ibarra parametrization [72] one obtains where √ m is a 3×N matrix containing the physical neutrino masses m i and R is a complex orthogonal N × N matrix. We restrict now our study to the case N = 2 where for the normal hierarchy (NH) and inverted hierarchy (IH) one has for the matrix while we parametrize the orthogonal matrix R in terms of the complex angle z = β + iγ as The active-sterile mixing angle is given by It's crucial that the angle z is, in general, a complex parameter. In fact, in the limit in which z is a real number, by taking U and R with entries of order unity and by assuming an equal value for the diagonal entries of the Majorana mass term for the two RH neutrino This relation is drastically modified by the imaginary part of z, that gives an exponential enhancement. In the limit γ 1 one has (2.9) Clearly the same enhancement is inherited by the active-sterile mixing, that now reads (2.10) We use α = 1, 2, 3 for the active neutrino flavor and i = 1, 2 for the RH neutrino flavor. This deviation from the naive see-saw scaling has a crucial impact on the RH neutrinos phenomenology, especially for what concerns their decay width and consequently their lifetime, with drastic implications for search strategies at future colliders as recently shown in [66,73]. 3 When needed, for our numerical estimate we take mν 2 = 8.6 × 10 −3 eV and mν 3 = 5.1 × 10 −2 eV for the NH while we take mν 1 = 4.9 × 10 −2 eV and mν 2 = 5.0 × 10 −2 eV for the IH. 4 We have assumed NH and fixed mν = mν 3 . The expression holds also for the IH case modulo order one factors.
Future Higgs factories
In this work we study the phenomenology of the νSMEFT at future Higgs factories, both at their low energy runs, relevant for physics at the Higgs-strahlung threshold and at the Z pole, together with high-energy multi TeV runs, which can greatly enhance the sensitivity on higher-dimensional operators which induce a quadratic grow with the energy, as for the case of four-Fermi operators. For what concerns the low energy runs, various e + e − prototypes, presently at different stages of their design, have been proposed. These include circular ones, as the Future Circular Collider (FCC-ee) [54][55][56][57] and the Circular Electron Positron Collider (CEPC) [58,59], and linear ones, as the International Linear Collider (ILC) [60][61][62] and the Compact Linear Collider (CLIC) [63,64]. Regarding colliders in the multi TeV regime, prototypes include CLIC with a center of mass energy of 3 TeV [63,64] and a µ + µ − colliders with various center of mass and luminosity options [65]. We report in Tab. 2 the main parameters of these colliders prototypes. For concreteness and clarity of presentation, in this work we will present our results only for the case of FCC-ee at √ s = m Z and √ s = 240 GeV, for a µµ collider at √ s = 3 TeV and for CLIC at 3 TeV, since the ILC and CEPC prototypes will have an overall similar behavior to the considered options.
Decay channels for RH neutrinos
At the renormalizable level, the RH neutrinos only decay thanks to the mixing with their SM active counterpart, a pattern which is not altered by the inclusion of d = 5 operators except in the case of a sufficiently large mass splitting m N 2 − m N 1 (with m N 2 > m N 1 ) in which the O 5 N B operator can trigger a non-negligible N 2 → N 1 γ decay rate [66]. The inclusion of d = 6 operators can dramatically alter this behavior, leading to new decay patterns, see also [74,75]. For example, the four-Fermi operators reported in Tab. 1 can induce the decay of a RH neutrino into three SM fermions, N → 3f . Depending on the operator, the rate for this decay may or may not be suppressed by the active-sterile mixing Operator Decay Mixing Loop Table 3. Decay modes for the RH neutrinos induced by higher-dimensional operators and renormalizable mixing. We highlight whether the corresponding rates are mixing and/or loop suppressed. Neutral and charged indicate the four-Fermi operators with two and one RH neutrino respectively.
angle. In particular, it is suppressed in the case of four-Fermi operators which contain two RH neutrino fields, while unsuppressed otherwise. On the other side, the operators involving the Higgs boson can induce, after EW symmetry breaking, the decay into a final state fermion and a massive SM boson, B = Z, W ± , h. Given the range of RH neutrino masses on which we are interested in, the SM boson turns out to be off shell and the resulting decays are thus N → νB * and N → B * , with the subsequent decay B * → ff . Also in this case the rate could be, or not, suppressed by the active-sterile mixing and again the final state is composed by three SM fermions, as for the case of the four-Fermi operators. However the kinematic and the flavor composition is generally different. Finally, the SM boson could be a massless photon, and the decay is thus simply N → νγ. We now discuss the various operators and the decay that they mediate in turn, summarizing their main properties in Tab. 3, where we highlight whether the decays that they generate are suppressed by mixing and/or loop effects. We then report in App. A the spin averaged amplitude squares for the considered three body decays.
Operators that induce N → νγ
This decay mode is induced at the d = 5 level by the O 5 N B operator and at the d = 6 level by the O 6 LN B,LN W operators.
This operator gives the N i → ν α γ decay only after a mixing insertion 5 . The rate for this decay reads [44] where c ω is the cosine of the Weinberg angle and where we have explicitly introduced a loop suppression factor, since in any weakly coupled UV completion this operator arises at loop level [76,77].
where, again, we have explicitly written the loop suppression factor. This decay is not suppressed by the active-sterile mixing.
Operators that induce N → 3f
This decay mode has contribution from both operators involving the Higgs boson as well as four-Fermi operators. Also the decay induced at the renormalizable level by the activesterile mixing produces the same final state.
where the factor N c = 3 is present if the final state is a quark-antiquark pair. In our numerical analysis we use the full expression for the decay and sum over the relevant ff final states for any N mass. For the decay into a bb final state, which is the relevant one for m N > 10 GeV, one has where the Wilson coefficient has been fixed to one.
N H
This operator induces the decay N i → ν α Z * and the rate is suppressed by a mixing insertion. For a generic ff final state arising from the Z * decay one has, in the limit m f = 0 with t 3 = ±1/2 and where q is the electric charge of the final state fermion pair. For example for the decay into a final state bottom pair, where t 3 = −1/2 and q = −1/3 one has where θ schematically indicates the relevant mixing angle.
Decay from O 6 N eH
This operator induces the mixing unsuppressed decay N i → α W * . Working again in the limit where all the final state fermions are massless, the decay for one of the two charge conjugate modes reads where the estimate is with N c = 3 and an O(1) Wilson coefficient.
The combination of these two operators orthogonal to the one that induces N → νγ gives again a N → νZ * decay. In addition, the operator with the W boson produces a N → W * decay. Both these rates are not suppressed by the active-sterile mixing. In the massless limit, the neutral decay width is while for the charged case we obtain where, again, the rate is for one of the two charged conjugated modes.
Decay from four-Fermi vector operators: The first operators are of the form (N R γ µ N R )(f L/R γ µ f L/R ). They mediate the decay N → νff which is suppressed by the active-sterile mixing angle. For simplicity we assume a diagonal flavor structure for the SM fermion pair final state. In the limit of massless final states the decay rate reads where α 6 is the Wilson coefficient of the four-Fermi operator and the factor 2 comes from summing over ν andν, since also the SM neutrino is Majorana. The charged operator O 6 N edu triggers a decay N → − ud + +ū d, which has a rate (4.12)
Decay from four-Fermi scalar operators
These operators induce the decay N i → α ff , where could be a charged or neutral lepton. Each decay proceeds with a rate where, once more, α 6 denotes the generic Wilson coefficient of the four-Fermi operator.
Which decay dominates?
We can now compare the decay rates computed in Secs. 4.1 and 4.2 to see which one dominates in the different regions of the νSMEFT parameter space. This is essentially determined by three parameters 6 : the mass of the RH neutrino m N , the active-sterile mixing θ and the EFT cut-off scale Λ. We take the latter to be the same for all the considered operators. Clearly, different UV completions will generate at low energy different operators, in general suppressed by different mass scales. We will comment in Sec. 4.4 and Sec. 4.5 on the independent limits on the scale Λ that can be set for the most relevant ones. For simplicity however, in performing our main analysis, we will assume that only four fermi operators and the dipole ones triggering the N → νγ decay are active, and that they are associated to a unique scale Λ.
The first question we want to address is in which region of the parameter space the decay induced at the renormalizable level by the active-sterile mixing dominates over the decay generated by higher-dimensional operators, taking into account that current constraints forces the squared mixing angle to be 10 −6 [79][80][81]. In order to do this we need to make some assumptions on the number of four-Fermi operators that are active, since each one can contribute with a multiplicity due to the flavor structure of the operator itself. To be practical, we parametrize this with a coefficient ξ which takes into account how many channels from four-Fermi operators contribute to the decay of a RH neutrino, for example for a decay into a pair of final state quarks ξ = N c = 3. Clearly, the most important four-Fermi operators for N decay are the ones that do not pay a mixing suppression, i.e. O 6 N edu and all the scalar ones. On the other side, for the operators that contribute to the 3f final state via an off-shell h, Z and W , we can consider all possible decays by summing on their decay modes, since those are fixed by the SM symmetries. In these calculation we retain the full expressions for the various decay rates. We then show in Fig. 1 the region of parameter space where the decay induced by the higher-dimensional operators dominate over the one induced by the mixing. We illustrate them for the degenerate RH neutrino masses m N = 1 GeV (left) and m N = 50 GeV (right) 7 . Above the black solid line the decay pattern is thus the one analyzed in [66], while effects from higher-dimensional operators become relevant in the lower part of the plot. The dashed gray lines indicate the experimental bound on θ α = i=1,2 |θ αi | 2 reported in [79][80][81]. We show only the bound on 6 While we already stated that we work in the limit where the two RH neutrinos are almost degenerate and the various entries of the active-sterile mixing matrix θ are determined by the choice of the NH or IH once the RH neutrino mass has been fixed, each higher-dimensional operator can in principle have a different Wilson coefficient. For concreteness, we work under the assumption that they are all equal. We also consider the NH scenario. Results in the IH case are almost identical. 7 The dependence on ξ turns out to be completely negligible for the N mass range of our interest up to |θ µ | 2 which turns out to be the most stringent one. Finally the gray shaded area represents the see-saw limit, below which the lightness of the neutrino masses cannot be explained by the see-saw mechanism. As we see, for small enough Λ the dominant decay mode of the RH neutrino can be induced by the higher-dimensional operators of the νSMEFT while retaining compatibility with existent active-sterile mixing bounds. As previously discussed, in this region two decay modes compete: N → 3f , which produces the same final state as the decay via mixing albeit with different kinematics, and N → νγ. For |θ e | 2 10 −6 one has that the ratio Γ N →νγ Γ N →3f is almost independent on Λ and that the νγ decay dominates over the N → 3f decay for m N 15 GeV . In this region the decay is driven by the d = 6 operators O 6 LN B,LN W , since the d = 5 operator O N B gives a rate which is mixing suppressed. For larger masses, the operator that dominates the N → 3f decays is O 6 N eH , which is again not mixing suppressed. Given that we are interested in the phenomenology of the d > 4 operators in the following we will focus in the region where the decay is dominated by higher-dimensional operators and work under the assumption of negligible active-sterile mixing.
Bounds from theoretical considerations
The computation of the neutrino properties outlined in Sec. 2 rests on the assumption that the d = 4 masses and Yukawa couplings dominate over the higher dimensional contributions. In order for this to be true, the NP scale will have to satisfy some conditions. Before enumerating them, it is useful to point out that, unlike what happens in the SMEFT, the νSMEFT is characterized by two expansion parameters: the active-sterile mixing θ and the cutoff scale Λ −1 . As previously discussed and shown in Fig. 1, the phenomenology will strongly depend on the interplay between the two. In order to understand the stability of the d = 4 parameters against the additional contributions, we will consider only those effects that solely depend on Λ, neglecting possible effects that are doubly suppressed by some power of θ and of 1/Λ. where the reference value |θ| 2 ∼ 10 −6 is the approximate experimental upper bound on the mixing angle for the RH neutrino mass range of our interest. As we can see, the theory bound on the scale of O 6 LN H is pretty strong, while the one on O 6 LN B /O 6 LN W is rather weak, at least for values of the mixing close to the allowed upper bound. In order for the bounds on the scale of these operators to be of the TeV order we would need |θ| ∼ 10 −14 , which is below the see-saw limit, see Fig. 1.
Bounds from precision measurements
The operators of Tab. 1 involving the Higgs bosons will also trigger additional decay of the SM bosons, which are constrained by precision measurements from LEP and LHC data. By asking that these additional decay modes do not exceed the absolute uncertainty on the measurement of the Z and W boson width, and that they contribute less than 10% to the SM Higgs boson width, one obtains that the strongest limit arises from the constraints on h → N N decay given by O 6 LN H that reads a result compatible with the one reported in [50]. This is due to the small total width of the SM Higgs boson, which compensates for the lower absolute precision on its determination with respect to the Z and W cases. For the latter we obtain a bound of Λ 0.8 TeV 8 We have explicitly checked that the contribution from the operators O 6 LN qu , O 6 LN qd and O 6 LdqN give weaker bounds with respect to the ones shown. and 0.6 TeV, respectively. While for O 6 LN H the theoretical bound discussed in the previous section is stronger, for the dipole operators the experimental bounds are stronger.
The interplay between the O 6 LN B,LN W operator and the active-sterile mixing also generates a magnetic moment d µν σ αβ νF αβ for the SM neutrinos which can be estimated as This is another example of effect which is suppressed by both θ and powers of 1/Λ. The value of the active-sterile dipole moments constrained by reactor, accelerator and solar neutrino data [82,83] which give Λ 4 × 10 −2 |θ| 2 10 −10 TeV.
that is weaker than Λ 1 TeV for the allowed mixing angles range.
Lifetime of RH neutrinos
After having discussed the main RH neutrinos decay modes, it is important to determine the lifetime of these state, to assess whether their decay happen with a prompt or displaced behaviour or if instead they are stable on collider lengths. We quantify the three behavior as follows: Prompt decay We consider a RH neutrino to decay promptly if its decay happens within ∼ 0.1 cm from the primary vertex. At the renormalizable level, prompt RH neutrino decays require a large breaking of the naive see-saw scaling. In the notation of Sec. 2.1, this is parametrized by a large value of the γ parameter, see Eq. (2.10). Large mixing angles are however constrained by a variety of experimental searches, and too large values of γ are thus ruled out.
Displaced decay A particle is considered to decay displaced if it decays away from the primary vertex but within the detector environment. The precise distance for defining a vertex to be displaced clearly depends on the specific detector geometry. Given that our study focuses on future proposed e + e − and µ + µ − colliders, for which detailed detector characteristics have not yet been settled, we consider as displaced particles decaying between 0.1 cm and 1 m from the primary vertex. Taking into account the preliminary nature of our study, we also consider the detector to have a spherical symmetry, instead of a cylindrical one.
Decays outside the detector Also in this case, the precise value of the decay length of the RH neutrinos needed for it to be considered detector stable depends on the specific geometry of the detector. We then consider as detector stable, RH neutrinos which decay more than 5 m away from the primary vertex. The decay length in the laboratory frame βγcτ can be readily obtained for the two dominant N production modes that will be discussed in Sec. 5, i.e. pair-production and singleproduction from four-Fermi operators. The βγ factor is fixed by the kinematic of the process and reads (4.20) As discussed in the previous section, in the region where the RH decay width is dominated by the d > 4 operators, two decays compete: N → νγ and N → 3f . As an example, we show in Fig. 2 the isocontours of βγcτ for the case of exclusive νγ (left) and 3f (right) decay, fixing √ s = 240 GeV and 3 TeV and considering the pair-production case. These lifetimes are dominated by mixing unsuppressed operators and thus do not strongly depend on the mixing angle. As in Sec. 4.3, the dependence on ξ is extremely mild. The case of single-production is qualitatively similar, with more pronounced differences appearing for large m N in the case √ s = m Z . From the figures we see that the RH neutrino can have, for both final states, a prompt, displaced and stable behaviour, depending on the values of m N and Λ considered, although a detector stable N can only arise for m N 20 GeV for Λ 100 TeV. Clearly, if one considers only the decay induced by mixing suppressed operators these will in general give larger values for the proper cτ decay length, which are compatible with a displaced or stable behavior for N and that can be of the same order of magnitude as the one induced by the active-sterile mixing.
Production modes for RH neutrinos
At the renormalizable level, RH neutrinos are produced only via their mixing with the active neutrinos, while at d = 5 two different production mechanisms arise: one from an exotic decay of the Higgs boson and one from the exotic decay of the Z boson. These have been studied in [66], where the N were considered to decay only via mixing, being this the dominant mechanism for d ≤ 5. The inclusion of d = 6 operators brings new production modes for RH neutrinos. The main mechanisms can be divided in two categories.
i ) Single-and pair-production of N via four-Fermi operators, ii ) N production via Z, W and h decay from d = 6 operators involving the Higgs boson.
In this work we focus on production via four-Fermi operators while we leave the analysis of the production from SM boson decay for future work.
Single and pair-production of N via four-Fermi operators
At lepton colliders there are three four-Fermi operators that can produce RH neutrinos. The O 6 N e and O 6 N L operators generate the process + − → N i N j with a rate where the numerical approximation is valid in the massless limit. In both cases we have set to unity the Wilson coefficient of the operator inducing the process and assumed fixed flavors. Appropriate multiciplicity factors must be included to compute the inclusive crosssections in all flavors.
As a preliminary indication, we can ask what is the maximum scale Λ that can be tested by requiring the production of at least one signal event before enforcing any BR factor and selection acceptance. As mentioned in Sec. 3, we take as benchmark colliders the FCC-ee at √ s = 240 GeV, the FCC-ee at the Z pole, a µµ collider with √ s = 3 TeV and CLIC at √ s = 3 TeV. For all these options, the considered integrated luminosities are reported in Tab. 2. The maximum scales that can be tested are show in Fig. 3, where the left and right panel are for N pair-and single-production respectively. By comparing this result with Fig. 1 we see that, for light N in the majority of the allowed parameter space that can be tested, the decay of the RH neutrino will proceed via higher-dimensional operators while for heavier N the decay might also proceed via active-sterile mixing.
Even if produced via a four-Fermi operator, the heavy N can nevertheless decay into a γν final state. For instance, four-Fermi operators of the form (N γ µ N )(f γ µ f ) will induce an unsuppressed pair-production cross-section e + e − → N N and a decay N → ν ¯ which, being mixing-suppressed, will typically be subdominant. In addition, this will also always In order to be concrete, we thus analyze the two possible signatures in turn separately, assuming a 100% exclusive decay for each mode and separately considering the possibility of a prompt, displaced and collider stable behavior.
N prompt decay
As shown in Fig. 2 the RH neutrino can promptly decay into a νγ and 3f final state in all the N mass range of our interest if Λ is sufficiently small. We start by considering the exclusive N → νγ decay, moving then to the N → 3f one for both N single-and pair-production.
Decay N → νγ
When the dominant decay mode is the one into a SM neutrino and a photon we consider the following processes for pair-and single-production of N 4. 95% CL exclusion limit for the prompt decay into νγ for N pair-production (left) and single-production (right) for various collider options. Also indicated is the region where the decay cannot be prompt so that the described analysis doesn't apply. See text for more details.
In the case of N pair-production, Eq. (6.1), the final state consists in a pair of γ and / E T . Two operators can mediate the N pair-production: O 6 N e,N L whose cross section is reported, for each process, in Eq. (5.1). For simplicity, and being conservative, we assume that only one of the two operators is present and only one pair of RH neutrino is produced. When the RH neutrino is singly produced, Eq. (6.2), the final state consist of a single photon and / E T . Only one operator can mediated this process, O 6 N eN L , whose cross-section is reported in Eq. (5.2). We have implemented 9 the relevant higher-dimensional operators in the Feynrules package [84] and exported it under the UFO format [85] in order to generate parton level signal events with MadGraph5 aMCNLO [86]. Events has been then analysed with the MadAnalysis5 package [87][88][89]. The irreducible SM backgrounds + − → γγ / E T and + − → γ / E T have been generated with the same prescription. At the analysis level, we require the photon to be reconstructed with |η γ | < 2.44 and, for the pair-production case, that they are separated as ∆R(γγ) > 0.1. We enforce the following cut on the photon(s): in the pair-production case we apply p γ T > 80 GeV, 20 GeV and 300 GeV for the FCC-ee at √ s = 240 GeV, the FCC-ee at √ s = m Z and CLIC and the µµ collider at 3 TeV respectively. In the single-production case we apply instead p γ T > 20 GeV, 20 GeV and 300 GeV for the same three collider options. The statistical significance is evaluated in units of standard deviations as S/ √ S + B where S and B are the final number of signal and background events respectively.
We then show in Fig. 4 the the 95% confidence level (CL) exclusion contours for the four collider options for the pair-production (left) and single-production (right) cases respectively. In the figures the gray shaded area is the region with βγcτ > 0.1 cm, that is where the RH neutrinos do not decay promptly and the analysis doesn't apply. This region is conservatively shown for √ s = 3 TeV and is smaller for lower collider energies, see Fig. 2. In the pair-production case we observe that the FCC-ee running at the Z mass has a higher sensitivity to this scenario with respect to the FCC-ee running at √ s = 240 GeV, thanks to the higher integrated luminosity of the first option. In the region where the prompt analysis applies, the bound reaches its maximum at around m N ∼ 30 GeV, then depleting at the mass threshold for N pair-production, where the 240 GeV run of FCC-ee will retain a sensitivity up to Λ ∼ 5 TeV. Note that the bound on Λ from Higgs precision measurements, see Eq. (4.18), partially covers these regions if the O 6 LN H operator is switched on. On the other side a µµ collider running at √ s = 3 TeV will be able to test in principle up to Λ ∼ 20 TeV, while CLIC at the same center of mass energy will be able to test scales up to Λ ∼ 25 TeV. However only lower scales will be effectively tested by this analysis since for higher values of Λ the RH neutrinos will not decay promptly. We also note that the reach is dramatically reduced with respect to the maximal one, left panel of Fig. 3, due to the non negligible SM background for this process. On this respect the limits obtained in Fig. 4 can however be considered as conservative and can be improved by dedicated background treatment and reduction, thus increasing the overall reach on Λ in a realistic analysis. The results in the single-production case are qualitatively similar, albeit slightly weaker, with respect to the pair-production scenario, due to the higher rate for the SM background.
Decay N → 3f
When the dominant decay mode is the one into three SM fermions, we consider the following processes for pair-and single-production of N : where the fermion final state could also include quarks. These final state are similar to the one that arises by singly or pair-produced N that decay via mixing, albeit with a different kinematics 10 . For the pair-production case we focus on the following process with a pair of same-sign (SS) leptons, which is expected to be particularly clean where the four quarks arise from the virtual W decay and can be in any flavor combination. As for the SM background, we follow the same procedure of [66] and compute the SM background + − → + − 4q, correcting it for a (flat) lepton charge misidentification probability factor of misID = 10 −3 [90], e.g. we compute the background 10 In practice, we consider a scenario where the decay is triggered by the O 6 N eH operator, which mediate N → W * . Not being mixing nor loop suppressed, this decay is the dominant one even when the O 6
LN Le
operator that mediate single-production and that can trigger N → ν is switched on. Figure 5. 95% CL exclusion limit for the prompt decay into 3f for N pair-production for various collider options. Also indicated is the region where the decay cannot be prompt so that the described analysis doesn't apply. See text for more details.
yield as σ + − 4q × 2 × misID (1 − misID ). At the analysis level, we require p T > 2.5 GeV, p j T > 5 GeV, |η | < 2.44, |η j | < 2.4 and ∆R > 0.1 11 between the two leptons and a lepton and jet pair 12 . We furthermore consider the correct mass dependent SS branching ratio from the N decay induced by O 6 N eH . We thus obtain the 95% CL exclusion limit shown in the left panel of Fig. 5, where we see that the FCC-ee will be able to test roughly Λ ∼ 5 TeV in the whole considered N mass range for both runs at the Z pole mass and at √ s = 240 GeV, while the high-energy colliders will be able to test up to Λ ∼ 20 − 25 TeV, although only in a smaller region the RH neutrino will decay promptly. For the singleproduction case, whose results are shown in the right panel of Fig. 5, we study the single lepton channel 6) and the corresponding SM irreducible background. Other than the same basic selection cuts imposed in the pair-production case, we further impose a requirement on the missing transverse energy / E miss T > √ s/3. This is motivated by the fact that in the signal case the light active neutrino carries away ∼ 50% of the available center of mass energy, while this is not the case for the background processes, for which the / E T distribution peaks at lower values.
N displaced decay
We now study the sensitivity for RH neutrinos decaying with a displacement which, as discussed in Sec. 4.6, we take to be between 1 cm and 100 cm from the primary vertex. The final event yield for having reconstructed displaced events is parametrized as where σ prod is the pair-production or single-production cross section for N and L denotes the total integrated luminosity. P ∆L represents the acceptance for having a RH neutrino decaying within a certain displacement from the primary vertex. This can be computed from the exponential decay law, taking into account the Lorentz time dilation factor. We then assign a probability for having the RH neutrino decaying at a distance ∆x = x f − x i which reads where the βγcτ factors are reported in Eq. (4.20) for pair-production and single-production cases, for which the parameter n in Eq. (7.1) takes the value of 2 and 1 respectively. This means that for the pair-production case we ask to reconstruct both RH neutrinos as decaying displaced. With disp we instead parametrize the acceptance for reconstructing the displaced decaying neutrino, which depend on the actual detector design and performances, and which therefore we assume as a free extra parameter in the analysis. The irreducible SM background is expected to be negligible on the considered decay lengths and we thus work in the zero background hypothesis. We then show the expected 95% CL exclusion limits, now obtained by requiring N s > 3, in Fig. 6 and Fig. 7 for the pair-production and single-production cased under the assumption of exclusive νγ and 3f decay respectively. The solid and dashed lines correspond to the choice disp = 1 and 0.3 respectively, while the different colors represents the different collider options. From the results we observe that a displaced analysis at the FCC-ee running at √ s = 240 GeV can be sensitive to O(10 TeV) NP scale with a 30% efficiency on the reconstruction of the displaced for m N 10 GeV in the pair-production case, while a higher reach can be attained in the single-production scenario. The FCC-ee running at the Z pole mass can slightly increase these reach due to the large integrated luminosity, while the 3 TeV collider prototypes can reach up to Λ ∼ 50 − 60 TeV for m N ∼ 40 GeV.
Detector stable N
Finally, we discuss the possibility of detector stable RH neutrinos, e.g. the case in which the decay happens more than 500 cm away from the interaction vertex. In this case, both pair-production and single-production give rise to a totally invisible final state. This process can be targeted through the emission of an initial state photon, producing a monoγ signature, + − → γ / E T , which has as SM background + − → νν / E T . In [91] exclusion prospects for various four-Fermi operators producing a weakly interacting massive particle dark matter candidate were given using a full detector simulation of the International Linear Detector prototype for the International Linear Collider. Moreover, rescaling factors for different collider energies, luminosities and beam polarizations where provided. Based on these results at the FCC-ee with 5 ab −1 of integrated luminosities, cutoff scales up to Λ ∼ 1.5 TeV can be tested in the pair-production case. In the single-production case the cross-section is larger than in the pair-production case but the photon spectrum is expected to be more similar to the SM due to the presence of only one heavy particle in the final state. Overall we thus expect the exclusion reach on Λ to be similar to the one of the pair-production case. However for such low scale the RH neutrino N → γν decay happens inside the detector, see Fig. 2, unless there is a cancellation among the α LN B and α LN W Wilson coefficient, see Eq. (4.2). If the dominant decay is N → 3f instead, the RH neutrino can be stable on detector lengths if Λ > 750 GeV and m N < 2 GeV, so that the derived limit of 1.5 TeV applies.
For higher center of mass energies we can again use as a guidance the results of [91]. Here the derived reach of CLIC at √ s = 3 TeV with 1 ab −1 of integrated luminosity is Λ ∼ 10 TeV. For CLIC and the 3 TeV µµ collider at the same center of mass energy we expect a reach in the same ballpark, although a dedicated study is required for a quantitative assessment. By again a comparison with Fig. 2 we see that a reach of 10 TeV on Λ will be able to prove detector stable RH neutrinos up to 5 GeV and 10 GeV if the only available decay mode is the one into νγ and 3f respectively.
Conclusions
In this paper we have considered the νSMEFT and studied how the RH neutrinos N production and decays may be affected by the inclusion of d = 6 operators. More specifically, we have studied the reach of future Higgs factories machines on the cutoff scale Λ at which the EFT is generated. We focused on four representative machines: the FCC-ee at two different center-of-mass energies, √ s = 90 GeV and √ s = 240 GeV, CLIC at a center of mass energy of 3 TeV and a representative muon collider with √ s = 3 TeV. The complete list of non-redundant d = 6 operators is presented in Tab. 1. At the level of production, the d = 6 operators induce either N pair-or single-production. On the other hand, at the level of decays, they induce the modes N → νγ and N → 3f , where various fermions combinations are possible. The former will dominate for RH neutrino masses m N 15 GeV, while the latter will dominate for larger masses, unless the only operators switched on induce a mixing-suppressed decay. Even more interestingly, depending on the RH neutrino mass and on the cutoff scale Λ at which the EFT is generated, the decays can be prompt, displaced or the RN neutrinos can be collider stable. The phenomenology crucially depends on their decay behavior and we have analyzed in detail all three possibilities. Our analysis is reported in Sec. 6, Sec. 7 and Sec. 8 for the three possible RH neutrinos lifetime. We then summarize the results for convenience in Fig. 8, in which, for the Higgs factories considered in this work, we show the 95% C.L. exclusion on the scale Λ as a function of m N . We consider RH neutrino masses up to 80 GeV. For larger masses, the W boson can be produced on-shell in the N decays and our analysis should be slightly modified. We postpone the analysis of such case to future work, although we do not expect major changes with respect to the results shown here. In the left panel we consider the decay channel N → νγ, while in the right panel we show the results for N → 3f . In both panels, the gray region denotes the parameter space in which the RH neutrino decay is displaced. The solid lines show the exclusion (combining pair and single-production) computed with prompt decays, an analysis valid in the white region. The dashed lines, on the contrary, show the exclusion limit considering displaced decays with an efficiency of reconstruction of 30%. In the region of validity of the prompt analysis, the FCC-ee will be able to probe scales up to Λ ∼ 7 TeV, while larger values, up to Λ ∼ 20 − 30 TeV, can be probed with a displaced analysis. These conclusions are valid for both decay channels. In the case of the colliders at 3 TeV, on the other hand, scales up to Λ ∼ 20 ÷ 30 TeV can be probed while the displaced analysis, on the other hand, allows to probe scales up to Λ ∼ 60 TeV.
A Spin averaged matrix elements for N decay
We list here the spin-averaged matrix elements |M| 2 = 1 2 spins |M| 2 for the three body decays of the RH neutrino via the d = 6 operators that proceed through an off-shell boson considered in the text. The kinematics is fixed as 1 → 2, 3, 4 and we define m 2 ij = (p i +p j ) 2 . The final state SM neutrino is always considered to be massless while, depending on the simplicity of the expressions, some of the amplitudes are reported in the limit of vanishing masses for the other final state fermions. From these amplitudes squared the partial widths are readily obtained as [92] dΓ = 1 (2π) 3 | 11,592 | 2022-01-27T00:00:00.000 | [
"Physics"
] |
THRESHOLD DYNAMICS OF A REACTION-DIFFUSION EPIDEMIC MODEL WITH STAGE STRUCTURE
. A time-delayed reaction-diffusion epidemic model with stage structure and spatial heterogeneity is investigated, which describes the dynamics of disease spread only proceeding in the adult population. We establish the basic reproduction number R 0 for the model system, which gives the threshold dynamics in the sense that the disease will die out if R 0 < 1 and the disease will be uniformly persistent if R 0 > 1 . Furthermore, it is shown that there is at least one positive steady state when R 0 > 1 . Finally, in terms of general birth function for adult individuals, through introducing two numbers ˇ R 0 and ˆ R 0 , we establish sufficient conditions for the persistence and global extinction of the disease, respectively.
1.
Introduction. As discussed in Thieme [30], when we describe the spread of infectious disease, all the interesting structures that could and should be considered. Spatial heterogeneity of the environment and spatial-temporal movement of individuals play an important role in the dynamics of infectious disease (see, e.g., [27,40]). Assuming some types of host random movement, there are increasing interests to formulate and analyze infectious disease by reaction-diffusion equations (see, e.g., [1,5,10,9]). Sometimes delay or non-local delay effects would be incorporated into reaction-diffusion epidemic models (see, e.g., [11,18,20,26,36] and the references therein). It is necessary to point that another common way to study the spread of disease in a heterogeneous population is to assume the immigration of infective individuals, which is described by patchy models (see, e.g., [17,19,34,35]). In fact, a constant immigration term has a mildly stabilizing effect on the dynamics and tends to increase the minimum number of infective individuals in the models (see, e.g., [2]).
In nature, as usual, the individual members of population undergo life history through two stages, immature and mature. For vector-borne disease, Dengue fever is transmitted to humans by the mature female Aedes aegypti mosquito (see, e.g., [36]). For some disease, such as sexual disease, it is reasonable to consider the disease transmission in adult population and neglect transmission in juveniles(see, e.g., [35]). Sometimes it seems unreasonable for us to assume that all the individuals in a bounded habitat are commonly susceptible for the disease and have the ability to 3798 LIANG ZHANG AND ZHI-CHENG WANG transmit the disease. Therefore, it is important for us to incorporate stage structure of individual into epidemic model to understand the transmission dynamics of the infectious disease. This work intends to take stage structure, spatial heterogeneity and spatial-temporal movement of individuals into consideration of epidemic models. So in the following, we consider that the host population has two stages: juvenile stage and adult stage. For simplicity, we assume that (see, e.g., [35]) (A1): disease transmission occurs only in adult individuals, and juvenile individuals are immune to the disease; (A2): juvenile individuals do not have the ability to reproduce, and adults are responsible for the reproduction of the population. Let u j (t, x) be the density of juvenile individuals at time t and location x. Then where u(t, a, x) is the density of individuals with age a at time t and location x, and τ the length of the juvenile period. Denote A(t, x) as the density of adult individuals at time t and location x. Then u(t, a, x) and A(t, x) satisfy (see, e.g., Metz and Diekmann [23]) where f (x, A(t, x)) and µ(x)A(t, x) is the birth and mortality function of adult individuals, respectively, and µ j (a) denotes the per capita mortality rate of juvenile at age a, ∆ is the Laplacian operator on R N , Ω is a bounded and open subset of R N with a smooth boundary ∂Ω. The term u(t, τ, x) of the third equation in (2) is the adults recruitment term, being those of maturation age τ . For simplicity, we assume d j (a) = d j , µ j (a) = µ j , that is, diffusion rate and mortality rate of juvenile individuals are independent of age a. Let v(r, a, x) = u(a + r, a, x) with r ≥ 0. Then it follows that Regarding r as a parameter and integrating the last equation, we obtain where Γ is the Green function associated with ∆ and the Neumann boundary condition. Since u(t, τ, x) = v(t − τ, τ, x), ∀t ≥ τ, we have Differentiating (1) with respect to t and making use of (2) and (3), it then follows that u j (t, x) and A(t, x) satisfy We consider a disease transmission of SIS type with nonlinear incidence. According to the principle of mass action, bilinear incidence rate which reflects mechanism of disease transmission could be adopted in classical epidemic model. It has been shown that the disease transmission process may have a nonlinear incidence rate (see, e.g. [15,14] and the reference therein). We employ saturating incidence to describe the transmission process of the disease. Let S = S(t, x), I = I(t, x) be sub-population of susceptible, infectious classes, respectively. Then A(t, x) = S(t, x) + I(t, x). Therefore, we obtain the following model: where g(x, I(t, x)) = β(x)I(t,x) 1+α(x)I(t,x) is saturating incidence, both α(x) and β(x) are positive Hölder continuous functions on Ω. Substituting (3) into the second equation of (4), and dropping the u j (t, x) equation from (4) (since u(t, τ, x) does not depend on the variables of juveniles) result in the following system containing S(t, x) and I(t, x) only: For simplicity, letting (u 1 , u 2 ) = (S, I), (d 1 , d 2 ) = (d S , d I ), we investigate the following time-delayed and non-local reaction-diffusion system with Neumann boundary condition: , ∀α ∈ (0, 1), A > 0. The rest of this paper is organized as follows. In the next section, we study the well-posedness of model system (5) and introduce the basic reproduction number for model (5). In section 3, based on the monotonicity of the birth function on the density of adult individuals, we establish threshold dynamics in terms of the basic reproduction number. Section 4 is devoted to establish sufficient conditions for the persistence and global extinction of disease under the general birth function. Furthermore, a spatially homogeneous case of model (5) with the same diffusion rate of susceptible and infectious adult individuals is studied.
For any ϕ = (ϕ 1 , ϕ 2 ) ∈ C + τ , consider the following linear cooperative reactiondiffusion system (6) By [8,Theorem 4.2], we conclude that the unique of the system (6) exists globally on [0, ∞). For any ϕ ∈ C + τ , let v + (t, x, ϕ(0, x)) be the solution of (6) with initial For any ϕ ∈ C + τ , set Then it is easy to see that the functions v Take B(ϕ) = F (ϕ) for any ϕ ∈ C + τ . Then B is Lipschitz continuous on C + τ . For any x) for any φ ∈ C + τ . Thus, the system (5) generates a semiflow Φ(t) = u t (·) : In the following we prove the point dissipativeness of the solution semiflow Φ(t). (5) and Green's formula, it follows that By (F) and the boundedness of Γ(d j τ, x, y), there exists a positive number k 1 independent of φ, such that Consequently, with the aid of [24, Lemma 3.1] (see also, [16, Theorem 1 and Corollary 1]), we conclude that there exists a positive constant K independent of φ such that which implies that the solutions of system (5) are ultimately bounded, and hence, Φ(t) : Consider the following time-delayed reaction-diffusion equation where d > 0, µ(x) is a positive Hölder continuous function on Ω. Let and (C, C + ) are strongly ordered spaces. In view of the proof of [41, Theorem 3.1], we have the following result.
Using arguments similar to those in [28, Theorem 7.6.1] (see also [32,Theorem 2.2]), it is shown that the following nonlocal elliptic eigenvalue problem has a principal eigenvalue denoted by λ 0 (d, τ, ∂ A f (·, 0)). By [32, Theorem 2.2], the following nonlocal elliptic eigenvalue problem For any ψ ∈ Z + , let A(t; ψ)(·) = A(t, ·; ψ) denote the solution of (7). At what follows, we establish the threshold dynamics for system (7). (7) admits at least one positive steady statē A * (·), and there exists a ς > 0 such that for every . then (7) admits a unique positive steady state A * , which satisfies The proofs of Lemma 2.3 (i) and (ii) are completely similar to those in [41, Theorem 3.1] and the proof of Lemma 2.3 (iii) is also similar to that in [41, Theorem 3.2 (1)], so we omit the details of the proofs of Lemma 2.3. In order to find the disease-free equilibrium (infection-free steady state), we set u 2 = 0 in system (5), leading to the following equation for the density of susceptible host population: As in Lemma 2.3, the nonlocal elliptic eigenvalue problem ∂ŵ(x) ∂n = 0, x ∈ ∂Ω has a principal eigenvalue, which is denoted by λ 0 (d 1 , τ, ∂ u1 f (y, 0)). We further make the following assumption: 1 (x) which is globally attractive in Y + \{0}, and hence, system (5) admits a unique disease-free equilibrium (u * 1 (x), 0). Linearizing system (5) at the disease-free equilibrium (u * 1 (x), 0), we get the following system for infectious component u 2 : Substituting u 2 (t, x) = e λt ϕ(x) into (9), we obtain the following eigenvalue problem: It then follows from [28, Theorem 7.6.1] that (10) has a principal eigenvalue denoted by λ(d 2 , u * 1 (·)) with a positive eigenfunction. In the following, we introduce the basic reproduction number for system (5). Suppose that host population is near the disease-free equilibrium. We introduce the distribution of initial infectious individuals ϕ(x) at time t = 0. Under the synthetical influences of mobility and mortality of infected individuals, the distribution of those infective members as time evolves becomes By using the ideas in [37], we define the next generation operator: Motivated by [7,33,31,36,37], we define the spectral radius of L as the basic reproduction number for model (5), that is, By [37, Theorem 3.1] with diffusion rate independent on spatial variable x, we have the following observation.
3. Threshold dynamics. In this section, we establish the threshold dynamics of the system (5) in terms of the basic reproduction number R 0 . Before we show the main results of this section, we will propose the following results which play an important role in establishing persistence of (5).
The following conclusion indicates that R 0 is a threshold index for disease extinction or persistence.
Claim 3. M 2 is a uniform weak repeller for W 0 in the sense that Then there exists t 0 > τ such that Letψ be the strongly positive eigenfunction corresponding to λ d 2 , tψ is a solution of the following linear system : In view of Lemma 3.1, there exists ε 0 > 0 such that for all x ∈ Ω. By the standard comparison principle, we have which implies u 2 (t, x; φ 0 ) is unbounded, a contradiction. Define a continuous function p : It is obvious that p −1 (0, ∞) ⊆ W 0 . By Lemma 3.1, p has the property that if p(φ) > 0 or φ ∈ W 0 with p(φ) = 0, then p(Φ(t)φ) > 0, ∀t > 0. That is, p is a generalized distance function for the semiflow Φ(t) : C + τ → C + τ (see, e.g., [29]). From the above claims, it follows that any forward orbit of Φ(t) in M ∂ converges to M 1 or M 2 . In view of Claim 2 and Claim 3, we conclude that M 1 and M 2 art two isolated invariant sets in C + τ , and that W s (M i ) ∩ W 0 = ∅, i = 1, 2, where W s (M i ) is the stable set of M i . It is clearly that no subset of {M 1 , M 2 } forms a cycle in ∂W 0 . It then follows from [29,Theorem 3] that there exists anη > 0 such that Hence, lim inf t→∞ u 2 (t, ·; φ) ≥η, ∀φ ∈ W 0 . On the other hand, according to Theorem 2.1 and Lemma 3.1, there exists a > 0 such that 0 < u 2 (t, ·; φ) ≤ , ∀t ≥ t 2 = t 2 (φ), x ∈ Ω. Consequently, for large enough t, u 1 (t, x) satisfies that By using similar arguments to [20, Lemma 1], it follows that the following reactiondiffusion equation admits a unique positive steady state w * (·) which is globally attractive in X 1 . With the aid of the standard parabolic comparison principle, we obtain that Therefore, there exists an ι with 0 < ι ≤η such that lim inf t→∞ u i (t, ·; φ) ≥ ι, ∀φ ∈ W 0 , i = 1, 2.
Thus, the global attractivity stated in conclusion holds.
General birth function.
In the previous section, under the condition (F1), we obtained some conclusions on the persistence and extinction of disease. It should be noted that in (F1), the birth function f is monotone on the density of adult individuals A ∈ (0, ∞). In this section, for more general birth function f , we intend to investigate the threshold dynamics for model (5) satisfying d 1 = d 2 = d, that is, Setting u 2 = 0 in system (23), we have the following equation for the density of susceptible host population: Assume that (F) holds. It then follows from Lemma 2.2 that (25) generates a semiflowQ(t) = u 1t (·) : C + → C + , t ≥ 0, (in this case of d 1 = d, we see that Y = X 1 ), which admits a global compact attractor B 0 . As in Lemma 2.3, the following nonlocal elliptic eigenvalue problem ∂ŵ(x) ∂n = 0, x ∈ ∂Ω has a principal eigenvalue, which is denoted by λ 0 (d, τ, ∂ u1 f (y, 0)). We further make the following assumption: (F2): λ 0 (d, τ, ∂ u1 f (y, 0)) > 0. Assume that (F) and (F2) hold. Then by Lemma 2.3(ii), we have that for φ 1 (0, ·) ≡ 0, where ς > 0 and t 0 are determined by Lemma 2.3(ii) with ψ(s, x) = φ 1 (s, x) for all s ∈ [−τ, 0] and x ∈ Ω. Hence, the solution semiflow of (25) defined by Q (t)φ 1 (s, x) := u 1 (t + s, x; φ 1 ) for s ∈ [−τ, 0] and x ∈ Ω admits a positive global compact attractor B 0 ⊂ int(C + ). We mention that under the conditions (F) and (F1), compact attractor B 0 degenerates into a singleton set (see Theorem 2.4). As such, in Section 2, with the aid of the unique disease-free equilibrium (u * 1 , 0), we can define the basic reproduction number R 0 via the next generation operator and get the threshold result, see Theorems 3.2 and 3.3. However, in the present section, due to the non-monotonicity of birth function, the compactor attractor B 0 may not be a singleton set. Therefore, it is impossible to get a threshold dynamics by defining a unique number R 0 as that in Section 2. To establish the similar threshold results, in the foolwing we introduce two R 0 -like numbersŘ 0 andR 0 by virtue of the lower and upper bounds of B 0 respectively and then establish the dynamics of system (23).
Proof. In the following, we shall use the previous analysis of this section and similar arguments to those in [42,Theorem 3.3] to prove the conclusion stated in (1). | 3,791.2 | 2017-07-01T00:00:00.000 | [
"Mathematics"
] |
MODEL OF STRUCTURAL TRANSFORMATION OF THE ECONOMY OF A MOUNTAIN AGRARIAN REGION
The paper focuses on the problem of structural transformation of the economy of a mountain agrarian region. Technological changes in the production functions of the agricultural sector cause adaptation of the employment structure and, as a consequence, the production structure of the economy of an open region in the medium term. The regional development of small mountain regions with a traditional structure of the economy largely depends on the trajectory for encouraging structural changes. We have presented a model of the impact of technological changes in the agricultural sector on structural changes in the economy of a mountain agrarian region in the medium term, and the classification of technological changes into three types: land-saving, labor-saving and neutral. The proposed model is a two-factor model of the aggregated production function in a small open regional economy, which describes the impact of technological changes on the transformation of the sectoral structure. In the model, the region is a small open agrarian economy with immobile production factors. The conditions of equilibrium in statics are considered and analyzed. It is evidenced that land and labor force as production factors are strong complements, which contribute to the outflow of labor force from the agricultural sector due to labor-saving technological changes in the agricultural sector. It is shown how the proposed model helps make a strategic choice of the program of agricultural extension in a small region with an open economy.
Introduction
Data on the development of mountain regions with an agrarian economy available in scientific literature confirm that the successful economic growth of most of these regions was accompanied by the structural transformation of the socio-economic system (Carter & Zimmerman, 2000;Gollin et al., 2014).
As the economy develops and new technologies are introduced, the share of agriculture in employment decreases, and the number of people migrating to cities in search for work in the industrial and service sectors increases (Hornbeck & Naidu, 2014). The migration can be both external and internal, and stimulate the growth of labor productivity in the region and regional economic development (Gollin et al., 2002;Kongsamut et al., 2001;Ngai & Pissarides, 2007). All this show that the identification of forces that are capable of initiating structural transformation is key to understanding of the process of managing the development of a mountain region. In particular, the increased agricultural productivity is an important condition for an agrarian-oriented economy, which ensures economic development and changes in the structure of the economy (Minh, 2009;Samygin, 2017). Paradoxical as it may seem, the increased agricultural productivity in a traditional agrarian region leads in the long term to the decreased proportion in the overall structure of gross output (Acemoglu, 2010). Modern formal models of structural transformation show how productivity growth in agriculture can release labor force or create demand for manufactured goods (Gurtuev et al., 2013;Nunn & Qian, 2011). At the same time, a great number of models consider the impact of agricultural productivity on industrialization in a closed economic system (Kislitsky et al., 2019;Pei et al., 2013), whereas in regions with an open economy, the comparative advantage in the agricultural sector can hamper the growth of other sectors of the economy. (Foster & Rosenzweig, 2008;Hornbeck & Keskin, 2015).
The paper presents a model of the impact of technological changes in the agricultural sector on structural changes in the economy of a mountain agrarian region in the medium term. The model shows that a Hicks-neutral increase in agricultural productivity reduces the size of the industry as the labor force is redistributed in favor of agriculture, as in classic open economy models (Acemoglu & Guerrieri, 2008;Herrendorf et al., 2013). Similar results are obtained for land-saving technologies. In contrast, if land and labor force as production factors are strong complements, labor-saving technological changes in the agricultural sector reduce the demand for labor force and cause the flow of labor into industry. Thus, the model predicts that the impact of agricultural productivity on structural transformation in an open economy of an agrarian region depends on the factor characteristics of the introduced technology, namely, on whether the balance of production factors will shift towards labor saving.
Problem Statement
The study presents a model of the impact of technological changes in the agricultural production industry on structural changes in the regional economy in the medium term. At the same time, the main issue is identification and quantification of the relationship between the types of technological innovations and the vector of structural transformations, and the direction of the flow of labor resources.
Research Questions
The model shows how an increase in agricultural productivity affects the economic structure of a small open mountain region. At the same time, three types of technological changes are considered: Hicks-neutral, labor-saving and land-saving.
Purpose of the Study
The purpose of the study is to develop a mathematical model of the impact of the nature of technological changes in the agricultural sector on the structure of the regional economy in the medium term.
Research Methods
The study employed the methods of mathematical modeling, in particular, a model of an equilibrium open market in statics was created.
Findings
Consider a simple model describing the impact of the factor of technological changes on structural transformation in an open regional economy. Let the mountain region represents a small open agrarian economy, that is goods can be freely sold in different regions (on the external market), but the production factors are immobile. Consider the simplest case that involves two aggregated sectors of the economy, agriculture and industry, and two production factors, land and labor.
A small open economy is characterized by a number of economic agents, each of which has L units of labor. There are two sectors, industry and agriculture, that produce goods available for trade.
Production of industrial goods requires only labor, and the labor productivity in industry is A m . Thus, the gross industrial output in our model will be Q m =A m L m , where L m is the amount of labor used in the industry. Production in the agricultural sector requires both land and labor, and takes the form of the production function with a constant elasticity of substitution: where Q a is the gross agricultural output, L a and T a are the production factors of labor and land, respectively,
A N is Hicks-neutral technological changes,
A L is technological changes that lead to a relative decrease in labor use, A T is technological changes that lead to a relative decrease in land use, σ is a positive parameter that indicates the elasticity of substitution between land and labor, γ is distribution of the shares of production factors, ∈ (0,1).
Production function (1) yields the expression for the marginal product of labor: 746 Therefore, neutral and land-saving technological changes increase the marginal product of labor.
However, labor-saving technological changes lead to two opposite effects on the marginal product of labor. First, an increase in A L means that each worker is more productive, as can be seen in the first term in the equation. Second, an increase in A L leads to a decrease in the amount of land per unit of labor in units of efficiency ( ⁄ ), which, in turn, leads to a decrease in the marginal product of labor. This effect is more obvious when land and labor force are weak substitutes as production factors.
Thus, the relative strengths of these two opposite effects depend on the value of the parameter σ.
In particular, ∂MPL a /∂A L < 0, when the substitution elasticity is less than the share of land as a production factor in the gross output. In this case, technological changes significantly reduce labor costs.
Consider an open economic system of a mountain agricultural region trading on the external market, where the relative internal and external prices for agricultural products are represented as where Г * = � � 1− is the equilibrium share of labor.
In turn, the equilibrium level of employment in industry, * , can be obtained from the equilibrium condition on the labor market, + = . Then, when * and * are known, the gross output of each industry is found using the production function (1).
Consider the impact of three types of technological changes, namely, Hicks-neutral, labor-saving and land-saving, on employment in both sectors of the regional economy in our model.
Labor-saving technological changes
The impact of labor-saving technological changes on employment in regional agriculture depends on the ratio of the substitution elasticity and the share of land as a factor of production in equilibrium If it is less than 1, land and labor in the production function can be considered strong complements. In this case, the following conditions are met: * < 0 An increase in A L triggers labor flaw from agriculture to industry. This can be explained by the fact that if the substitution elasticity between labor and land is less than the share of land as a production factor in the gross output, labor-saving technological changes decrease the marginal product of labor in agriculture. Since in equilibrium the marginal product of labor in agriculture is determined by world https: //doi.org/10.15405/epsbs.2021.11.99 Corresponding Author: Ivanov Zaur Zuberovich Selection and peer-review under 747 prices and labor productivity in industry, it does not change with increasing A L . Thus, to increase the marginal product of labor to its equilibrium level, employment in agriculture should decrease.
In the case when land and labor in the production function cannot be considered as strong complements, the following conditions are met: * > 0 In this case, an increase in A L causes, in our model, labor flow from industry to agriculture. This is due to the fact that if the elasticity of substitution exceeds the share of land as a production factor in the gross output, labor-saving technological changes increase the marginal product of labor in agriculture.
Land-saving technological changes
In the model, an increase in A T leads to labor flow from industry to agriculture due to an increase in the marginal product of labor in agriculture because of the introduction of land-saving technologies (2).
Hicks-neutral technological changes
An increase in A N also leads to labor flow from industry to agriculture. It should be noted that a Hicks-neutral increase in agricultural productivity also leads to an increase in the marginal product of labor (2). (Lagakos & Waugh, 2013;Min et al., 2017). However, the conclusions yielded by the model do not lose their force. In the case of soybeans, the advantage of genetically modified seeds over traditional seeds is that they are resistant to herbicides, which reduces the need for preparatory work. As a result, the technology requires less labor per unit of land to produce the same product. As for corn, the introduction of cultivation technology that allows two harvests per year increases the efficiency of land use. When analyzing real data, the impact of these two types of technological changes on the observed variables in the agricultural and industrial sectors should be quantified and reflection of the patterns predicted by the model should be varified.
Conclusion
The proposed model of the impact of technological changes in the agricultural sector on structural changes in the economy of a mountain agrarian region in the medium term can be used to analyze the real data of the consequences of agricultural extension. The model shows that a Hicks-neutral increase in agricultural productivity decreases the size of industry due to the labor force flow to agriculture, as in classic open economy models (Acemoglu & Guerrieri, 2008;Herrendorf et al., 2013). Similar results are obtained for land-saving technologies. In contrast, if land and labor force as production factors are strong complements, labor-saving technological changes in agriculture reduce the demand for labor force and cause the labor flow to industry. Thus, the model predicts that the impact of agricultural productivity on structural transformation in an open economy of an agrarian region depends on the factor characteristics of the introduced technology, namely, on whether the balance of production factors will shift towards labor saving. | 2,821 | 2021-11-29T00:00:00.000 | [
"Economics",
"Agricultural and Food Sciences"
] |
Roll-to-roll slot-die coating of 400 mm wide, flexible, transparent Ag nanowire films for flexible touch screen panels
We report fabrication of large area Ag nanowire (NW) film coated using a continuous roll-to-roll (RTR) slot die coater as a viable alternative to conventional ITO electrodes for cost-effective and large-area flexible touch screen panels (TSPs). By controlling the flow rate of shear-thinning Ag NW ink in the slot die, we fabricated Ag NW percolating network films with different sheet resistances (30–70 Ohm/square), optical transmittance values (89–90%), and haze (0.5–1%) percentages. Outer/inner bending, twisting, and rolling tests as well as dynamic fatigue tests demonstrated that the mechanical flexibility of the slot-die coated Ag NW films was superior to that of conventional ITO films. Using diamond-shape patterned Ag NW layer electrodes (50 Ohm/square, 90% optical transmittance), we fabricated 12-inch flexible film-film type and rigid glass-film-film type TSPs. Successful operation of flexible TSPs with Ag NW electrodes indicates that slot-die-coated large-area Ag NW films are promising low cost, high performance, and flexible transparent electrodes for cost-effective large-area flexible TSPs and can be substituted for ITO films, which have high sheet resistance and are brittle.
unwinding and rewinding system, the flexible PET substrate was continuously passed through the slot die coating head. In addition, the tension of the flexible PET substrate was controlled by a load cell in the rolling system. PET substrate with a width of 500 mm and thickness of 125 μm was passed over the heating chamber and UV treatment zone as shown in Figure S1 c and d. The rolling speed of the PET substrate could be exactly controlled by the motor speeds of the unwind and rewind roller. A TACMINA pump with the property of non-pulsation was installed into the RTR coating system as shown in Figure S1e. The Ag NW network density was controlled by pump frequency (Motor RPM). Figure S1. (a) Pictures of the R2R slot-die coating system equipped with an unwinder, rewinder, heating chamber, UV zone, slot die coating head, Ag ink and over-coating ink tank with pump. Picture of (b) slot-die head for Ag NW ink coating, (c) heating chamber to remove solvent in the slot-die coated films, and (d) UV irradiation chamber. (e) Ink supply system for injecting Ag NW ink into the slot die using TACMINA pump. Figure S1e schematically illustrates process used to coat the Ag NW layer using slot-die coating head with a TACAMINA pump. With increasing the motor rpm, the amount of Ag NW ink coated on the PET substrate was increased through the slot die coating head. The Ag NW layer was coated onto the PET substrate by using a slot die coating head, and then passed through the heating chamber at 120 ºC by means of unwinding and rewinding at a roller constant speed of 2 m/min ( Figure S1c). After coating the Ag NW layer, an over-coating layer was coated on the Ag NW layer using the slot-die coating head and passed through the heating chamber at 80 ºC, after which the film was exposed to a UV-mercury type lamp with an intensity of 1000 mJ under a nitrogen ambient by means of unwinding and rewinding rollers at a constant speed of 2 m/min.
Slot-die coating process:
In the slot-die apparatus, liquid solution is pumped to the inner part of the slot-die head and ejected through a narrow slot, which is a gap between upstream lip and downstream lip 1,2 .
Figure S2a
show schematics of the slot-die apparatus for coating of Ag NW ink and over coating layer. In general, the shim, which is injected into the slot-die plays an important role to control the thickness and density of Ag NWs. In our slot-die coating process, we employed a shim with thickness of 100 μm as shown in Figure 2Sb. The 500 mm wide shim with a thickness of 100 μm was installed between upstream and downstream lips as shown in Figure S2c. Finally, we controlled the pressure of Ag NW ink using the capsule filter, which is connected to the inner part of the slot die head, to optimize the uniformity of the Ag NW layer on PET substrate as shown in Figure S2d. This capsule filter also remove the bubble in the Ag NW ink.
Diamond-shaped patterning of OC/Ag NWs electrode films: OC-Ag NW films were annealed in box oven at 130 °C for 20 min to prevent film shrinkage as shown in Figure S3-a. Then, the LPR-coated OC-Ag NW films were annealed at 90°C for 2min to bake in box oven as shown in Figure S3-c. The LPR-coated OC-Ag NW films were then exposed to UV light at 60 mJ using a positive diamond mask, as shown in Figure S3 d. The UV-exposed OC-Ag NW films were patterned by a hand-develop dipping process using a developing solution (EN-DT238E : tetramethylammonium hydroxide 3%, surfactant 2%, deionized water 95%).
Diamond-patterned OC-Ag NW films were subsequently etched by a hand-etch dipping process using etching solution (EO-NS100: nitric acid & deionized water). The wet-etched OC-Ag NW films were stripped by a hand-strip dipping process using stripping solution (EN-S800Mo: glycol ethers 10%, sodium gluconate 10%, EDTA 10%, surfactant 5%, deionized water 65%). Finally, the stripped OC-Ag NWs films were cleaned by a spray-type rinse system using deionized water, as shown in Figure S3 | 1,236.2 | 2016-09-28T00:00:00.000 | [
"Materials Science"
] |
Molecular Characterization of Laboratory Mutants of Fusarium oxysporum f. sp. niveum Resistant to Prothioconazole, a Demethylation Inhibitor (DMI) Fungicide
Fusarium oxysporum f. sp. niveum (FON) is the causal agent of Fusarium wilt in watermelon, an international growth-limiting pathogen of watermelon cultivation. A single demethylation inhibitor (DMI) fungicide, prothioconazole, is registered to control this pathogen, so the risk of resistance arising in the field is high. To determine and predict the mechanism by which FON could develop resistance to prothioconazole, FON isolates were mutagenized using UV irradiation and subsequent fungicide exposure to create artificially resistant mutants. Isolates were then put into three groups based on the EC50 values: sensitive, intermediately resistant, and highly resistant. The mean EC50 values were 4.98 µg/mL for the sensitive, 31.77 µg/mL for the intermediately resistant, and 108.33 µg/mL for the highly resistant isolates. Isolates were then sequenced and analyzed for differences in both the coding and promoter regions. Two mutations were found that conferred amino acid changes in the target gene, CYP51A, in both intermediately and highly resistant mutants. An expression analysis for the gene CYP51A also showed a significant increase in the expression of the highly resistant mutants compared to the sensitive controls. In this study, we were able to identify two potential mechanisms of resistance to the DMI fungicide prothioconazole in FON isolates: gene overexpression and multiple point mutations. This research should expedite growers’ and researchers’ ability to detect and manage fungicide-resistant phytopathogens.
Introduction
Fusarium wilt of watermelon, caused by the ascomycete fungus Fusarium oxysporum f. sp. niveum (FON), is a leading factor limiting watermelon production worldwide [1][2][3][4][5]. Symptoms include single vine wilting, tip necrosis, dieback, and eventual plant death. This widespread pathogen is soil-borne and produces three different spore types: microconidia, macroconidia, and chlamydospores [3,6]. Symptoms are caused by the host defense response to develop tyloses which attempt to block the vascular spread of the pathogen. Developing tyloses then clog up the passage of water and nutrients within the plant, causing loss of turgor pressure and wilting [7,8]. While micro-and macroconidia cause inseason spread of FON and hyphal structures can survive overwinter, chlamydospores can survive in soils for up to 10 years and are resistant to current management measures [9][10][11]. In addition to resistant spore types, FON has evolved multiple races (0, 1, 2, 3), some of which are highly aggressive on all commercial watermelon cultivars [12,13].
Management strategies have been reduced since the phasing out of methyl bromide as a soil fumigant due to its negative effect on the ozone layer [14]. Other soil fumigants have been used (chloropicrin and metam sodium), but they are not as effective as methyl bromide, so new chemistries and strategies are needed [2,3,15]. Crop rotation and nematode management have shown some success, but due to the prolonged survival of chlamydospores, these strategies have proven insufficient to halt their spread [16,17]. Apart from fumigants, a single fungicide, prothioconazole (Proline 480 SC; Bayer CropScience, Research Triangle Park, NC), is labeled for control of FON on watermelons [7]. Prothioconazole is a demethylation inhibitor (DMI) fungicide and has been tested in several studies to determine the sensitivity of FON populations [7,18,19]. To date, no reports of resistance have been made; however, management continues to be problematic [7,19]. While other fungicides are being developed to control FON on watermelon, growers' options are limited, and reports of insensitivity do occur when talking with growers (personal communication) [19,20]. Previous studies on FON sensitivity to prothioconazole determined that 10 µg/mL inhibited growth of all isolates, though spore germination was not inhibited greatly [7,19].
DMI fungicides are under a medium risk of developing resistance; however, due to the single active ingredient registered for the pathogen, this likelihood is increased [21,22]. DMI fungicides work by inhibiting the biosynthesis of ergosterol, a crucial component of fungal plasma membranes which is required for growth and development [21]. Specifically, DMI fungicides bind to the cytochrome P450 lanosterol 14α-demethylase (CYP51) to inhibit ergosterol biosynthesis [23].
There are three known mechanisms of fungicide resistance for DMI fungicides, each of which has variants of the specific aberration that conveys the resistance [24]. The first mechanism is single nucleotide polymorphisms (SNPs), which alter the amino acid product and thus do not allow for proper binding of the fungicide to the gene product [25,26]. There are a number of these SNPs reported to confer resistance; some are common across multiple genera, others are specific to species or even individuals [27]. The second mechanism is overexpression of the CYP51 gene, often due to insertions or deletions within the upstream promoter region of CYP51 [28][29][30]. The third mechanism is increased effectivity of drug efflux transporters such as ATP binding cassette (ABC) transporter genes [31][32][33][34]. In many Fusarium species, three copies of CYP51 exist: CYP51A, CYP51B, and CYP51C, each with a different level of activity and the ability to "cover" for a separate copy [25,27,35]. As no mechanism for resistance has been determined for FON, the objective of this study was to artificially mutate a FON isolate to become resistant to prothioconazole, then determine the mechanism by which the resistance had arisen. Greenhouse assays were included to assess the real-world impacts of the mutagenesis and resulting fungicide resistance. This study will provide a plausible mechanism for researchers to detect when resistance occurs naturally.
FON Isolates
Isolates of FON were obtained from commercial watermelon fields in Georgia by taking samples from infected plants and culturing them on semi-selective peptone pentachloronitrobenzene agar plates [36]. To test initial in vitro fungicide sensitivity, isolates were grown on full-strength potato dextrose agar (PDA) plates and subcultured on PDA plates amended with 10 µg/mL prothioconazole (pure product, Chem Service, West Chester, PA) ( Figure S1). The value of 10 µg/mL was used to determine sensitivity since it completely inhibited growth of FON isolates from Georgia as reported previously [19]. The isolate B3-12 was chosen for mutagenesis because it was the most sensitive to the fungicide and allowed to compare the effects of resistance.
Generation of FON Mutants Resistant to Prothioconazole
Mycelial plugs of isolate B3-12 from a PDA plate were transferred to 1 /2-strength potato dextrose broth (PDB) and incubated at room temperature under continuous light with shaking at 150 rpm. After 10 days, the liquid medium was filtered through a sterilized cheesecloth and spore concentration was quantified using a hemocytometer and then concentrated to 10 5 spores/mL via centrifugation and decantation. A 100-microliter aliquot of the spore suspension was then spread on the fungicide-amended media and incubated for 5 h in the dark at 26 • C for spore germination. After 5 h, plates were taken to a sterile hood and exposed to UV light at a distance of 20 cm for 30 s before being incubated again for 7 days in the dark at 26 • C. The UV light was a germicidal far-UV producing a range of 254 nm. This was replicated in 10 separate plates, and three plates were subjected to the same treatment without UV exposure. After 7 days, UV-irradiated plates were inspected for growing colonies which were then transferred to PDA with no fungicide for another 7 days in the dark at 26 • C. These isolates were then plated on PDA with 10 µg/mL prothioconazole before being transferred to plates with increased fungicide concentrations (+5 µg/mL every subsequent week) until reaching 50 µg/mL, then repeated at 50 µg/mL for 3 weeks. Control isolates (not exposed to UV) were transferred to PDA with no fungicide each time mutants were transferred.
EC 50 Value Determination for Sensitive and Resistant Isolates
After 20 weeks, resistant and sensitive isolates were plated on various concentrations of fungicide-amended PDA to determine EC 50 values. Based on the growth results, isolates were separated into three groups to better categorize the EC 50 values: sensitive, intermediately resistant, and highly resistant. The fungicide concentrations increased by a factor of ten, starting with 0 µg/mL, then 0.1, 1.0, 10, and finally 100 µg/mL. An additional concentration of 50 µg/mL was made for visualization of the mycelial growth inhibition but was not used in calculating EC 50 values. After 14 days, five measurements per isolate were made from the center of the colony to the growing edge (radius), and the average length was calculated. This was conducted for nine resistant and four sensitive isolates in duplicate, and the values were again averaged for each concentration to obtain a mean value for each group. Using average EC 50 values, the resistance factor (RF) was additionally calculated. RF values were calculated according to Lin et al. (2020) (using sensitive isolate EC 50 mean value) and correlated to FON resistance levels, listed in Table 1 [37,38].
DNA and RNA Extraction
After determining significant differences in growth between sensitive and resistant isolates, isolates were grown on full-strength PDA plates for two weeks before 100 mg of mycelium was scraped from the plate and placed in a 1.5-milliliter safe-lock tube (Eppendorf Canada Ltd., Mississauga, ON, Canada). Four steel balls were added to each tube and homogenized using a FastPrep FP120 cell disruptor (Qbiogene, Carlsbad, CA, USA) for three rounds of speed 4.0 for 30 seconds. Samples were then extracted using DNeasy (DNA) and RNeasy (RNA) plant mini-kits (Qiagen, Valencia, CA, USA) according to the manufacturer's protocol. Total DNA and RNA were quantified, and purity was estimated by measuring OD 260 nm and OD 260/280 nm using a NanoDrop spectrophotometer (NANODROP LITE, Thermo Scientific, Waltham, MA, USA).
Primer Design
The primers used in this study are listed in Table S1 and contain a mix of previously published primers and new primers developed for this study specifically. The three primers from Zheng et al. [35,39,40]. All novel primer sets used in concert with previously published primers were developed and used the same whole genome sequences mapped to the Fusarium oxysporum f. sp. lycopersici 4287 (FOL) reference genome (BioProject PRJNA342688) on the Integrative Genomics Viewer (Broad Institute, Cambridge, MA, USA). Each copy of the CYP51 gene (A, B, and C) was identified from the FOL reference CYP51 gene (XP_018249826.1) and aligned to the FON WGS. Primers were developed on the Integrated DNA Technologies Primer Quest TM Tool. Downstream primers were designed to overlap upstream primers to obtain full coverage of the gene sequence. PCR primers ranged in size from 336 to 712 bp to obtain high-quality reads. The quantitative PCR (qPCR) primers used in the expression analysis were developed using the same method but for a product size of <200 bp.
Sequencing of Coding and Promoter Regions of CYP51
Extracted DNA was then amplified using a polymerase chain reaction (PCR) with the primer sets specific to each gene copy. PCR solutions totaled 50 µL, consisting of complete Taq polymerase (25 µL) (New England Biolabs, Ipswich, MA, USA), forward primer (20 µM), reverse primer (20 µM), and 2 µL of 150 ng/µL genomic DNA, and the rest was filled with PCR-grade H 2 O. Samples for the amplification of both coding and promoter regions were then added to a thermal cycler with the conditions listed in Table S1. PCR amplicons were confirmed as positive without contamination by running them on a 1% agarose gel and imaging using a UV geldoc (Analytik Jena, Upland, CA, USA). Samples were then purified using a commercial cleanup column (BioRad Laboratories, Hercules, CA, USA) and submitted to Retrogen (Retrogen, San Diego, CA, USA) for Sanger sequencing.
Exon and Promoter Sequence Analysis
Upon receipt of the sequencing results, fasta files were downloaded and aligned on Geneious V 11.1.5 (https://www.geneious.com) to one another. The sequences were separated into individual gene copies (CYP51A, -B, -C) and then aligned to the reference genome sequences of each copy, using both Bioproject PRJNA342688 (FOL) and Bioproject PRJNA656528 (FON) for alignment ( Figures S2 and S3). Introns were then removed based on the alignment with the FOL reference genome gene CYP51 (ID 28952942). Isolate sequences were then compared across each gene copy at the individual nucleotide level. Differences were identified when the sensitive (parental) isolate was compared with resistant isolates. Single nucleotide polymorphisms (SNPs) were determined to confer amino acid changes by translating the nucleotide sequence to the amino acid sequence on Geneious. Promoter sequences were submitted to this same process of alignment but no amino acid translation. Promoter sequences were sequenced until the first TATA box, 747 bp upstream from the start codon of the first exon.
Gene Expression Analysis
To further investigate the effects of mutagenesis, an expression analysis was performed to determine the relative expression levels of CYP51A in resistant and sensitive isolates of FON. For the expression analysis, total RNA extracted from fungal mycelium was converted into cDNA using the iScript TM cDNA Synthesis Kit (Bio-Rad Laboratories, Hercules, CA, USA) according to the manufacturer's instruction. A quantitative real-time PCR (qPCR) assay was performed on a BIORAD CFX connect real-time system (Bio-Rad Laboratories) in 10-microliter reactions consisting of 5 µL SsoAdvanced Universal SYBR ® Green Supermix (Bio-Rad Laboratories), 10 ng cDNA, 300 nM forward and reverse primers, and the rest was filled with dH 2 O. Newly developed primers specific to FON CYP51A were used to determine the expression of the candidate gene. Expression of FON from Zhang et al. (2006) was used as an endogenous control [40]. The recommended thermal cycling protocol for SsoAdvanced SYBR Green was used: activation/DNA denaturation at 95 • C for 30 s, denaturation at 95 • C for 10 s, and annealing/extension at 60 • C for 30 s for 40 cycles. A melt curve analysis was included: 65 to 95 • C in 0.5 • C increments, 5 s per step. Samples were run in Bio-Rad plastics and sealed with optical adhesive seals (Bio-Rad Laboratories). All assays included reverse-transcription-negative controls to check for genomic DNA contamination and no template controls to check for other contamination. Each reaction was run in technical triplicate. The 2 −∆∆Ct equation by Livak and Schmittgen (2001) was used to determine the relative gene expression [41]. Three isolates of each resistance level were run in triplicate and averaged for each group pertaining to resistance (highly resistant, intermediately resistant, and sensitive).
Statistical Analysis
Data are represented as mean ± SEM. Graphs were prepared and all data were analyzed using GraphPad Prism 8. Statistical significance was determined using the two-tailed Student's t-test and Pearson's R. p < 0.05 was considered statistically significant.
Molecular Modeling
Molecular models of CYP51A protein were created using SWISS-MODEL with the CYP51 gene copy from Aspergillus fumigatus as the model reference [42]. Alignments of FONCYP51A were performed after intron removal using UniProtKB-A0A0D2Y5I9 on Geneious software to confirm the coding region as similar (Gene ID: 28952942). Zoomed-in regions highlight the point mutation impact on molecular structure as determined from sequencing data and SNP determination.
Greenhouse Trial
To prepare FON isolates for inoculation, the three FON isolates-B3-12 (not mutated sensitive isolate) (S), highly resistant (HR), and intermediately resistant (IR)-were grown on full-strength PDA for two weeks at 25 • C. Five mycelial plugs (5 mm in diameter) from the edge of the growing isolate colony were transferred aseptically to a 250-milliliter flask with 200 mL of 1 /4-strength potato dextrose broth (PDB). The liquid cultures were incubated for 2 weeks on an orbital shaker (G10 Gyrotory Shaker, New Brunswick Scientific Company, NJ, USA) at 130 rpm at room temperature (23 • C). After two weeks, the colonized liquid PDB was filtered through a sterile cheesecloth to remove mycelia and retain spores. The concentration of the spore suspension was adjusted to 1 × 10 6 spores/mL by adding sterile distilled water (SDW).
In the greenhouse evaluation, watermelon seedlings (Sugar Baby) were grown in pots of 9 cm in diameter containing a mixture of sand:peat:vermiculite (4:1:1, v:v:v). Seedlings were inoculated after the first true leaf stage fully emerged by pipetting 5 mL of the conidial suspension near the base of each watermelon seedling. Half of the treatments received 20 mL of Proline at commercial concentrations 24 h before FON inoculations, and the rest of the plants received sterile water 24 h before FON inoculation. These were applied at the base of the crown where the soil meets the plant. Eighteen plants were grown per treatment (7 treatments) and sterile water was added for the negative control treatment. After inoculation, seedlings were maintained at 28 • C during the day and 20 • C in the evening with 70-80% relative humidity in the greenhouse. Disease severity was recorded after 4 weeks on a scale from 0 to 9, with a score of 0 for asymptomatic plants, 3
EC 50 Value and Resistance Factor Determination
In total, nine FON mutants were generated using the UV irradiation method described in the methods section that showed resistance to prothioconazole. Both resistant and sensitive parental isolates were tested to determine their EC 50 values using a mycelial growth inhibition assay (Figure 1). For sensitive isolates, the mean EC 50 value was 4.98 µg/mL. Resistant isolates were separated into two groups, one as intermediately resistant (IR) and the other as highly resistant (HR). Intermediately resistant isolates had a mean EC 50 value of 31.77 µg/mL, and the highly resistant isolates had a mean EC 50 value of 108.33 µg/mL ( Figure 2). Resistance factor (RF) values were calculated from the average EC 50 values and determined to be 21.72 for the highly resistant isolate mean and 6.37 for the intermediately resistant isolate mean (Table S2). Unpaired two-tailed Student's t-tests showed a significant difference between sensitive isolates and intermediately resistant (p = 0.001) and highly resistant (p = 0.042) isolates.
Coding Region and Promoter Sequence Analysis
CYP51A is 1574 nucleotides long in FON (a total of 524 amino acids) and contains one intron of 53 bp. Three primers (FCypA1, FCypA2, and FCypA3) successfully amplified this region (Figure 3). Several mutations were seen in the coding region sequence of the resistant isolates compared to the control sensitive isolates, all of which occurred in CYP51A and none in the other two copies, CYP51B and CYP51C. In CYP51A, three point mutations occurred in the highly resistant isolate sequence and only two in the intermediately resistant isolate (Figure 3). The first mutation, at nucleotide position 847, changed from a thymine to a cytosine in both resistant isolates. This mutation conferred the amino acid change Y283H, changing a tyrosine to a histidine at amino acid position 283 (Figures 3 and 4). The second mutation occurred in only the highly resistant isolate at nucleotide position 1101 and changed an adenine to a guanine. This mutation was silent, conferring no amino acid changes. The final mutation was observed at nucleotide position 1294 in both resistant isolates and changed a thymine to an adenine, conferring the amino acid change S432T (serine to threonine) (Figures 3 and 4). Three SNPs were seen in the highly resistant isolate sequence and two resulted in changes in the amino acid sequence, both of which were seen in the intermediately resistant isolate (Figures 3 and 4). The promoter region sequenced was 747 bp upstream from the initial start codon to reach the first TATA box. Promoter sequences did not differ in any nucleotide across any CYP51 gene copy, and resistant isolates were identical to the sensitive parental isolate.
Gene Expression Analysis
Evaluation of the relative expression (RE) of the CYP51A gene among the mutants revealed that it was increased two-fold among the intermediately resistant isolates and four-fold among highly resistant isolates from the sensitive isolates ( Figure 5A).
Differences in RE of CYP51A were statistically significant between both the sensitive and highly resistant isolates and the sensitive and intermediately resistant isolates. The sensitive isolate's mean RE was 8.39, whereas the highly and intermediately resistant isolates had REs of 35.95 and 18.16, respectively. These results are 4.28 times (highly resistant) and 2.16 times (intermediately resistant) higher than that of the sensitive isolate. Log 10 (RE) and Log 10 (EC 50 ) values were positively and significantly correlated, with an R 2 of 0.8652 (Y = 1.8x − 0.7785) ( Figure 5B).
Greenhouse Assay Results
Results from the greenhouse assay were averaged for each treatment across all replications (Table 2). The treatments were then compared using several ANOVA tests comparing the means of two separate groups. First, treatments 0-3 were used to test for a difference in disease severity without the fungicide present. Second, treatments 0 and 4-6 were used to test for a difference in disease severity with the fungicide present. Finally, all treatments were analyzed using a two-tailed t-test of significance to determine whether there was a difference between the treatments receiving the spore solution and those receiving the spore solution and the fungicide (Table 3). Table 3. T-test on each treatment with the same isolate across all replicates. The ANOVA tests revealed no significant difference between the means of the two different groups. The group without the fungicide added had a p-value of 0.076, and the groups with the fungicide had a p-value of 0.673. The fungicide therefore reduced the variance in disease severity. The disease severity between the same isolates was greater without the fungicide in all cases, although t-tests revealed the highly resistant isolate replicates to have the lowest p-value of 0.089, which was still not statistically significant (Table 3).
Discussion
While watermelon cultivars resistant to some races of the Fusarium wilt pathogen have been developed, new races have evolved to overcome the resistance, so growers have to use other disease control methods such as chemical control. For control of Fusarium oxysporum f. sp. niveum, only prothioconazole (Proline 480 SC; Bayer CropScience, Research Triangle Park, NC, USA) is currently registered [7]. Although it is expected that other fungicides will be registered, repeated use of a single fungicide incurs significant risk of developing resistance. It is currently unknown whether FON isolates resistant to DMI fungicides (to which prothioconazole belongs) exist, but this class additionally has a medium risk of developing resistance. To better understand and predict how resistance might arise, we developed prothioconazole-resistant FON mutants that could grow well on fungicide-amended media (Figure 1).
Two resistant groups were proposed based on the EC 50 values of prothioconazoleresistant mutants and subsequent resistant factors (RFs): intermediately resistant (IR) and highly resistant (HR) isolates. The mean EC 50 values of the HR and IR groups compared to that of the sensitive (S) group showed resistance factors of 21.72 and 6.37, respectively ( Figure 3 and Table S2). These groups were then analyzed with an unpaired two-tailed t-test for significance, revealing a significant difference between IR and sensitive (p = 0.001), HR and sensitive (p = 0.042), and HR and IR (p = 0.0413) (Figure 2).
Sequencing and analysis of cytochrome P450 lanosterol 14α-demethylase (CYP51) copies A, B, and C revealed that only CYP51A had mutations. While both the intermediately and highly resistant isolates had two mutations conferring amino acid changes, Y283H and S432T, the highly resistant isolate had an additional silent mutation at nucleotide position 1101 (Figure 3). Of the two mutations conferring amino acid changes, changing a tyrosine to a histidine was previously reported by Qian et al. (2017) as a mechanism for resistance of Fusarium graminearum to a different demethylation inhibitor (DMI), tebuconazole. Although the mutation was seen at amino acid position 137 and occurred in the CYP51B copy in that study, similar molecular binding alterations conferring resistance could be occurring in this study [25]. The second mutation, S432T, is not a well-characterized mutation when investigating DMI resistance, although central serine amino acids have been found to be important to molecular structure [43]. The final mutation, which was silent, occurred only in the most resistant isolate as determined by the growth assay and changed an adenine to a guanine at nucleotide position 1101. Silent mutations are not known to cause resistance to DMI fungicides; however, there is an increased presence of amino acid changes in resistant isolates of multiple phytopathogens, although often more than one [24,[44][45][46]. Due to the similarities between the results in this study and the results from other studies mentioned previously, we believe it reasonable to consider these mutations to at least contribute to the fungicide resistance seen in the growth assays. Neither gene copy CYP51B nor CYP51C had any nucleotide changes in either of the resistant isolates when compared to the sensitive parental isolate. No differences were seen across the sequenced 747 bp of the promoter regions in any of the three gene copies of CYP51 (Figures S2 and S3).
As CYP51A incurred mutations from the irradiation, further investigation by way of an expression analysis took place and revealed statistically significant differences between the highly resistant and sensitive isolates ( Figure 5A). The RE analysis revealed that the highly resistant isolate had an expression level 2.16 times that of the intermediately resistant isolate and 4.28 times that of the sensitive parental isolate (35.95 = HR, 18.16 = IR). No mechanism was determined for the differences in expression when analyzing the promoter sequences, but it should be noted that only 747 bp of the promoter was sequenced, and additional aberrations could have occurred upstream of the first TATA box. Increases in CYP51 gene expression have been correlated multiple times to resistance in DMI fungicides due to the increased target gene availability; thus, it is reasonable to attribute a significant level of resistance to the differences in relative expression [33,47,48].
FON greenhouse studies revealed differences in both sensitivity to the fungicide and virulence with and without the fungicide. Treatments receiving both the spore solution and the fungicide showed lower disease severity than those same treatments without the fungicide. Plants receiving the sensitive isolate spore solution were lower both with and without the fungicide, followed by the intermediately resistant isolate and, finally, the highly resistant isolate. Plants infected with sensitive isolates were almost brought down to the level of the negative control, illustrating the ability of the fungicide to reduce symptoms. Plants receiving spore solutions with the mutated isolates (HR and IR) showed a slightly higher impact (+0.27 disease severity compared with sensitive) from receiving the fungicide than the sensitive isolate but still showed higher disease severity with the resistant isolates. This implies a slightly reduced impact from the resistance detected in the morphological growth assays, which could be a result of the mutagenesis or a drawback for the pathogen to sacrifice pathogenicity for fungicide resistance.
While definitive conclusions about the source of DMI resistance in FON populations should not be drawn from these data, the detected mutations and differences in gene expression suggest two possible mechanisms. These changes were characterized to better predict possible mechanisms of resistance to the only class of fungicides registered for FON. Further analysis of ABC transporters and other efflux transporters or expression of other gene copies should additionally be considered as they were not studied here but could be contributing to resistance. In the case of DMI resistance in FON field isolates, we hope that this research can assist in detecting the mechanism rapidly, saving resources for researchers and growers.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/jof7090704/s1, Figure S1: Molecular models of Prothioconazole; Figure S2: Nucleotide sequence of sensitive and resistant isolates CYP51A coding region; Figure S3: Amino Acid sequence of sensitive and resistant isolates; Table S1: List of primers used in this study; Table S2: Resistant phenotype and the relative expression of the FON mutants.
Data Availability Statement:
The data presented in this study are available within the article or supplementary material. | 6,367.2 | 2021-08-28T00:00:00.000 | [
"Biology",
"Agricultural And Food Sciences"
] |
Long-range prediction and the stratosphere
. Over recent years there have been concomitant advances in the development of stratosphere-resolving numerical models, our understanding of stratosphere–troposphere interaction, and the extension of long-range forecasts to explicitly include the stratosphere. These advances are now allowing for new and improved capability in long-range prediction. We present an overview of this development and show how the inclusion of the stratosphere in forecast systems aids monthly, seasonal, and annual-to-decadal climate predictions and multi-decadal projections. We end with an outlook towards the future and identify areas of improvement that could further benefit these rapidly evolving predictions.
Introduction
Daily weather fluctuations are thought to have a deterministic predictability horizon of around 2 weeks due to the sensitivity of the evolution of the atmospheric state to small errors in initial conditions (Lorenz, 1969) -the so-called "butterfly effect". Recent estimates (Leung et al., 2020;Domeisen et al., 2018) as well as tests of the predictability of midlatitude daily weather using the latest global prediction models (Zhang et al., 2019;Son et al., 2020) produce similar estimates for this predictability limit. However, this does not preclude skilful forecasts of the statistics (most notably the average) of conditions at long range beyond this timescale (e.g. Shukla, 1981). This predictability owes its existence to slowly varying predictable components of the climate system in the ocean and in some cases the atmosphere, as well as externally forced changes such as volcanic or solar variability effects (e.g. Kushnir et al., 2019). Some of the more prominent examples of stratospheric variability such as sudden stratospheric warmings and their subsequent impact on the stratosphere and the troposphere (Baldwin et al., 2021) or the quasi-biennial oscillation and its associated teleconnections (Scaife et al., 2014a) have been shown to be predictable out to timescales well beyond the traditional 2-week predictability horizon from initial tropospheric conditions alone. Other examples involve stratospheric pathways for teleconnections originating in the troposphere or ocean (e.g. Schwartz and Garfinkel, 2017;Byrne et al., 2019) and are shown in Fig. 1. On longer timescales, boundary forcing, for example from composition changes such as ozone depletion and recovery, allows the stratosphere to provide relatively slowly varying conditions to guide the turbulent troposphere and hence provide long-range predictability (e.g. Thompson et al., 2011). The relative importance of stratospheric initial conditions to boundary conditions decreases with lead time as shown in the schematic in Fig. 1.
The extension of long-range prediction systems to explicitly include the representation of the stratosphere follows many years of development of stratosphere-resolving general circulation models (GCMs). By the late 20th century many leading centres for climate research had started to include the stratosphere in versions of their GCMs (Pawson et al., 2000;Gerber et al., 2012). Much of the early model development was motivated by the discovery of the ozone hole in the 1980s (Farman et al., 1985) and the need for simulations of ozone depletion and potential recovery of the ozone hole following the 1987 Montreal Protocol, which required atmospheric models that represented both the atmospheric dynamics and chemistry of stratospheric ozone depletion (Molina and Rowland, 1974;Crutzen, 1974). In most cases this was achieved by adding further quasi-horizontal layers to the domain of existing climate models to extend their representation of the atmosphere to the stratopause or beyond (e.g. Rind et al., 1988;Beagley et al., 1997;Swinbank et al., 1998;Sassi et al., 2002) while also incorporating key radiative (e.g. Fels et al., 1985), chemical (e.g. Steil et al., 1998), and dynamical (e.g. Scaife et al., 2000) processes.
The early development of so-called "high-top" climate models, which represent the whole depth of the stratosphere, in general preceded the discovery of the main body of evidence that the variability of the stratosphere is not only affected by but also interacts with the lower atmosphere and surface climate. Pioneering early studies suggested that the stratosphere might have direct effects on the troposphere and surface climate (e.g. Labitzke, 1965;Boville, 1984;Kodera et al., 1990Kodera et al., , 1995Haynes et al., 1991;Perlwitz and Graf, 1995). In subsequent years, as reliable observational records lengthened and large enough samples of stratospheric variability were amassed, it was unequivocally demonstrated that stratospheric variability precedes important tropospheric changes in the extratropics Dunkerton, 1999, 2001). There was debate about causality and whether the stratosphere really does affect the atmosphere below (e.g. Plumb and Semeniuk, 2003). However, experiments where the stratosphere is perturbed in numerical models show changes in surface climate and reproduce similar patterns of response at the surface to those found in real-world observations (e.g. Polvani and Kushner, 2002;Norton et al., 2003;Scaife et al., 2005;Joshi et al., 2006;Douville, 2009;Hitchcock and Haynes, 2016;White et al., 2020). These involve changes to planetary-scale waves and also baroclinic eddies in the troposphere that are consistent with changes in baroclinicity near the tropopause (Kushner and Song and Robinson, 2004;Wittman et al., 2004Wittman et al., , 2007Scaife et al., 2012;Domeisen et al., 2013;Hitchcock and Simpson, 2014;White et al., 2020). Importantly, as we discuss below, the same mechanisms also appear to be at work across a broad range of timescales (Kidston et al., 2015).
In recent years, motivated by the evidence of surface effects of stratospheric variability in the midlatitudes, the hightop model configurations used for stratospheric research were incorporated into leading prediction systems. Improved vertical resolution was already known to improve the atmospheric data assimilation of satellite instrument observations whose sensitivity was often heavily weighted towards stratospheric altitudes. This also provided initial stratospheric conditions for sets of retrospective forecasts, some of which were internationally coordinated (e.g. Butler et al., 2016;Tompkins et al., 2017). A growing number of operational systems are now producing regular ensembles of predictions at lead times of months or years with coupled oceanatmosphere models that extend to the stratopause or beyond, for example at Environment Canada , the Met Office in the UK (MacLachlan et al., 2015), the German Weather Service (DWD; Baehr et al., 2015), the Japan Figure 1. Schematic representation of the role of the stratosphere in long-range prediction showing the transition from initial-condition predictability in the atmosphere (blue) and the ocean (green) to boundary-condition predictability at longer timescales (orange). Individual mechanisms involving the stratosphere are labelled in black. The width of the ellipses in the timescale direction shows the approximate range over which each phenomenon provides predictability. The width of the ellipses in the variance direction shows their relative contributions to forecast variance.
Meteorological Agency , and the European Centre for Medium-Range Weather Forecasts (Johnson et al., 2019). In the following sections we document the emerging impacts and benefits of this new capability for surface climate predictions at monthly, seasonal, and annualto-decadal lead times starting with the shorter-range initialcondition cases and ending with the longer-range boundarycondition cases.
The stratosphere and monthly prediction
The best-established phenomenon that gives rise to the predictability of surface climate from the stratosphere is the tropospheric circulation changes that follow strong and weak conditions in the stratospheric polar vortex Dunkerton, 1999, 2001). For example, weak vortex conditions such as those found in a sudden stratospheric warming (SSW; Baldwin et al., 2021) are typically followed by a weakening and southward shift of the tropospheric midlatitude jet stream (see e.g. Kidston et al., 2015, and references therein) and thus the negative polarity of the North Atlantic Oscillation (NAO), Arctic Oscillation (AO), and Northern Annular Mode (NAM). These fluctuations also show a tendency to vacillate between strong westerly and weak (SSW) states on subseasonal timescales (Kuroda and Kodera, 2001;Hardiman et al., 2020a). The changes in the troposphere persist roughly as long as those in the lower stratosphere and last for around 2 months (Baldwin and Dunkerton, 2001;Baldwin et al., 2003;Hitchcock et al., 2013;Son et al., 2020;Domeisen, 2019). The impacts on surface climate also in-clude changes in the frequency of extremes of temperature and rainfall King et al., 2019;Cai et al., 2016;Domeisen et al., 2020b).
Although major SSW events, involving a complete reversal of the zonal flow in the mid stratosphere, are rare in the Southern Hemisphere (Wang et al., 2020;Jucker et al., 2021), variations of the Antarctic polar vortex are likewise followed by similar signatures in the underlying tropospheric flow, in this case via the Southern Annular Mode (SAM). Weakening of the vortex is typically followed by a negative shift in the SAM and associated changes in rainfall and near-surface temperature (Thompson et al., 2005;Lim et al., 2018Lim et al., , 2019aLim et al., , 2021Rao et al., 2020d). These changes in Southern Hemisphere circulation typically take longer to reach the surface than their Northern Hemisphere counterparts (Graverson and Christiansen, 2003), perhaps due to the stronger stratospheric polar vortex and weaker wave driving in the Southern Hemisphere, but they are nonetheless better predicted by improving stratospheric resolution of forecast models (Roff et al., 2011). The timescale of weeks for the predictability of sudden warmings is limited by the predictability of weather patterns in the troposphere which might trigger SSW events (e.g. Mukougawa et al., 2005;Taguchi, 2016;Garfinkel and Schwarz, 2017;Jucker and Reichler, 2018;Lee et al., 2020a). However, if we add this timescale to the timescale of a month or more for the persistence of lower-stratospheric anomalies and their surface effects (e.g. Baldwin et al., 2003;Butler et al., 2019a), we arrive at the conclusion that on these occasions at least, initial conditions in the atmosphere can provide Predictability of the atmosphere at monthly lead times is also known to originate in part from the Madden-Julian oscillation (MJO) in the troposphere and its teleconnection to the extratropics (e.g. Vitart, 2017). The circulation pattern associated with the MJO resembles a poleward-and eastwardpropagating Rossby wave with centres of action over the Pacific and extending into the Atlantic sector where it also maps strongly onto the North Atlantic Oscillation. The lead time of around 10 d for the impact of a change in the MJO to appear in the extratropical flow (e.g. Cassou, 2008;Lin et al., 2009) is also consistent with the timescale for the poleward propagation of Rossby waves (e.g. Scaife et al., 2017). It turns out that this tropospheric MJO teleconnection on monthly timescales also interacts with the stratosphere . The MJO teleconnection to the North Pacific affects the region most strongly associated with tropospheric precursors to SSW events, and consistent with this, SSWs in the observational record have tended to follow certain MJO phases. The subsequent weak vortex anomaly then propagates down to the troposphere (Garfinkel et al., 2012b), where it may strengthen and prolong any existing negative NAO signal that is directly linked to the MJO via the troposphere Garfinkel, 2017, 2020;Barnes et al., 2019).
In addition to the interaction of the MJO with the extratropical stratosphere, a further, completely different link between the stratosphere and the MJO has recently been uncovered which modulates MJO amplitude and persistence in the troposphere via the phase of the quasi-biennial oscillation (QBO) in the tropical lower stratosphere (Liu et al., 2014;Yoo and Son, 2016;Martin et al., 2021). In this case, easterly phases of the QBO appear to energize the MJO compared to westerly QBO phases, likely due to changes in temperature and hence static stability close to the tropopause (Hendon and Abhik, 2018;Martin et al., 2019) with a potential contribution of cloud-radiation feedbacks see Martin et al., 2021, for a review). This modulation of the MJO is in turn important for predictability, as it gives rise to higher monthly prediction skill of the MJO and its surface teleconnections during the easterly phase of the QBO (Marshall et al., 2017;Abhik and Hendon, 2019;Lim et al., 2019b).
The traditional view of stratosphere-troposphere interaction involves upward propagation of planetary-scale Rossby waves (Charney and Drazin, 1961), but this linear theory applies equally well to downward propagation. Harnik and Lindzen (2001) and Perlwitz and Harnik (2003) identified a possible source of downward-propagating planetary waves in the form of reflecting surfaces in the winter stratosphere. Examples of specific reflection events, showing upward and then downward propagation have since been observed (e.g. Kodera et al., 2008;Harnik, 2009;Kodera and Mukougawa, 2017;Mukougawa et al., 2017;Matthias and Kretschmer, 2020). These results suggest that the details of the stratospheric circulation such as regions of negative vertical wind shear could be important for the formation of reflecting conditions (Shaw and Perlwitz, 2013) and may yet provide a further mechanism by which the stratosphere can affect the troposphere Butler et al., 2019b).
Following studies demonstrating enhanced tropospheric predictability after SSW events in individual climate models (e.g. Kuroda, 2008;Mukougawa et al., 2009;Marshall and Scaife, 2010;Sigmond et al., 2013), subseasonalforecast systems which explicitly represent the stratosphere in the climate system were developed and implemented at operational-prediction centres worldwide. It is often difficult to demonstrate significant increases in overall skill (e.g. Richter et al., 2020a), but routinely produced ensembles of subseasonal predictions show that both stratospheric variability and its subsequent tropospheric signature are predictable at monthly lead times (Domeisen et al., 2020a, b). The strongest surface impacts occur if the polar vortex in the lower stratosphere is in a weakened state at the time of the SSW (Karpechko et al., 2017), and there appears to be a roughly linear relationship between the strength of these lower-stratospheric anomalies and the tropospheric response (e.g. Runde et al., 2016;White et al., 2020;see Baldwin et al., 2019, for a review). We should note however that there is no one-to-one correspondence between stratospheric variability and tropospheric events, and some prominent examples of sudden stratospheric warmings are followed by differing tropospheric anomalies (e.g. Charlton-Perez et al., 2018;Knight et al., 2020;Butler et al., 2020;Rao et al., 2020a). Nevertheless, the canonical response is seen in the majority (∼ 70 %) of cases, and periods of intense wintertime stratospheric variability are important windows of opportunity to provide skilful monthly forecasts (Mariotti et al., 2020;Tripathi et al., 2015a).
These forecast systems are now important tools for national meteorological and hydrological services to monitor impending stratospheric variability and associated surface impacts in real time. Recent extreme examples illustrate the importance of this activity. In February 2018 a major SSW occurred and was followed by a strong negative NAO-like pattern at the surface with easterly wind anomalies over Europe and multiple cold-air outbreaks over the following weeks, including extreme snowfall across northern Europe ( Fig. 2; Karpechko et al., 2018;Knight et al., 2020;Rao et al., 2020a) and an abrupt end to Iberian drought in southern Europe (Ayarzagueña et al., 2018b). Studies of monthly ensemble predictions of this event with operational stratosphere-resolving systems showed that the stratospheric event was predictable at least 2 weeks in advance (Fig. 2) and that the ensemble forecasts indicated an increased likelihood of cold surface conditions for several weeks after the event (Karpechko, 2018;Butler et al., 2020;Statnaia et al., 2020;Rao et al., 2020a). Again, as in the analysis of previous events, there was also a strong association with the MJO en-tering phase 7 with increased convection in the West Pacific (cf. Garfinkel and Schwartz, 2017) in the 2018 event. Finally, we should also note that cases of monthly forecasts where the stratosphere plays an important role are not restricted to winters with sudden stratospheric warmings; periods when the stratospheric polar vortex is above normal strength also provide opportunities for skilful monthly forecasts (Tripathi et al., 2015b;Scaife et al., 2016). In this case an opposite but symmetric surface response results, with a strong positive NAO. A very recent example occurred in February 2020, when, following an extremely strong polar vortex (Hardiman et al., 2020b;Lee et al., 2020b;Lawrence et al., 2020;Rao and Garfinkel, 2021), the tropospheric jet in the Atlantic sector strengthened, and the associated increased storminess and rainfall in this case resulted in UK monthly rainfall reaching a new record high (Davies et al., 2021).
The stratosphere and seasonal prediction
Prior to the advent of dynamical forecast systems which explicitly represent the stratosphere, seasonal forecasts using empirical relationships and statistical methods were proposed. These relied on the prior state of the polar vortex and other predictable factors such as the QBO that are known to have links to surface climate Charlton et al., 2003;Christiansen, 2005;Boer and Hamilton, 2008). In some cases they indicated additional predictability that was absent in existing operational forecast systems, providing further evidence of predictability involving the stratosphere and further motivating the extension of dynamical forecast systems to properly represent the stratosphere. Similar empirical forecast studies continue, and although they cannot provide evidence of predictability that is as strong as from GCM experiments based on fundamental physical principles, they do continue to be useful to indicate sources of predictability that need to be properly represented in comprehensive forecast systems (e.g. Folland et al., 2012;Wang et al., 2017;Hall et al., 2017;Byrne and Shepherd, 2018).
Following the introduction of dynamical seasonal-forecast systems with a good representation of the stratosphere, clear links between successful seasonal prediction of the North Atlantic Oscillation, the closely related Arctic Oscillation, and the state of the stratospheric polar vortex have been identified in forecast output (e.g. Scaife et al., 2014b;Stockdale et al., 2015;Jia et al., 2017). Similar signals are also seen in the Southern Hemisphere in relation to predictability of the Southern Annular Mode (Seviour et al., 2014;Byrne et al., 2019;Lim et al., 2021). Statistically significant increases in overall skill directly attributable to the inclusion of the stratosphere in prediction systems is sometimes difficult to demonstrate (e.g. Butler et al., 2016), especially given that other factors such as horizontal resolution and physical parametrizations are often simultaneously changed. Nevertheless, the body of evidence now weighs heavily in favour of predictability of the NAO and SAM from the stratospheric polar vortex and from analyses showing reduced surface prediction skill in the absence of stratospheric variability (e.g. Hardiman et al., 2011;Sigmond et al., 2013;Scaife et al., 2016).
A second clear example of seasonal predictability originating in the stratosphere is the quasi-biennial oscillation (QBO). The QBO has such inherently long timescales that it persists for several months in seasonal forecasts from initial atmospheric conditions alone, and its regularity means that it can be predicted from simple composites of earlier cycles. Nevertheless, a growing number of numerical models used in seasonal-forecast systems can now simulate and predict the oscillation within climate forecasts Richter et al., 2020b;Stockdale et al., 2021) with the aid of forcing from parametrized non-orographic gravity waves, and there is skill in predicting QBO phase changes at lead times of a few months (e.g. Pohlman et al., 2013;Scaife et al., 2014a). The surface impact of the QBO is also well established and has stood the test of time since it was first identified in the 1970s (Ebdon, 1975;Anstey and Shepherd, 2014;Gray et al., 2018). Yet again this response projects closely onto the North Atlantic Oscillation (and hence the Arctic Oscillation-Northern Annular Mode) and the Southern Annular Mode. The favoured mechanism involves refraction of vertically propagating Rossby waves in the lower stratosphere (Holton and Tan, 1980), although other pathways may also be involved (e.g. Inoue et al., 2011;Yamazaki et al., 2020;Rao et al., 2020bRao et al., , 2021. The observed magnitude of the QBO teleconnection is also large enough to provide seasonal predictability of surface climate (Boer and Hamilton, 2008), but its modelled amplitude at the surface appears to be underrepresented in current operational-prediction systems and models (Scaife et al., 2014b;Garfinkel et al., 2018;O'Reilly et al., 2019;Rao et al., 2020b;Anstey et al., 2021).
In addition to the stratosphere acting as a source of predictability, other mechanisms by which the stratosphere plays a role in seasonal predictions involve a pathway for globalscale teleconnections. These often originate in the tropics where the longer timescales of coupled ocean-atmosphere variability such as the El Niño-Southern Oscillation (ENSO; L'Heureux et al., 2020) provide a predictable source of lowfrequency variability. Effects on the extratropics can occur by tropical excitation of anomalous Rossby waves which propagate not only poleward but also upward into the stratosphere, as in the case of ENSO (Manzini et al., 2006;Domeisen et al., 2019), giving two pathways for extratropical influence (Butler et al., 2014;Kretschmer et al., 2021). These highly predictable tropical sources of climate variability alter the strength and position of the stratospheric polar vortex in the extratropics as well as the frequency of SSWs (Polvani et al., 2017), and these are followed by changes in the seasonal westerly jets in the troposphere and surface climate via the North Atlantic Oscillation ; . Sea level pressure is measured in hectopascals (hPa), and the polar cap index is the geopotential height anomaly (m) averaged over 65 • N to the North Pole. Cagnazzo and Manzini, 2009) or the Southern Annular Mode (Byrne et al., 2019). As might be expected, both the QBO and ENSO teleconnections are best represented in seasonalforecast systems which contain a well-resolved stratosphere . We note that new examples of the stratosphere acting as a conduit for seasonal teleconnections are still being uncovered (Hurwitz et al., 2012;Woo et al., 2015). For example, the Indian Ocean Dipole (IOD) received little attention in this context until the recent record event of late 2019, when it appears to have driven an extreme winter strengthening of the Northern Hemisphere stratospheric polar vortex. This strengthening took many weeks to decay, giving rise to extreme yet highly predictable conditions in the stratosphere and around the Atlantic sector in late boreal winter (Hardiman et al., 2020b;Lee et al., 2020b). The same event was also implicated in extreme changes in the polar vortex and the near SSW in the Southern Hemisphere (Rao et al., 2020d), an event that itself likely helped to drive the extreme summer conditions and wildfires over Australia that year (Lim et al., 2021).
Apparent links between Arctic sea ice and seasonal winter climate in the midlatitudes have also been suggested to be mediated by the stratosphere, with increased Rossby wave activity and a weakening of the stratospheric polar vortex in response to reduced sea ice, especially in the Barents-Kara Sea (Honda et al., 2009;Jaiser et al., 2013;Kim et al., 2014;King et al., 2016;Kretschmer et al., 2016). Some studies also reproduced surface signals in response to sea ice anomalies in seasonal forecasts of particular years that are in apparent agreement with observational estimates (e.g. Balmaseda et al., 2010;Orsolini et al., 2012). However, recent updates to observational records show a weakening of these apparent effects (Blackport and Screen, 2020) and significant non-stationarity (Kolstad and Screen, 2019). Subsequent modelling studies with larger samples of simulations have provided mixed results Dai and Song, 2020), and some have argued that the atmospheric response to sea ice is weak (Smith et al., 2022) and that while the sensitivity to Barents-Kara sea ice may be stronger, the stratospheric response in particular is highly variable (McKenna et al., 2018). While there may well be a longer-term effect via the stratosphere from sea ice decline (Sun et al., 2015;Screen and Blackport, 2019;Kretschmer et al., 2020), sensitivity of the response to the background state complicates the issue (Labe et al., 2019;Smith et al., 2017), as do possible confounding influences from the tropics (Warner et al., 2020), and to date there is no clear consensus for strong enough year-to-year effects to provide significant seasonal predictability.
Other proposed teleconnections acting via the stratosphere have been found in observations but remain to be confirmed with successful reproduction in physically based climate models. A prominent example involves a proposed link between Eurasian snow amounts and the stratosphere, followed by a return influence on the NAO and surface climate. In this case, enhanced snow cover or depth is associated with high pressure over northern Eurasia, an increase in the flux of Rossby wave activity into the stratosphere, and a subsequent weakening of the stratospheric polar vortex, followed by the expected negative shift in the NAO and AO (Cohen and Entekhabi, 1999;Cohen and Jones, 2011;Cohen et al., 2014;Furtado et al., 2015). However, the strength of this link in climate models and seasonal predictions is modest (Fletcher et al., 2009;Riddle et al., 2013;Tyrrell et al., 2018Tyrrell et al., , 2019 and does not agree with apparent links to the AO in observations (Kretschmer et al., 2016;Garfinkel et al., 2020) even when model mean state biases are corrected (Tyrrell et al., 2020). It has also been suggested that teleconnections to snow are non-stationary or non-causal, and there is continued debate about its long-term robustness (Peings et al., 2013;Henderson et al., 2018).
In summary, a number of mechanisms by which the stratosphere acts to provide seasonal predictability by acting directly either as a source of predictable variability (e.g. the QBO and SSWs) or as a conduit for teleconnections (e.g. ENSO, MJO, and IOD) have now been established in observations and have been confirmed using climate model simulations based on first principles. These operate in seasonalforecast systems, albeit with remaining errors such as the weakness of the QBO connection to surface climate. Meanwhile, other mechanisms involving the stratosphere (for example the response to snow cover variations) have been proposed based on apparent observed relationships, but until we have agreement between these observations and theory (model simulations), scientists remain sceptical of whether they represent actual sources of seasonal predictability, and these remain topics of current research.
The stratosphere and annual-to-decadal prediction
In recent years, initialized predictions on longer timescales were developed on the premise of multiyear memory in the ocean (e.g. Smith et al., 2007), and following the development pathway mapped out by seasonal forecasts in the past, these are now being run operationally to produce real time multimodel forecasts . Kushnir et al. (2019) mapped out this operational development of annual-to-decadal predictions and highlighted a number of sources of predictability, some of which involve the stratosphere ( Fig. 3) but not all of which are fully represented in climate prediction systems. Despite common misconceptions, not all annual-todecadal predictability stems from the ocean. Indeed, it has been clearly demonstrated that multiyear predictability of the QBO exists in current decadal predictions systems out to lead times of several years (Pohlman et al., 2013;Scaife et al., 2014a). This offers the prospect of a stratospheric contribution to multiyear predictability of the extratropics through the teleconnection with the Arctic Oscillation (Anstey and Shepherd 2014; Gray et al., 2018) and to tropical predictability through links to the MJO (e.g. Martin et al., 2021) and wider tropical climate variability (Haynes et al., 2021).
Although it is more important on multidecadal timescales (see below), external forcing of the stratosphere can also act as a source of decadal predictability. Forced climate signals from changes in greenhouse gases or stratospheric effects such as ozone depletion occur on a much longer timescale than the lead time of decadal forecasts, but their contribution to the skill of predictions is not trivial. For example, it is not immediately obvious whether the slow changes from multidecadal forced signals would simply be swamped by unpredictable internal variability on decadal timescales, rendering long-term external forcing changes useless for decadal predictions. However, this is not the case and long-term forcing is now known to be an important source of decadal prediction skill .
External forcing involving the stratosphere on shorter timescales is also important for annual-to-decadal predictions. The stratosphere has long been known to be influenced by volcanic eruptions, particularly in the case of tropical volcanic eruptions which are powerful enough to inject significant quantities of sulfur dioxide into the atmosphere. Here it reacts with water to form sulfuric acid and persists in aerosol form, leading to predictable multiyear global surface cooling, tropical stratospheric warming, and an intensification of the westerly stratospheric polar vortex in the extratropics (Robock and Mao, 1992). Although the sample of observed events is limited, modelling studies have reproduced an observed post-eruption intensification of the westerly winds in the stratosphere and some impacts on the surface Arctic Oscillation. However, generations of models have struggled to reproduce the 2-year persistence of volcanic effects seen in observations and the observed magnitude of the effect on the winter AO (e.g. Stenchikov et al., 2006;Marshall et al., 2009;Charlton-Perez et al., 2013;Bittner et al., 2016). In addition to these changes in the atmosphere, the intensification of stratospheric westerlies and hence Arctic Oscillation also combines with surface cooling of the ocean to generate predictable changes in the Atlantic meridional overturning circulation (Reichler et al., 2012) which can extend the volcanic influence to decadal timescales (Swingedouw et al., 2015). Finally, although the mechanism is debated, there is also evidence of a multiyear effect of tropical volcanic eruptions on ENSO, presumably requiring the persistent radiative forcing that arises through the long residence time of volcanic products, particularly sulfate aerosols, in the stratosphere. This reportedly increases the frequency of El Niño events by a factor of 2 in the years following volcanic eruptions (Adams et al., 2003), again suggesting an important source of multiannual predictability via the stratosphere.
A second source of multiannual predictability from external forcing originates from solar variability and in particular the 11-year solar activity cycle. Although a number of alternative mechanisms have been proposed (see Gray et al., 2010, for a review), the established mechanism for surface effects via the stratosphere is the change in the polar vortex that results from changes in upper-stratospheric heating over the course of each cycle between solar minimum and solar maximum. Interactions of atmospheric waves and mean flow amplify the initial radiatively driven change and drive its descent to the troposphere (Kodera and Kuroda, 2002;Marsh et al., 2007;Ineson et al., 2011;Givon et al., 2021), where changes in the extratropical jets result in a negative (positive) Arctic Oscillation pattern following solar minimum (maximum). There is also evidence that it contributes to interannual prediction skill , and an interesting aspect that has emerged in recent years is the integrat- ing effect of the ocean on solar-induced changes in the NAO via interannual persistence of ocean heat content anomalies which lead to a lag of around 3 years (π/2 cycles) in the peak response, as would be expected if the ocean is integrating the effects of a periodic solar forcing Gray et al., 2013;Andrews et al., 2015;Thiéblemont et al., 2015). However, debate continues as to whether the solar signal is indeed large enough to be detectable in observations in the presence of large internal tropospheric variability (Chiodo et al., 2019).
Perhaps the longest known timescale for predictability from initial conditions, which also involves the stratosphere, is the interaction of Atlantic multidecadal variability (AMV) with the stratospheric circulation. The Atlantic has followed pronounced multidecadal variations over the last century (Mann et al., 1995), and these variations are predictable out to years ahead (Hermanson et al., 2014). Some studies link these variations to the stratosphere and the NAO-AO (Reichler et al., 2012;Omrani et al., 2014). Indeed, the pronounced multidecadal increase in the surface NAO between the 1960s and 1990s is strongly coupled to changes in the strength of the stratospheric polar night jet (Scaife et al., 2005). Although current models simulate weak coupling between the AMV and the free atmosphere, this coupling appears to increase with model resolution (Lai et al., 2021), suggesting that the links between AMV, the stratosphere, and the NAO offer potential for improved decadal-scale prediction involving the stratosphere.
The currently recognized role of the stratosphere in decadal forecasts of surface climate again appears mainly via the impact on annular modes and, in the Northern Hemisphere, the North Atlantic Oscillation. Indeed, while current decadal prediction systems are now able to produce skilful predictions of variations in the NAO on multiyear lead times Athanassiadis et al., 2020), much work is still needed to attribute these variations to external forcing or internal variability and to understand the interaction between boundary and initial conditions, which blurs the simple distinction between the two. These new results are important because they indicate newfound decadal pre-dictability of events like the high NAO of the 1990s which yielded a run of mild but wet and stormy winters in northern Europe and the eastern USA. These winters are well known to have caused significant impact for example on the insurance sector (Leckebusch et al., 2007) and coincided with the longest observed absence of SSW events (Pawson and Naujokat, 1999;Domeisen, 2019). Given the indications of coupled stratosphere-troposphere variations on decadal timescales (Scaife et al., 2005;Omrani et al., 2014;Woo et al., 2015), understanding the role of the stratosphere in extratropical decadal predictions needs further investigation.
The stratosphere and multidecadal projection
The importance of the stratosphere for climate projections on multidecadal timescales was generally recognized before its role in predictions on shorter timescales. This is in part a legacy of the early development of stratosphere-troposphere models for ozone depletion studies described in the Introduction. On these longer timescales, coupling between stratospheric composition, thermal structure, and atmospheric circulation gives rise to improved climate projections.
Perhaps the best-known case for the stratosphere affecting multidecadal projections of surface climate is the influence of ozone depletion on the Southern Annular Mode (SAM; Thompson et al., 2005;McLandress et al., 2011;Polvani et al., 2011;Son et al., 2008, where decreasing ozone in the late 20th century led to a strengthened pole-to-Equator temperature gradient, a stronger stratospheric polar vortex, and a shift to strong positive SAM phases at the surface. In this case, studies again show the importance of stratospheric resolution to generate the full response, consistent with a genuine downward influence (Karpechko et al., 2008). The associated poleward shift in the tropospheric jet is connected to a delay in the spring breakdown of the stratospheric polar vortex (Byrne et al., 2017) and delivered significant and prolonged changes in rainfall across many regions of the Southern Hemisphere (Kang et al., 2011b;Purich and Son, 2012). Implementation of the Montreal Protocol in 1987 and subsequent reductions in the rate of ozone depletion mean that recovery of the ozone layer is now expected over the coming decades, and the reversible effects of this on the surface climate form an important element of current multidecadal projections Previdi and Polvani, 2014;Solomon et al., 2016;Banarjee et al., 2020;Zambri et al., 2021), where they are expected to play an important role alongside other changes in the southern stratosphere due to continuing increases in greenhouse gases (Son et al., 2009;Barnes et al., 2014), some of which occur via the stratospheric polar vortex in a similar way to those from ozone depletion and recovery (Ceppi and Shepherd, 2019).
The more limited effects of ozone depletion in the Northern Hemisphere meant that the role of the stratosphere in multidecadal projections took longer to become established. Some early studies found potential amplification of positive Arctic Oscillation trends under climate change when the stratosphere was included (Shindell et al., 2001). However, this was not borne out in later studies as simulations with other fully coupled ocean-troposphere-stratosphere models, suggesting weakening of the stratospheric polar vortex (e.g. Huebener et al., 2007). Subsequent studies with multiple models also indicated a southward shift in the polar night jet with weakening high-latitude winds and strengthening subtropical winds Manzini et al., 2014). These changes result from increased atmospheric wave driving of the winds which can overwhelm the cooling effect of greenhouse gases (Karpechko and Manzini, 2012) and can lead to important differences in future surface climate, for example in regional rainfall in areas typically affected by the stratosphere via the Arctic Oscillation and NAO . There is still significant uncertainty due to the diversity of modelled stratospheric responses to greenhouse gas increases Simpson et al., 2018;Zappa and Shepherd, 2017), and it has proved difficult to identify any clear change in the frequency of sudden stratospheric warmings (Ayarzagüena et al., 2018a(Ayarzagüena et al., , 2020. This is perhaps due to the competition between strengthening latitudinal temperature gradients near the tropopause and enhanced meridional overturning in the mid stratosphere. There is also strong inherent unpredictable variability from decade to decade in the frequency of SSW occurrence McLandress and Shepherd, 2009).
Other aspects of future climate change where the stratosphere plays a role have also been identified, for example, in the debate over the response to future levels of Arctic sea ice. In this case it seems that the response of the midlatitude circulation involves a negative shift in the Arctic Oscillation (Screen et al., 2018;Zappa et al., 2018;McKenna et al., 2018). This could again be amplified by interaction with the stratosphere, as some studies suggest that the stratospheric response is necessary for a large surface response (Kim et al., 2014), while others highlight that the stratospheric interaction is sensitive to the regional pattern of sea ice decline (McKenna et al., 2018), and still others show evidence of nonlinear stratospheric and stratosphere-mediated surface response (Manzini et al., 2018), coincident with the time when the Barents and Kara seas become ice-free . Furthermore, studies also indicate that the surface climate response to sea ice decline depends systematically on the phase of the stratospheric QBO (Labe et al., 2019).
Although it is much less certain than anthropogenic climate change, there have also been suggestions of a multidecadal decline of external solar irradiance which can impact multidecadal climate projections via the stratosphere. Previous multidecadal solar minima, so-called "grand minima", have occurred in sunspot records and have been connected to the Little Ice Age period around the end of the 17th century using proxy and other data (Owens et al., 2017). Given recent weak-amplitude 11-year solar cycles, there are now suggestions of a future solar "grand minimum", where the 11-year cycle described above could become muted or even absent for a prolonged period . In this case, the upper-stratospheric cooling in the tropics and summer hemisphere can change the meridional temperature gradient in a similar fashion to the 11-year cycle and leads to a negative shift in the AO and the NAO and hence affects regional climate . However, in this case it appears that while regional changes could be significant, they are generally much smaller than the surface warming due to anticipated levels of anthropogenic greenhouse gases (Anet et al., 2003;Ineson et al., 2015;Maycock et al., 2015).
Finally, we note that although low-frequency variability in teleconnections is observed (e.g. Garfinkel et al., 2019), it is often unclear whether this is a systematic variation or simply due to sampling variability of an underlying stationary process (Jain et al., 2019). Nevertheless, there is growing evidence for systematic climate change in some of the teleconnections by which the stratosphere enables surface predictability. Under future climate change it appears that some of the teleconnections discussed above may strengthen in amplitude. For example, the strengthening of ENSO-induced anomalies in the extratropical Atlantic-European sector increases in future climate projections (Müller and Roeckner, 2006;Fereday et al., 2020). Similarly, recent analyses suggest that the MJO teleconnection to the extratropics increases in amplitude under climate change (Samarasinghe et al., 2021). The same is also true of the extratropical effects of the stratospheric QBO, where in this case, the amplitude of the teleconnection in composite anomalies doubles under future climate change (Rao et al., 2020c) despite the QBO itself becoming weaker (Richter et al., 2020c).
Outlook
Long-range prediction has evolved quickly in recent years Butler et al., 2019b;Meehl et al., 2021), and this rapid development is due in part to the improved representation of stratospheric processes and stratospheric initial conditions in ensemble prediction systems. The long-range forecast community originally focused on predictability from initial ocean conditions, and this remains the primary source of long-range predictability, for example from ENSO, but some of these long-range prediction systems contained poor representations of the stratosphere. In the meantime, those working in parallel on climate modelling of the stratosphere were rarely involved in initialized long-range prediction, instead being driven primarily by the ozone depletion problem. Knowledge exchange across fields is important in science and precursors to a new paradigm often occur when a topic is investigated by researchers from outside the field (Kuhn, 1970). The crossover and collaboration between long-range prediction and stratospheric research communities is no exception, and the interaction between these communities has yielded rapid progress and new insights. Examples where initial atmospheric conditions can provide predictability beyond the usually assumed limit have been demonstrated, not only for the extratropics but also for the tropics, and we now know that in some situations, for example when sudden stratospheric warmings occur, the initial conditions in the stratosphere can have more impact than initial conditions in the ocean Polvani et al., 2017). This suggests that initial atmospheric conditions in the stratosphere are likely to be more important for long-range forecasts than previously assumed (Mukougawa et al., 2005Stockdale et al., 2015;Noguchi et al., 2016Noguchi et al., , 2020aChoi and Son, 2019;O'Reilly et al., 2019;Nie et al., 2019), not least because the overturning and breaking of Rossby waves in the stratosphere is followed by long-lived atmospheric anomalies due to synoptic-scale eddy feedbacks that prolong the effects in the troposphere (Kunz and Greatbatch, 2013;Kang et al., 2011a;White et al., 2020). More research on the initial conditions in the stratosphere might therefore help to reveal potential for further improvements in prediction skill.
A notable simplification to understanding the role of the stratosphere, at least in extratropical long-range predictions, is its apparently seamless mechanism across different timescales and different phenomena. Following the early ground-breaking studies showing surface impacts of stratospheric variability (e.g. Labitzke, 1965;Boville, 1984) and a multitude of studies on individual teleconnections between the stratosphere and surface climate, the projection of stratospheric variability onto the Arctic Oscillation-North Atlantic Oscillation-Northern Annular Mode circulation patterns across timescales and hemispheres is now well established (see the review by Kidston et al., 2015). This suggests that similar coupling processes occur between the stratosphere and troposphere from months to decades, and these processes lead to some of the most intense extratropical climate extremes, in winter in the Northern Hemisphere and in late spring-early summer in the Southern Hemisphere Fereday et al., 2012;Kautz et al., 2019;Domeisen and Butler, 2020). While studies point to changes in upper-tropospheric baroclinicity and tropospheric eddy feedbacks as crucial in these teleconnections, a full mechanistic understanding of how this occurs is still lacking.
Some, but not all, leading forecast systems now include a well-resolved stratosphere with a reasonable representation of relevant processes such as the body force from subgrid orographic and non-orographic gravity waves. However, many outstanding problems remain. Although their number is increasing, only a subset of current GCMs have the ability to simulate a realistic QBO beyond its decay from initial con-ditions, and it seems that all GCMs have problems with the fidelity of modelled QBO teleconnections, which are either too weak or absent altogether (Scaife et al., 2014a;Kim et al., 2020;Anstey et al., 2021). Even the relatively well-studied ENSO teleconnection via the stratosphere to the extratropics still has outstanding questions, such as whether the Northern Hemisphere stratosphere exhibits more SSW events during the La Niña phase (Butler and Polvani, 2011;Song and Son, 2018). This is not generally reproduced in modelling systems (Garfinkel et al., 2012a) but occurred in the recent La Niña winter of 2020/21. Similarly, while the increased monthly predictability from the MJO during the easterly phase of the QBO has been detected in monthly forecast experiments, the QBO-MJO connection does not persist in longer predictions and simulations with current models (Kim et al., 2020). Research and model development on stratosphere-troposphere interaction, including tropical effects (Noguchi et al., 2020b), will no doubt lead to further progress in resolving this issue (Haynes et al., 2021).
Errors in the modelled climatological mean climate are inevitably present to varying degrees in even the latest climate models. The common protocol of running a set of retrospective predictions to allow these mean biases to be estimated and hence subtracted from real-time predictions may well correct for much of this error. However, the degree to which biases have a nonlinear, state-dependent impact on the predictions is not fully understood. In some contexts, the nonlinear impacts of biases may be minimal (Karpechko et al., 2021), while others show sensitivity (Sigmond et al., 2008(Sigmond et al., , 2010 and increases of prediction skill occur under certain background conditions, for example during easterly QBO phases (Taguchi, 2018). Other processes generally omitted from long-range predictions include interactive variations of ozone and other trace gases. Although reports of impacts and benefits have varied, it is thought that surface signals on interannual timescales come mainly from dynamical rather than chemical changes (Seviour et al., 2014;Harari et al., 2019). Nevertheless, some studies suggest detectable effects from interannual variability of ozone, and it may be that ozone fluctuations could help to amplify surface signals Son et al., 2013;Smith and Polvani, 2014;Oehrlein et al., 2020;Hendon et al., 2020), providing a further area for future development. Given that the cost of full atmospheric chemistry schemes remains computationally expensive, it seems likely that simple parametrizations of ozone chemistry (e.g. Monge-Sanz et al., 2021) would be valuable in this context.
We end with a pointer to an issue that has now been found to affect long-range predictions from monthly to seasonal to decadal and multidecadal timescales, particularly in the extratropics. So-called "perfect model studies", which test the ability of models to predict their own ensemble members, are now known to underestimate the true predictability of climate in some regions, particularly around the Atlantic basin, and so models are better at predicting real-world vari-ations than they are at predicting themselves. This so-called "signal-to-noise paradox" is at first surprising, because perfect model prediction scores are often assumed to represent an upper (rather than lower) limit for prediction skill of the real world. The problem can be understood in terms of unrealistically weak ensemble mean predictions (e.g. Eade et al., 2014), but whether the stratosphere is involved directly in the cause of this problem remains to be seen (Saito et al., 2017;Stockdale et al., 2015), as it initially appears in the troposphere rather than the stratosphere in long-range forecasts (Domeisen et al., 2020a). Nevertheless, the unrealistically weak amplitude of ensemble mean predictions may well have the same root cause as the weakerthan-observed amplitude of modelled teleconnections to the stratosphere discussed in this review, including, for example, the underrepresentation of the surface impact of the QBO. Resolving this problem will therefore likely amplify these signals, provide greater levels of prediction skill, and further strengthen the role of the stratosphere in long-range predictions of surface climate. Data availability. No data sets were used in this article.
Author contributions. AAS wrote the draft manuscript. All other co-authors contributed relevant references and input to revisions and edits of the manuscript. SWS helped produce Fig. 1.
Competing interests.
The contact author has declared that neither they nor their co-authors have any competing interests. Review statement. This paper was edited by Martin Dameris and reviewed by two anonymous referees. | 10,775.8 | 2021-09-02T00:00:00.000 | [
"Environmental Science",
"Physics"
] |
Taming perturbative divergences in asymptotically safe gravity
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.
I. INTRODUCTION
Quantized general relativity is notoriously non-renormalizable at the perturbative level.
Such an understanding has been achieved after a number of celebrated calculations that, starting with 't Hooft and Veltman's seminal work [1], have disclosed the appearance of non-renormalizable divergences already at one-loop in the presence of matter [1,2], and at two-loop for pure gravity [3,4]. The situation is neither improved by the presence of a cosmological constant [5], nor by non-minimal couplings [6,7].
The general conclusion usually taken out of these results is that general relativity is not fundamental and can only be quantized as an effective field theory. In this approach (see [8,9]), the gravitational action is organized in an energy expansion in curvature invariants.
Once the scale for an experiment is identified, only the pertinent terms are then retained, allowing one to make predictions. A problem arises, however, once the energy is such that the curvature in Planck units reaches unity. At this point all curvature invariants are of the same order and an infinite number of couplings has to be fixed, so that the predictive power is lost.
A different conclusion can be attained if instead gravity turns out to be asymptotically safe (AS) [10] (see [11,12,13,14] for recent reviews). This scenario is based on Wilson's modern viewpoint on renormalization [15] and envisages the existence of a non-Gaussian fixed point (NGFP) of the renormalization group (RG) flow with a finite number of ultraviolet-attractive (relevant) directions. For RG trajectories attracted to the NGFP in the UV (spanning the UV critical surface of the fixed point), the fixed point ensures that the theory is free from uncontrollable UV-divergences, while the finite dimensionality of the surface ensures the predictivity of the theory at all energy scales. These criteria represent a non-perturbative analogue of the requirements underlying the usual perturbative renormalizability, which is recovered in the case of the fixed point being the Gaussian one.
In recent years, significant evidence for the asymptotic safety of gravity has been gathered by use of functional RG techniques [16,17,18,19,20,21,22,23,24,25,26,27,28,29], though support also comes from lattice simulations [30]. The former approach generally employs a Functional Renormalization Group Equation (FRGE) for the effective average action originally derived in [31] and first applied to gravity in [16]. Since an analysis based on the full equation is probably impossible, investigations usually rely on truncations of the theory space, whereby only a finite number of interaction-terms are retained. The reliability of the results found within such approximations can then be supported by considering their stability under a gradual extension of the truncation subspace. Indeed, all truncations studied so far, from the Einstein-Hilbert-, to the R 2 -and general f (R)-, up to the R 2 + C 2truncations, give rise to a coherent picture, pointing at the existence of a NGFP dominating the UV behavior of gravity.
A possible criticism on these results is that they are based on truncations which only contain interactions that are also unproblematic for the on-shell perturbative renormalizability. It is therefore a fundamental test for AS to include potentially dangerous terms in the truncation ansatz and study their effect on the fixed point structure of the theory. In pure gravity, the first non-trivial counterterm would be the Riemann-cube term of [3,4].
Including this term in the truncation ansatz is, however, technically very involved and beyond the current FRGE-techniques, even though the work presented in [28], which for the first time permitted us to go beyond the class of f (R)-truncations, constitutes significant progress in that direction.
A technically less demanding, but equally illuminating, alternative is to study truncations for matter-coupled gravity. In this case the non-renormalizable counterterms already appear at one-loop and the occurrence of divergences proportional to R 2 and C µνρσ C µνρσ , which do not vanish on-shell, signal the break down of perturbative renormalizability. To date, investigations of matter-coupled truncations, while also corroborating the asymptotic safety scenario, have remained restricted to the Einstein-Hilbert case [27,32,33,34,35]. In the present paper, we go beyond this restriction, and study the non-perturbative RG flow of gravitational higher-derivative terms in the presence of a free, massless, minimally coupled scalar field, cf. eqs. (12) and (25) below. Anticipating our main result, we find that the NGFP previously reported for the Einstein-Hilbert case persists under the extension of the truncation subspace. This constitutes further evidence for the non-perturbative renormalizability of the theory, and, in particular, confirms that the non-renormalizable perturbative counterterms play no special role in the asymptotic safety scenario.
The rest of the paper is organized as follows. In Section II we review the counterterms arising from the perturbative quantization of general relativity coupled to a free scalar field, while in Section III we introduce the renormalization group methods employed. In Section IV we revisit the Einstein-Hilbert truncation, for the pure gravity and matter-coupled cases, and finally in Section V we present the results for our full fourth-order truncation. We conclude with a discussion of our results in Section VI. All the details of the calculations are cointained in the three appendices: Appendix A contains the Hessians entering the FRGE for our truncation ansatz, Appendix B presents the heat-kernel expansion for Lichnerowicz Laplacians, and finally Appendix C details the evaluation of the traces.
II. PERTURBATIVE NON-RENORMALIZABILITY AND COUNTERTERMS
We start by reviewing the perturbative quantization of the Einstein-Hilbert action minimally coupled to a free scalar field. This provides the prototypical example of a gravitational theory which is perturbatively non-renormalizable at one-loop order [1], as may be seen by computing its one-loop counterterms ∆Γ div . In general, the one-loop effective action for a gauge theory takes the form where Φ A is the full set of fields (including auxiliary fields and ghosts), is the total action of the theory including the gauge-fixing and ghost terms S gf and S gh , and STr is a generalized functional trace carrying a minus sign for fermionic fields and a factor 2 for complex fields. Typically, this trace contains divergences which require regularization.
Our starting point is the action supplemented by the gauge-fixing term and the corresponding ghost action. Here, κ 2 = 16πG, G and Λ are the dimensionful Newton's and cosmological constant, respectively, g µν denotes the Euclidean space-time metric, and φ is a real scalar field. The gauge-fixing is carried out via the background field method, splitting the metric and scalar fluctuations into a background part,ḡ µν ,φ, and fluctuations around this background, h µν , f , according to g µν =ḡ µν + h µν and φ = φ + f . Adapting the results [6,7] obtained via the Schwinger-DeWitt technique, the oneloop divergences arising from (2) are readily found to be 1 where ǫ = (d−4) and E = C µνρσ C µνρσ −2R µν R µν + 2 3 R 2 is the integrand of the Gauss-Bonnet term in four dimensions, with C µνρσ being the Weyl tensor.
In order to get information on the renormalizability, the divergences (4) have to be considered on-shell. The equations of motion resulting from (2) are Substituting these, eq. (4) can suggestively be written as 2 As the R 2 and E-terms are not of the form of the terms contained in the initial action, they cannot be absorbed by a renormalization of the coupling constants, indicating that the action (2) is indeed perturbatively non-renormalizable. The non-renormalizable on-shell counterterms are thus of fourth order in the gravitational sector and can be rewritten as There is a common prejudice (see, for example [36]) that these interactions have a devastating effect also on the possible non-perturbative renormalizability (asymptotic safety) of the theory. Utilizing the new computational techniques developed in [28], we will now show that this is not the case. 1 There is a typo in the coefficient of the squared potential in [7], the correct formula is given in [6]. 2 Note that this expression agrees both with the one-loop counterterm found by 't Hooft and Veltman [1] for Λ = E = 0, and with the one of Christensen and Duff [5] once the contribution of the scalar field is subtracted.
III. THE FUNCTIONAL RENORMALIZATION GROUP EQUATION
A powerful tool in the study of the renormalization properties of a theory is the Functional where Φ denotes the physical fields andΦ their background value. The FRGE describes the dependence of the effective average action Γ k [Φ,Φ] on the coarse-graining (or renormalization group) scale k. Here, t = log(k/k 0 ) and R k (p 2 ) is a (matrix-valued) infrared cutoff which provides a k-dependent mass-term for fluctuations with momenta p 2 < k 2 . Apart from the requirement that it interpolates monotonically between R k (p 2 ) = 0 as p 2 /k 2 → ∞ and R k (p 2 ) ∝ k 2 as p 2 /k 2 → 0, this cutoff can be arbitrarily chosen. For technical simplicity, our subsequent analysis will be based on the optimized cutoff [37], whose scalar part takes The FRGE has two key features, owing mainly to the IR regulator structure. First, its solutions interpolate between the ordinary effective action Γ ≡ Γ k→0 and an initial action Γ Λ at the UV cutoff scale, which in the limit Λ → ∞ essentially reduces to the bare action (see [38] for more details). The effective average action is obtained by integrating out modes in the path integral from a UV cutoff scale Λ down to the scale k, as in a Wilsonian coarse graining procedure, with the modes below k being suppressed. Secondly, due to the derivative ∂ t R k (p 2 ) in the numerator, the contributions to the flow equation are localized on modes with momenta near k 2 , so that the trace remains finite and locally well-defined at all scales. In particular, while a theory might require a UV regulator at the level of its path integral, at the FRGE level this UV regularization is superfluous.
The main shortcoming of the FRGE, however, is that it cannot be solved exactly. In order to extract physics from it, one therefore has to resort to approximations. One possibility is, of course, perturbation theory. In the one-loop approximation, where Γ k under the STr is replaced by the k-independent bare action, one then recovers upon integration the usual non-renormalizable logarithmic divergences [27].
Going beyond perturbation theory, a standard approximation scheme is the truncation of the RG flow, whereby the flow of the full theory is projected onto a subspace spanned by a finite number of interaction monomials. Making an ansatz a finite subset of the interaction monomials O i and substituting this ansatz into the FRGE, this technique allows one to extract the β-functions for the dimensionful coupling constants u i . When analyzing the properties of the RG flow, it is then most convenient to switch to the dimensionless coupling constants g i = k −d i u i , with d i being the mass-dimension of u i , which results in autonomous β-functions ∂ t g i = β g i (g i ). Within Wilson's modern perspective on renormalization, the renormalizability of the theory is then determined by the fixed points . Around any such FP, the linearized RG flow is governed by the stability matrix Defining the stability coefficients θ i as minus the eigenvalues of B, the relevant (irrelevant) directions are associated to the eigenvectors corresponding to stability coefficients with a positive (negative) real part.
In general, it is useful to cast the effective average action into the form [16] In this decompositionΓ k [Φ] depends on the physical fields only, and S gf and S gh denote the classical gauge-fixing and ghost-terms respectively. Γ k encodes the deviations Φ −Φ, thus vanishing for Φ =Φ, and captures the quantum corrections to the gauge-fixing and ghost sector of the effective average action. For the remainder of this work, we will focus on truncations of the formΓ Here Γ grav k is the gravitational part of the effective average action, for which we will specify two different truncations in Sec. IV and Sec. V while is the (k-independent) action for a minimally coupled free scalar field. Furthermore, we set Γ k [Φ−Φ,Φ] = 0 in the sequel. 3 For S gf , we consider the following generalization of (3), which 3 Of course, it would also be desireable to obtain a better understanding of the influence of Γ k [Φ −Φ,Φ] on the RG flow. In this context, the adaptation of the background independent version of Γ k , discussed for Yang-Mills theories in [39], could provide a valuable tool.
allows for a straightforward application to gravitational actions including higher-derivative The gauge-fixing (3) is obtained as the limit ρ = 1, α = 1, β = 0. When analyzing the RG flows in sections IV and V, however, it will be more convenient to set Here, the arrow indicates that the limit is to be taken under the trace of the flow equation.
The key step in utilizing (8) for extracting β-functions is the evaluation of the operator trace appearing on its r.h.s. For the ansatz (11), this STr decomposes into a trace over the gravitational and the matter sector, respectively.
The contribution from the gravitational sector is obtained as follows [28] (for further details, see the Appendices). We first compute the second variation of Γ grav i.e., minimal second order differential operators ∆ sL = −D 2 + Q s , with spin-dependent matrix potentials Q s acting on transverse-traceless matrices (s = 2), transverse vectors (s = 1) and scalars (s = 0). This feature is crucial for the non-perturbative evaluation of the traces, as it makes them amenable to standard heat kernel techniques without having to resort to non-minimal (or k-dependent) differential operators. The final steps in this computation then follow the standard FRGE procedure (see e.g. [13]). First, the cutoff operators R s,k are constructed in such a way that the modified propagators are obtained by replacing ∆ sL → P s,k (∆ sL ) = ∆ sL + R s,k (∆ sL ). Then, the traces in the flow equation are evaluated using the "early-time expansion" of the heat kernel adapted to the Lichnerowicz Laplacians.
Written in terms of operator traces, the flow equation then takes the following generic where n s gives the number of matter fields and the subscripts "2T", "1T" and "0" indicate traces taken on the space of symmetric transverse-traceless matrices, transverse vectors and scalars, respectively. Applying the background-field method (settingφ = 0, for convenience), it is straightforward to find the matter contribution to the flow equation [32], Furthermore, owed to the special gauge choices (13) with (14) and (15), S 1T and S 0 are universal, in the sense that they are independent of the particular Γ grav k [g] adopted here, Following the computations outlined in Appendix C, the evaluation of the traces can be carried out using the early-time heat-kernel expansion for Lichnerowicz-operators. The resulting expressions are given in eqs. (C9) and (C10), respectively. We should also note that it is straightforward to consider the effect of a number n s of scalar fields by adding further copies of (C9) to the RG equations. In what follows, however, we will mostly focus on the cases n s = 0, 1, keeping the label n s only to highlight the matter contribution.
IV. FIXED POINTS OF THE EINSTEIN-HILBERT TRUNCATION
In this section, we approximate Γ grav k by the Einstein-Hilbert action with scale dependent coupling constants, This truncation has already been considered in the context of pure gravity in [17,18,19,20] and in the matter-coupled case in [27,32,34,35]. Here, we complement this analysis by implementing the gauge-fixing (13)(14) and organizing the operators inside the trace in terms of Lichnerowicz Laplacians on a generic Einstein space, lending further evidence to the robustness of these earlier works.
Using the results of Appendix A, the non-universal traces resulting from (20) are where the coupling constants u i are defined in (27). Adapting the computations outlined in [13,27] to the steps described in Section III, the β-functions of the dimensionless Newton's constant g k = G k k 2 and cosmological constant λ k = Λ k k −2 then read where, denotes the anomalous dimension of Newton's constant and where we have defined We can see that the inclusion of matter fields simply results in a shift by a constant in the equations above. In a sense, "small" values of n s could therefore be interpreted as a "perturbation" of the β-functions for pure gravity, which are recovered in the limit n s = 0.
Note that these β-functions are non-perturbative, in the sense that the anomalous dimension η EH N contains infinitely many powers of g.
Analyzing the fixed point structure of the β-functions (22), we first note that both the one-loop and the non-perturbative β-functions possess a GFP at λ * = 0, g * = 0 for all values of n s , corresponding to the free theory. Its stability coefficients are given by the canonical mass-dimensions of Λ and G, that is, θ 1 = 2 and θ 2 = −2. Owing to the negative mass dimension of Newton's constant, the only relevant direction is at G = 0, amounting to a trivial theory with just the cosmological term. As soon as we turn on Newton's constant, the flow is carried away from the GFP in the UV. Thus, our gravity-matter theory is not inside the UV critical surface of the GFP, verifying its perturbative non-renormalizability from the Wilsonian viewpoint. Note that this behavior is independent of n s .
Ref. [19] (RS), [18] (LR), [20] (L), and [27] (CPR), respectively. The cutoff classification as Type I, II or III follows [27], while with "opt", "sharp" and "exp" we refer to the shape function being of the optimized, sharp or exponential type respectively. The fixed point is robust under variation of the gauge-fixing parameter α, the shape function used in the IR regulator, and the implementation of the regularization.
Remarkably, the β-functions (22) also give rise to a NGFP at positive values λ * > 0, g * > 0. Its position and stability coefficients for n s = 0, 1 are given in Tables I and II (together with a comparison to earlier works). Note that this NGFP is UV-attractive for both the dimensionless Newton's constant and the cosmological constant. The gravity-matter theory considered here is within the UV critical surface of the NGFP. In other words, mattercoupled gravity in the Einstein-Hilbert truncation is asymptotically safe. Note also that making the transition from pure gravity to gravity coupled to a free scalar field has a rather small effect on the numerical values obtained for the NGFP.
V. FIXED POINTS OF THE HIGHER-DERIVATIVE-MATTER TRUNCATION
The key question raised by the results obtained within the Einstein-Hilbert truncation is whether the resulting fixed points survive in the full theory and, in particular, whether the NGFP will persist, with similar characteristics, once the perturbative counterterms (7) are from gravity coupled minimally to a real scalar field. The first line is obtained from the "universal gaugefixing", while the data of the second and third line has been obtained in [34,35] (PP), and is given for further comparative purposes. Again, the fixed point is robust under variation of the gauge-fixing parameter α, the shape function used in the IR regulator, and the implementation of the regularization.
included in the truncation subspace. While the former is a million-dollar question (recession notwithstanding), the latter can be answered positively.
To this effect, we enhance the truncation subspace (20) and consider the ansatz which is precisely of the form Einstein-Hilbert-action plus perturbative counterterms. In the spirit of the RG, the numerical coefficients in the latter have been replaced by the canonical (scale-dependent) coupling constants.
Following the derivation given in Appendix A, the gravitational contribution to (17) enters into S 2T and S hh only and is given by The coupling constants appearing in these expressions are related to (25) via and u ♭ = 2u 2 − 1 3 u 3 . Note that, because of the Einstein-space choice, we can distinguish only two of the three higher-derivative couplings. Lastly, note also that including S matter has a similar effect as in the Einstein-Hilbert case, leading to shifts in certain coefficients appearing in the β-functions.
The projection of the traces onto the truncation subspace spanned by (25) can again be carried out utilizing the early time expansion of the heat kernel adapted to the Lichnerowicz operators on a general Einstein background, as detailed in Appendix B. Following the computation outlined in Appendix C, and introducing the dimensionless couplings the β-functions following from our truncation are given by where the threshold functions Φ p n , ϕ are respectively defined in (C3) and (C7), with the former evaluated at zero argument. The expansion coefficients C i and C i arise from evaluating the traces S 2T and S hh , respectively, and are defined in eqs. (C14) and (C16). For notational reasons, the β-functions (29) are given implicit form. In particular, we stress that both the left and right-and-side contains derivatives ∂ t g i . The "standard" β-functions ∂ t g i = β i (g i ) can then be obtained by solving these equations for ∂ t g i , which can be straightforwardly done using algebraic manipulation software.
The resulting expressions may again be expanded for small g and, here, σ. In this respect, we first note that (29) contains contributions from arbitrary powers in g, σ, and hence that the β-functions capture some truly non-perturbative information. Secondly, we have verified that the leading contributions in this expansion reproduce the known universal parts of the one-loop β-functions in higher-derivative gravity, providing an important confirmation of the correctness of our derivation.
Remarkably, the fixed point structure originating from these higher-derivative β-functions is very similar to the Einstein-Hilbert case. First, we recover the two generalizations of the GFP, familiar from perturbation theory 4 , existing for 0 ≤ n s ≤ 155 and with stability properties given by the following eigensystem These GFPs correspond to the free theory, and their stability coefficients are given by the canonical mass dimension of the corresponding (dimensionful) couplings. In particular, the eigendirection associated with Newton's constant is still UV repulsive, while the directions associated with the new couplings σ k , ω k are marginal. Going beyond the linear approximation, the marginal directions are found to be UV-attractive, in accordance with the one-loop calculations [40].
Most importantly, the matter-coupled higher-derivative truncation also gives rise to the generalization of the NGFP. Its corresponding position and stability coefficients are given in Tables III and IV (under the entries "R 2 + C 2 +scalar"). For completeness, these tables also include the data on the NGFP for the pure gravity case ("R 2 + C 2 "), first reported in [28], and we note that its properties are again very similar to those in the gravity-matter case, thus giving rise to essentially the same picture.
One salient difference with the Einstein-Hilbert case is the fact that all stability coefficients are now real. This is in agreement with the one-loop results of [40], but it is surprising that, unlike in the Einstein-Hilbert case, the transition from the one-loop to the non-perturbative treatment does not give rise to complex eigenvalues. We can trace this result to the contribution of the C 2 terms coming out of the traces: indeed, restricting our computation to a spherically symmetric space we again find complex eigenvalues.
Crucially, increasing the dimension of the truncation subspace, with respect to the Einstein-Hilbert case, adds one UV-attractive and one UV-repulsive eigendirection to the stability matrix, so that the UV critical hypersurface in the truncation subspace is now three-dimensional. We then have a three-dimensional subspace of RG trajectories which are attracted to the NGFP in the UV and are therefore "asymptotically safe". Thus, nonperturbative renormalizability persists also in the presence of the one-loop perturbative counterterms in the truncation ansatz.
VI. DISCUSSION AND CONCLUSION
In this paper, we have analyzed the fixed point structure underlying the renormalization group (RG) flow of gravity minimally coupled to a free scalar field, within a truncation approximation. From the viewpoint of perturbative quantization, this setup provides a prototypical example of a quantum theory of gravity which is perturbatively non-renormalizable at the one-loop level [1]. Here, higher-derivative interactions arise as perturbative counterterms, signaling the presence of divergences which cannot be absorbed by the renormalization of the coupling constants. However, despite the breakdown of the perturbative quantization scheme, there is the possibility that this gravity-scalar theory constitutes a well-defined and predictive quantum theory within the realm of asymptotic safety [34,35]. With this in mind, we first considered the case of the Einstein-Hilbert truncation, before extending it to a higher-derivative truncation by including the interactions of the form of the one-loop counterterms.
As our main result, we show that all these truncations give rise to a non-Gaussian fixed point, which underlies the conjectured asymptotic safety of the theory, in addition to a Gaussian fixed point linked to the perturbative quantization. Both fixed points are robust under the extension of the truncation subspace by higher derivative terms. This result explicitly shows that, contrary to a common worry, the inclusion of perturbative counterterms in the truncation subspace of a gravity-matter theory has no qualitative effect on its fixed point structure. In particular, we find no indication that these interactions are fatal to non-perturbative renormalizability of the theory. the UV behavior of the gravity-matter theory is still dominated by its gravitational sector, so that it still behaves "essentially gravitational" at high energies. Following [34,41], it would be very interesting to determine which matter sectors lead to asymptotically safety gravity-matter theories (which we might dub the "asymptotic safety territories"), taking the higher-derivative terms (25) into account.
While our results on the interplay between the perturbative counterterms and asymptotic safety in the gravity-matter case are already trend-setting, it would nevertheless be desirable to carry out an analogous computation for pure gravity, where non-renormalizable divergences set in at two-loop level [3,4]. This is, however, still beyond the current technical scope of the functional renormalization group techniques employed in this paper.
Nevertheless, various arguments have been put forward [27,42] that the situation there will be similar to the one encountered here: perturbative counterterms are likely to have no special effect on the asymptotic safety of the theory.
Constructing the argument of the traces entering into the FRGE requires the second variation of these invariants. In this context, we first note that I 4 is a topological quantity, so that its variation with respect to the metric vanishes. To obtain the hessians of the other invariants, we split g µν =ḡ µν + h µν , whereḡ µν denotes a fixed background metric and h µν is an arbitrary fluctuation. The general expressions for these variations, valid for an arbitrary backgroundḡ µν , can be found in [45] (see also [46,47,48,49]). For our purposes, however, it suffices to consider these variations on backgroundsḡ µν =ḡ E µν , where the index E indicates that the background metric is a generic Einstein metric. These are metrics satisfyingR µν =R dḡ µν (but not necessarilyC µνρσ = 0) and, using the contracted Bianchi identity, this condition also implies thatD λR λσµν = 0. For these spaces, the Hessians of I n then simplify considerably. At the two-derivative level, we obtain while the variations of the four-derivative terms yield and respectively. Here, the bar denotes that the corresponding quantity is constructed from the background metric and h =ḡ µν h µν .
A remarkable feature of these variations is that they can naturally be written in terms of second order minimal operators of Lichnerowicz form (16). In particular, the four-derivative operators appearing in (A4) and (A3) factorize into squares of these (modified) Laplacians.
Performing the TT-decomposition (B10) for the metric, a brief computation establishes For the four-derivative terms, an analogous computation shows and As a welcome side-effect, we also observe that the introduction of the Lichnerowicz-Laplacians diagonalizes the transverse-traceless sector of the fluctuations. With respect to "off-diagonal" terms in the metric sector of Γ (2) k [ḡ], the R 2 + C 2 -truncation has thus the same level of complexity as previous computations which included (polynomials of) the Ricci-scalar only and referred to a maximally symmetric background.
In order to complete the construction of the operator traces, we now turn to the gaugefixing and ghost terms originating from (13). For the higher-derivative action of Section V, we thereby work with α = 0, ρ = 0. In this case, the TT-decomposition of S gf yields The ghost sector now contains, in addition to the usual (complex)C, C-ghost fields, a third ghost [45] due to the two-derivative contribution (det βD 2 ) 1/2 . Introducing the complexvalued Grassmann fieldsB µ , B µ and the real field b µ for the latter term, and TT-decomposing the ghost sector of the resulting action then leads to Note that, in the literature on higher-derivative gravity, the contribution of theB, B-ghost field is usually absorbed into the usualC, C-ghost, hence the need of only a third (real) ghost. We prefer here to introduce a fourth ghost to clearly separate the higher-derivative contribution from the usual second order term. The two choices are of course equivalent.
In the following, we impose a "mode by mode" cancellation between the gauge-degrees of freedom in the metric and the ghost sector [25], which results in a precise cancellation of all the "unphysical mode contributions" to (19).
Finally, there are additional contributions to the flow equation arising from the Jacobideterminants introduced via the TT-decomposition, Here, the primes indicate that the unphysical modes are left out from the determinants.
Furthermore, M (µ,ν) is a (d + 1) × (d + 1)-matrix differential operator whose first d columns act on the transverse spin one fields ξ µ and whose last column acts on the spin zero fields σ and which reads In order to account for these contributions, we follow earlier works [25,26,27] and introduce appropriate auxiliary fields so as to exponentiate these determinants via the Faddeev-Popov trick. The resulting "auxiliary action" then becomes Here the gravitational sector contains the transverse ghostc T µ , c Tµ , a "longitudinal" Grassmann scalarc, c, a transverse vector ζ T µ and a real scalar ω, while the ghost determinants are captured by the contribution of the complex scalar fields s,s, t,t, the complex Grassmann fieldsχ, χ, and the real scalar field φ.
We now have all the ingredients for constructing all the Hessians Γ (26) and (19) it is thereby useful to note that the σ-h-crossterm vanishes in the limit β → ∞. Thus, the combined contribution from σ and h splits into the sum of the hh-trace (26) and the contribution of the σσ-part. The latter can be combined with the contribution of all the other scalar fields to give rise to the universal scalar trace Lastly, we note that the derivation of the flow equation for the Einstein-Hilbert truncation proceeds in an entirely analogous manner. In this case, the gravitational sector arises from the contributions of (A5) with the TT-decomposed gauge-fixing term (13) in the limit α → ∞, β = 0 and ρ = 0, with a similar vanishing of the σ-h-crossterm and decoupling of the h and σ traces. The ghost sector now contains only the C-ghosts, and the auxiliary sector consequently does not contain the φ, χ and t fields. Combining the σσ with all the other scalar field traces and the ξξ with all the other transverse vector traces then results in the universal traces S 0 and S 1T , respectively, which are again given by (19). The remaining S 2T and S hh traces can then be straightforwardly constructed from Table V by setting the higher-derivative couplings to zero. This concludes our derivation of the gravitational sector of the flow equation (17).
LAPLACIANS
For evaluating the operator traces appearing in Section V, we require the heat-kernel expansion for the Lichnerowicz operators (16), evaluated at a generic Einstein manifold, up to fourth order in the derivative expansion. In this appendix we derive the corresponding coefficients starting from the early time heat-kernel expansion of a generic two-derivative differential operator [43,44] (see also [27] for a nice exposition in the context of the FRG).
Heat-kernel coefficients for unconstrained fields
In general, the early time heat-kernel expansion of a generic second order differential operator ∆ = −D 2 + Q takes the form with the heat-kernel coefficients a 2k given by [43] a 0 = 1 , a 2 = P , Here, D 2 is the covariant Laplacian with respect to the (background) metric, Q is a matrixvalued potential, P = 1 6 R1 + Q, R µν = 2D [µ D ν] is the commutator of the covariant derivatives, and tr denotes a trace with respect to the spin-indices of the fields on which ∆ acts.
For the purpose of this paper, we have to evaluate tr s a 2k for scalars (s = 0), vectors (s = 1), and symmetric tensors (s = 2). In the latter two cases, the tr s are defined as respectively. The matrices R µν R µν are trivial for the scalar case, whereas for vectors and tensors they respectively read (B4) The differential operators appearing in the traces (26) and (19) are the Lichnerowicz operators (16), i.e., second order differential operators with matrix-potentials Their heat-kernel coefficients on a generic four-dimensional Einstein manifold without boundary can be obtained by substituting these potentials into the expressions for the generic heat-kernel expansion. Evaluating the spin-traces, we obtain tr 0 a 0 = 1 , tr 0 a 2 = 1 6 R , tr 0 a 4 = 1 180 R µναβ R µναβ + 1 80 R 2 , tr 1 a 0 = 4 , tr 1 a 2 = 5 3 R , tr 1 a 4 = − 11 180 R µναβ R µναβ + 41 120 R 2 , tr 2 a 0 = 10 , tr 2 a 2 = 2 3 R , tr 2 a 4 = 19 18 R µναβ R µναβ − 1 24 R 2 .
(B6)
This result completes the heat-kernel expansion for unconstrained fields.
Heat-kernel coefficients for fields with differential constraints
In order to apply the early-time heat-kernel expansion to the operator traces (26), and (19) the heat-kernel coefficients for the unconstrained fields given in the last subsection must be converted into the expansion coefficients for the transverse vectors (1T) and transversetraceless symmetric matrices (2T) entering into the TT-decomposition.
In the decomposition of a vector field into its transverse and longitudinal parts, the spectra of D µ Φ and Φ are related by where the components appearing on the RHS of this decomposition are subject to the In this case, one can use to relate the spectrum of ∆ 2L to the ones of the vector and scalar fields. Furthermore, (B10) indicates that the constant mode in σ, scalars subject to D µ D ν + 1 4 g µν ∆ 0L σ = 0, and transverse vectors satisfying D (µ ξ ν) = 0 do not contribute to h µν , so that the corresponding modes have to be removed from the decomposed spectrum. By contracting the last two equations with D ν , one can show that these are eigenmodes of ∆ 0L and ∆ 1L with eigenvalues Λ 0L = 0, Λ 0L = R 3 , and Λ 1L = 0, respectively. 5 The multiplicity of the latter two is given by the number of Killing vectors n KV and conformal Killing vectors n CKV of the background.
Taking into account (B9), the operator trace for transverse-traceless tensors field can then be expressed in terms of traces over unconstrained fields Tr 2T e it∆ 2L = Tr 2 e it∆ 2L − Tr 1 e it∆ 1L − Tr 0 e it(∆ 0L −R/2) + n KV + n CKV e −itR/6 . (B13) In the following, we will assume that our background is generic, in the sense that its metric does not admit Killing or conformal Killing vectors.
From eqs. (B9) and (B13) it is then straightforward to compute the heat-kernel coefficients for Lichnerowicz Laplacians acting on transverse vectors and transverse traceless symmetric matrices. For a generic Einstein background, these read tr 0 a 0 = 1 , tr 0 a 2 = 1 6 R , These coefficients are the key ingredient for evaluating the operator traces (26) and (19) and constitute the main result of this appendix.
APPENDIX C: OPERATOR TRACES AND β-FUNCTIONS
In this appendix, we evaluate the operator traces appearing on the r.h.s. of eq. (17). We start with reviewing some general properties and definitions before computing the traces entering into our truncations explicitly.
General trace technology
The key observation for evaluating the traces entering (17) is that they contain only minimal second order differential operators, which commute with all other elements (like the curvature scalars) inside the trace. Their projection onto the truncation subspace can then be found using the heat-kernel coefficients for constrained fields given in (B14). Here, the key formula is where W (z) is a smooth function whose argument has been replaced by the Lichnerowicz operators and where the dots indicate higher-derivative terms at order six and higher, which are outside our truncation subspace. The functionals Q n [W ], n ≥ 0 are defined as Here, β(−1, n, l) denotes the incomplete beta function. For fixed values n, l, these become constants. This property leads to considerable simplifications in the analysis of the corresponding β-functions.
Evaluation of the traces
The evaluation of the operator traces proceeds by expanding the arguments in a Taylor series in R around R = 0, keeping terms up to R 2 only. The operator traces appearing as "expansion coefficients" can then be evaluated with the heat-kernel techniques introduced in the last subsection, c.f. eq. (C1). In particular, the functionals Q n [W ] arising in these cases are of the form (C5) or (C6), so that expressing them in terms of the generalized threshold functions is rather straightforward. We will now give the results for this evaluation for the various traces appearing in the main part of the paper, projecting the resulting RG flow onto the subspaces spanned by our truncations.
The functions Q n [W ] featuring in the universal traces S 0 and S 1T and the matter trace (18) are a special case of (C5) with c k = 0 and g k a k-independent constant, which we can set to one. Following the strategy outlined above, the evaluation of the matter trace (18) results in while the expansion of the universal traces (19) results in S 0 = − 1 (4π) 2 d 4 x √ g k 4 Φ 1 2 + 1 6 (Φ 1 1 + 2Φ 2 2 )k 2 R + ( ϕ 160 + 1 18 Φ 2 1 + 1 9 Φ 3 2 )R 2 + ϕ 360 R µνρσ R µνρσ , Here, all the Φ p n are evaluated at zero argument, and for the optimized cutoff they are trivially obtained from (C7).
Substituting these expressions into the generic form of the flow equation (17) and comparing the coefficients on the left and the right-hand-side then gives rise to the β-functions (22) for the Einstein-Hilbert case and (29) for the C 2 + R 2 -truncation, respectively. | 9,403.8 | 2009-02-26T00:00:00.000 | [
"Physics"
] |
Competitiveness and Public Debts in Times of Crisis
It is observed that countries, possibly more than ever, try to remain or become (more) competitive. This has been felt especially during the recent economic crisis, when countries facing a high debt or deficit attempted to find solutions to overcome it. In most cases the first measures attempted to confront debt or deficit, whatever the problem was. Competitiveness and growth have been discussed but always came second. Sometimes, they were not even considered early enough, although they are of equal or even higher importance. We believe that a country should remain competitive at all times, especially at times of crisis, as it can help it contain its debt (public and private). We even trust that countries that maintain their competitiveness are more capable in weathering adverse economic environments. The purpose of this article is to prove, using an econometric model, the existence of a relationship between the external competitiveness of an economy and its public and private sector deficits, as measured by the relevant debt levels. We indeed find evidence that public and private debt is definitely linked to the country competitiveness as measured by GDP growth, GDP per capita, ease of doing business, tax rate, pensions and unemployment. This can be of use to institutions and policy makers when they want to decide how they will secure that their country is and remains competitive, especially in times of crisis.
Introduction
Competitiveness affects all sectors of economy, products and services produced by the private sector, products and services produced by the public sector, mar- ketable goods and services, non-market goods and services, financial services, businesses operating in the real economy-households, and the state.All the above factors and sectors are directly linked to public debt, something that might have been felt in countries especially in Europe during the economic crisis of the last decade, when the twin debt and competitiveness deficits made their presence strongly felt.
Using a combination of the basic definitions that exist in international bibliography, competitiveness refers to the whole economic life of a country in an internationalized environment and describes the country's ability to achieve continuous improvements in the living standards and employment opportunities of its citizens.At the same time, the economic crisis is still the point of interest, especially for the countries of the European South.Today the Eurozone faces a crisis of both public debt and public deficits, particularly for the countries of the South, with significant consequences both to the development process as well as to the competitiveness of these countries.
In this paper we try to analyze the relationship between the deterioration of macroeconomic data and the debt crisis that followed the global financial crisis and has led the institutions and member states of the European Union (i.e., Austria, Italy, Belgium, Latvia, Bulgaria, Lithuania, Croatia, Luxembourg, Cyprus, Malta, Czech Republic, Netherlands, Denmark, Poland, Estonia, Portugal, Finland, Romania, France, Slovakia, Germany, Slovenia, Greece, Spain, Hungary, Sweden, Ireland, United Kingdom) to adopt policies designed to address these imbalances, both in fiscal and monetary terms, in direct correlation with the competitiveness of these countries.Our data sources are the OECD, Eurostat, and AMECO.We use an econometric approach to identify the direct relationship between public or private debt and the factors that affect competitiveness.
It seems that this relationship has been researched in the past; however each author addresses it from a different perspective or with a more focused approach in terms of variables, period of investigation or countries of interest.In our paper 1) we consider a relatively long period of time, incorporating the period before the crisis, during the crisis and after the crisis; 2) we expand our research to all the countries of the European Union (19) for which we could find all relevant data-most of them being also in the Eurozone (13); and 3) we test the explanatory capacity of the biggest set of macroeconomic country-specific variables to the public and private debt.Here lies the contribution of our research to the available empirical knowledge in the area, as we manage to find a relationship between the debt (public and private) and competitiveness (as measured by GDP growth, GDP per capita, ease of doing business, tax rate, pensions and unemployment), with the afore mentioned novelties introduced.
The paper is structured as follows: Section 2 discusses the existing literature, Section 3 describes the problem under investigation, Section 4 presents the data, the variables and the methodology, Section 5 shows the regressions run as well as the relevant tables, Section 6 analyzes the results and their implications and
Literature Review
The impact of competitiveness on economic growth and public debt has been the subject of several scientific papers and studies, especially in the last decade.
Afonso and Jalles [1] tried to link growth, productivity, and government debt using a panel of 155 developed and developing countries (period 1970-2008).
They used growth equations and growth-accounting techniques, also focusing on a number of econometric issues that can have an important bearing on the results, notably, simultaneity, endogeneity, the relevance of nonlinearities, and threshold effects.The results confirm the negative effect of the government debt ratio.In the case of OECD countries, they also concluded that the longer the maturity of the debt, the higher the economic growth.Moreover, the financial crisis is detrimental to growth.Growth is promoted by fiscal consolidation, and higher debt ratios are beneficial to total factor productivity (TFP) growth.The growth impact of a 10% increase in the debt ratio is −0.2% (0.1%) for countries with debt ratios above (below) 90% (30%) and an endogenous debt ratio threshold of 59% can be derived.Their research also showed that the budget balance is positively correlated to the TFP growth, capital stock growth, and private investment.
In a similar research, Panizza and Presbitero [2] used an instrumental variable approach on a sample of OECD countries, in order to examine whether public debt has a causal effect on economic growth.The results are consistent with the existing literature that points to a negative correlation between debt and growth.
However, if one corrects for endogeneity, the link between debt and growth no longer exists.The tests show that the results are not affected by weak instrument problems, and are robust to relaxing the exclusion restriction.Their finding that there is no evidence that public debt has a causal effect on economic growth is important in light of the fact that the negative correlation between debt and growth is sometimes used to justify policies that assume that debt has a negative causal effect on economic growth.They conclude that 1) there are many papers that show that public debt is negatively correlated with economic growth in advanced economies; 2) there is no paper that makes a convincing case for a causal link going from public debt to economic growth in advanced economies; and 3) such a causal link may not exist, and the case that debt has a causal effect on growth in advanced economies still needs to be made.
At the same time, Greiner [3] has analyzed the basic AK endogenous growth model with elastic labor supply and public debt.He has shown that higher debt ratios lead to a crowding-out of private investment and, thus, to lower long-run growth when the government reduces public spending to fulfill its inter-temporal budget constraint.This holds for non-distortionary and non-productive public spending so that there are no allocative effects of government spending.The reason for that outcome is that higher public debt leads to a lower shadow price of private capital and to less labor supply, causing households to reduce their savings and investment, leading to lower long-run growth.This effect does not occur when the government reduces lump-sum transfers as a consequence of a higher debt ratio.In this case, the reduction of lump-sum transfers can be seen as a lump-sum tax for households that does not affect the allocation of resources.
Consequently, public debt does not affect the long-run balanced growth rate.
Egert [4], contributes to the empirical literature on the debt threshold beyond which negative effects for economic growth appear.He put a variant of the Reinhart-Rogoff dataset to a formal econometric testing.Using nonlinear threshold models, he found very limited evidence in favor of a negative nonlinear relationship between debt and growth for the period from 1946 to 2009.The estimation results are indeed extremely sensitive to non-linear relationships among the time dimension and country coverage considered, data frequency, and assumptions on the minimum number of observations required in each nonlinear regime.In the few cases when a negative nonlinear effect could be identified, a positive relationship between debt and growth was identified below the estimated debt and a negative relationship was identified above the estimated debt.The negative correlation is found to kick in at a much lower level of public debt (between 20% and 60% of GDP).This suggests that high-return public investment opportunities may exist at low levels of public infrastructure and debt.
These results, based on bivariate regressions on secular time series of central government debt, are largely confirmed on a shorter dataset including general government debt (1960-2010) when using a multivariate growth framework that accounts for traditional drivers of long-term economic growth and model uncertainty.
A theoretical model of endogenous growth, in which the level of the public debt-to-GDP ratio can negatively impact the effects of productive public expenditures on growth, is the main proposition of Teles and Mussolini [5].This effect occurs because government indebtedness extracts a portion of the young people's savings to pay interest on the debt.The main conclusions obtained from the theoretical model are verified through the use of an econometric model that provides evidence of the validity of the theoretical model.Their empirical analysis controls for time-invariant, country-specific heterogeneity in the growth rates.Furthermore, they addressed endogeneity issues and allowed for heterogeneity across countries in terms of the model parameters.Their approach has enabled them to verify the existence of effects that have already been predicted in the literature, such as the non-linear effects of productive expenditures on growth given the size of the tax burden or given the indebtedness rate.Such effects are negative for direct capital accumulation because they lead to diminishing marginal net returns of capital or savings extracted from the economy to finance public expenditures.In addition to isolating the above effects, they were able to observe that the impact of productive expenditures on growth depends on the size of the debt-to-GDP ratio, because an increase in the magnitude of productive expenditures leads to an increase in the productivity of the economy and, thus, to an equilibrium of interest rates.In addition to incorporating the effect of public debt on the relationship between productive expenditures and economic growth, the model also demonstrates that increases in the size of the debt can lead to higher economic growth; the status quo is a healthy fiscal situation, and indebtedness is associated with an increase in productive expenditures.
Gomez-Puig and Sosvilla-Rivero [6] provide new evidence on the possible existence of bi-directional causal relationships between public debt and economic growth in both central and peripheral countries of the European Economic and Monetary Union.They tested for heterogeneity in the bi-directional Granger-causality across both time and space during the period between 1980 and 2013.The results suggest evidence of a "diabolic loop" between low economic growth and high public debt levels in Spain after 2009.Moreover, in the case of Belgium, Greece, Italy, and the Netherlands, variations in public debt have a negative effect on growth after an endogenously determined breakpoint and above a debt threshold that ranges from 56% to 103%, depending on the country.In addition, their findings suggest that the EMU countries that were studied not only face different initial conditions, but also have heterogeneous relations both between public debt and economic growth and between economic growth and public debt.Their evidence suggests that an increase in the level of public indebtedness, which might be accompanied by a relaxation of austerity programs, may not boost economic growth, but accelerate its decline.Nevertheless, even though they agree that it is imperative to lower public debt over time, they also think that European policymakers need to be aware of the negative short-run effects of fiscal adjustments on growth prospects.
Tamai [7] examined the relationship between deficit-financed fiscal policy and economic growth in the stochastic economy with disturbances attributable to private and public investment volatility.The analysis showed that a higher tax rate on income eliminates fluctuations in the growth rate and increases (decreases) the mean growth rate when the income tax rate is sufficiently low (high).This result implies that promoting economic growth and eliminating fluctuations in growth are (never) compatible if the income tax rate is sufficiently low (high).In response to increased taxation, households can be induced to vary their portfolios to hedge investment risk in a stochastic economy.That is, deficit-financed fiscal policy affects economic growth and its stability not only through investment in private capital and disposal income of households but also through changes in the portfolios of households.Furthermore, it was demonstrated that public finance reforms, such as tax hikes, do not always improve the treasury budget and therefore do not always reduce the debt-to-GDP ratio.
Égert [4] examined whether public debt has a negative nonlinear effect on growth if public debt exceeds 90% of GDP, by putting a variant of the Reinhart-Rogoff dataset to formal econometric testing.He used nonlinear threshold models and showed that finding a negative nonlinear relationship between the public debt-to-GDP ratio and economic growth is extremely difficult and sensitive to modeling choices and data coverage.This suggests that high-return public investment opportunities may exist at low levels of public infrastructure and debt.The main conclusion is that the results broadly confirm findings of the recent literature.The paper also showed that the negative nonlinear relationship between public debt and economic growth cannot be taken for granted.Indeed, nonlinear effects might be more complex and difficult to model than previously thought.
Gossé and Serranito [8] studied the long-run determinants of current account balances in 21 OECD countries.Specifically, they define long-run targets to determine whether actual current account balances are in line with their equilibrium values.The main conclusion is that the speed of convergence is much faster in deficit countries than in surplus ones.Since 2003, the main northern euro area countries did not show any tendency towards convergence.After the financial crisis, the United Stated and Japan returned towards their long-run targets.In parallel, the actual current account balances of the FANG (Finland, Austria, the Netherlands and Germany) have diverged significantly from their structural levels, whereas in the GIIPS (Greece, Ireland, Italy, Portugal and Spain) the current account balances are much more in line with their long-term targets, with the exception of Greece and Spain.
Moreover, the analysis of Checherita-Westphal and Rother [9] [10] in their 2013 paper "The impact of high government debt on economic growth and its channels: An empirical investigation for the euro area" concludes that public debt has a non-linear impact on per-capita GDP growth across twelve euro area countries for the period since 1970.The paper shows that public debt is associated, on average, with lower long-term growth rates at debt levels above the range of 90% -100% of GDP.The long-term perspective is reinforced by the evidence of a similar impact of public debt on the potential/trend GDP growth rate.From an econometric perspective, the paper deals with the potential endogeneity problem, in particular with the issue of simultaneity or reverse causation, in various ways.They also suggest that the current debt levels of many countries may already have a detrimental impact on their GDP growth, given that the euro area average debt-to-GDP ratio is already above the lower confidence threshold.Private savings, public investment and total factor productivity are the channels through which public debt is found to have a non-linear impact on economic growth.Moreover they suggest that while these relationships are estimated individually, the public debt may influence economic growth through several channels simultaneously.Kourtellos, Stengos, and Tan [11] investigated the heterogeneous effects of debt on growth, using public debt as a threshold variable, as well as several other plausible variables and employing a structural threshold regression methodology.Their paper shifted the focus of research on the long-run effects of ''high levels'' of public debt towards its interplay with the deep (fundamental) determinants of growth, as recently proposed by the new growth theories.The findings showed that, once a rich set of alternative theories are considered, there is very little evidence for such nonlinearities.Also, they showed that the relationship between public debt and growth is mitigated crucially by the quality of a country's institutions.When a country's institutions are below a particular quality level, more public debt leads to lower growth (all else equal).At the same time, gathering Greek data for a 40-year period (1970-2010), Spilioti and Vamvoukas [12] examine the link between economic growth and government debt.They have taken into account the different levels of economic growth in the country during that period.They also included indicators related to fiscal policy-which affects economic growth-to country's ability to invest and in the short run finance its expenses, and to the openness and external competitiveness of the economy, as well as variables that are related to its demographic characteristics.The results suggested that key factors such as government debt, per capita gross domestic product and gross national savings represent important determinants of the growth rate of the gross domestic product.The results also suggested that the inclusion of some other control variables in the estimation of growth equation has an important impact on GDP growth.More specifically, other independent variables such as the sum of imports and exports, the trade of goods and services and the growth rate of trade in goods and services, the balance of current transactions with the rest of the world, unemployment, total population and the growth rate of population, are statistically significant and explain a large portion of the variability of the dependent variable.The results support the existence of a statistically significant relationship between government debt and GDP growth.
Ca' Zorzi, Chudik, and Dieppe [13] investigated the importance of evaluating model and parameter uncertainty prior to reaching any firm conclusion, with the aim to contribute to the existing literature.They used three alternative econometric strategies: examining all models, selecting a few, and combining them all.The paper showed that there are thousands, if not millions, of models, which may lead to different conclusions on whether disequilibria exist, as well as on their size.As regards policy conclusions, they explored different routes corresponding to three alternative plausible econometric strategies: examining all models, selecting a few, and combining them all.The main conclusion is that, based on this approach, the chance that current accounts were aligned with fundamentals prior to the financial crisis appears to be minimal.
In conclusion, many scientific studies clearly identify the factors that make up the systems of measuring competitiveness and economic growth, and are more or less related with public debt.However, there seems to be no direct correlation between public debt and competitiveness indicators, as well as the factors that influence competitiveness, especially in countries hit by the European debt crisis in Europe over the past decade, which is also the subject of this paper.
Problem Description
The problem addressed is the effect of the competitiveness of a country on the public and private debt of that country.The country competitiveness is captured by the competitiveness index, imports, gross fixed capital formation, the investments/GDP ratio, consumption, labor cost, exports, the CPI (consumer price index), GDP per capita and productivity, FDI inflows, the GDP, GDP growth, political stability, the corporate income tax rate, the ease of doing business, corruption, the number of labor unions, the pensioners (as a percentage), unemployment (as a percent), the pensions (as a percent of GDP), and the corporate tax rate.The debt is measured by public debt (as a percentage of GDP), private sector debt (consolidated as a percentage of GDP), the net external debt (as a percentage of GDP), total financial sector liabilities (consolidated and as a percentage change from the previous period), and total financial sector liabilities by subsectors (consolidated, as a percentage of GDP and for financial corporations).
We chose this approach as we observed that countries that exhibit certain competitiveness characteristics in terms of their economic activity seem to have lower public debt.We wanted to investigate that also for private debt, as it is anticipated that the competitiveness of a country can have benefits for the private sector as well.
Data
Our dataset consists of nineteen countries of the European Union (Austria, Belgium, Czech Republic, Denmark, Estonia, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Netherlands, Poland, Portugal, Slovak Republic, Slovenia, Spain, and the UK).The relevant country figures are for the period 2000-2016 and come from the OECD, Eurostat, the World Bank and AMECO [14]- [23].
We use averages for the period under investigation, as on one hand we wanted to capture the global trend of that period that contained also the crisis and on the other hand we did not have data for the same years for all the variables and all the countries.
Descriptive Statistics
We hereby present the main descriptive statistics of our dataset, i.e. the average, the standard deviation, the minimum, the maximum, as well as the number of observations.We only kept the countries for which we could find data for all variables (Table 1).To make sure that for all these countries we would have comparable results we took averages for the years under investigation (2000-2016).
Variables
The variables that are used as measures of the competitiveness of an economy-and are the independent variables in our model-are the competitiveness index, imports, gross fixed capital formation, the investments/GDP ratio, consumption, labor cost, exports, the CPI (consumer price index), GDP per capita and productivity, FDI inflows, the GDP, GDP growth, political stability, the corporate income tax rate, the ease of doing business, corruption, the number of labor unions, the pensioners (as a percentage), unemployment (as a percent), the pensions (as a percent of GDP), and the corporate tax rate.We use public debt (as a percentage of GDP), private sector debt (consolidated as a percentage of GDP), the net external debt (as a percentage of GDP), total financial sector liabilities (consolidated and as a percentage change from the previous period), and total financial sector liabilities by subsectors (consolidated, as a percentage of GDP and for financial corporations) as determinants of public and private sector debt.These are the dependent variables of our model.We use the averages for the years 2000-2016 of the above variables, so as to have an indication of the trend.
We note here that public debt (as a percentage of GDP) is defined as the general government debt-to-GDP ratio.According to the OECD (2018), "this is the amount of a country's total gross government debt as a percentage of its GDP.It is an indicator of an economy's health and a key factor for the sustainability of government finance.'Debt' is commonly defined as a specific subset of liabilities identified according to the types of financial instruments included or excluded.Debt is thus obtained as the sum of the following liability categories (as applicable): currency and deposits; securities other than shares, except financial derivatives; loans; insurance technical reserves; and other accounts payable.Changes in government debt over time reflect the impact of government deficits.This indicator is measured as a percentage of GDP." Private sector debt according to Eurostat [20] [21] [22] [23] is "the stock of liabilities held by the sectors Non-Financial corporations and Households and Non-Profit institutions serving households.The instruments that are taken into account to compile private sector debt are Debt securities and Loans.Data are presented in consolidated terms, i.e. do not take into account transactions within the same sector, and expressed in % of GDP." The net external (or foreign) debtat any given time, as per the Eurostat definition [20] [21] [22] [23], is "the outstanding amount of the actual current (and not contingent) liabilities that require payment(s) of principal and/or interest by the debtor at some point(s) in the future and that are owed to non-residents by residents of an economy.The external debt is the portion of a country's debt that was borrowed from creditors outside the country, including commercial banks, other governments or international financial institutions (such as the International Monetary Fund (IMF) and the World Bank).The assets/liabilities include debt securities, such as bonds, notes and money market instruments, as well as loans, deposits, currency, trade credits and advances due to non-residents.The loans must usually be paid in the currency in which they were made.In order to earn the needed currency, the borrowing country may sell and export goods to the lender's country.The data are expressed in % of GDP." Total financial sector liabilities [20] [21] [22] [23] "measure the evolution of the sum of all liabilities (which includes Currency and deposits, Debt securities, Loans, Equity and investment fund shares/units, Insurance, pensions and standardized guarantee schemes, Financial derivatives and employee stock options and Other accounts payable) of the financial corporation sector.The data are presented in consolidated terms, i.e. data do not take into account transactions within the same sector.The data are expressed as 1 year % change of the % of GDP." Modern Economy Total financial sector liabilities by subsectors according to Eurostat [20] [21] [22] [23] measure "the evolution of the sum of all liabilities (which includes Currency and deposits, Debt securities, Loans, Equity and investment fund shares/units, Insurance, pensions and standardized guarantee schemes, Financial derivatives and employee stock options and Other accounts payable) of the financial corporation sector.Data are presented in consolidated terms (i.e.data do not take into account transactions within the same sector), in % of GDP and for the sub-sectors: Central bank; Deposit-taking corporations except the central bank; MMF; Non-MMF investment funds; Other financial intermediaries, except insurance corporations and pension funds; Financial auxiliaries; Captive financial institutions and money lenders; Insurance corporations and Pension funds."
Methodology
We attempt to use linear regression in order to link the measures of a country's competitiveness with the determinants of the effectiveness of an adjustment program.The regressions we run use one dependent and one independent variable.The general form of the regression equation is: where Debt is any of the above variables that reflect the public or private sector debtor liability and Competitiveness is any of the variables that determine the competitiveness of a country.We use the Stata econometric software to run these linear regressions with Ordinary Least Squares (OLS).We use White's test to detect potential heteroskedasticity and we use Robust Standard Errors to tackle it when present.
Regressions
We regressed each of the independent variables with each of the dependent variables that are shown in the following Table 2 & Table 3 and explained in the results section below.
Results and Implications
The regressions of public debt with each of the independent variables show that it is negatively correlated with the investment/GDP ratio, GDP growth, GDP per capita at all levels, as well as the ease of doing business at the 10% level.It is positively correlated with the corporate income tax rate and the pensions (as a percentage of GDP) at all significance levels.The remaining variables show no statistical significance.This means that the higher the investments as a portion of GDP, the lower the public debt.The same applies to GDP growth, GDP per capita, and the ease of doing business.This means that competitive economies attract sources of income that allow for low levels of public debt.On the other hand, the positive relation of public debt with the corporate income tax rate and pensions is probably explained by the fact that countries which are perceived as (c) non-competitive due to their high corporate tax rate and pensions cannot attract other sources of funds.Consequently their public debt is higher.Moreover it could be that part of the public debt is due to the fact that pensions account for a larger portion of GDP.Private debt is positively correlated with the labor cost, the CPI, the GDP per capita, the ease of doing business, the corruption index at all levels, the competitiveness index, and FDI inflows at the 5% significance level, and with the number of labor unions at the 10% level.It is negatively correlated with the pensioners at all levels, the pensions as a percentage of GDP at the 5% level, and the investments/GDP ratio, unemployment, and the corporate tax rate at the 10% level.The rest of the variables exhibit no statistical significance.These findings mostly show that the higher the competitiveness as measured by the relevant indexes (ease of doing business, corruption), the higher the private sector debt.This can be explained by the fact that lenders trust the corporations of positively perceived countries.In addition, the higher CPI and GDP per capita could indicate some degree of prosperity that allows higher private sector debt.Moreover, countries that attract higher FDI inflows, also justify higher private sector debt.Labor costs and the number of labor unions could account for increased borrowing to cover increased labor-related expenses.On the other hand, the high number of pensioners, the high percentage of pensions compared to GDP, high unemployment and the high corporate tax rate could be viewed as creating unfavorable conditions for lending corporations, meaning that private sector debt is lower in such countries.Moreover, if investments are high as a percentage of GDP, then private sector lending may not be as necessary, and hence it is negatively correlated with such investments.
The net external debt is positively correlated with the corporate income tax rate, the pensioners, and the pensions (as a % of GDP) at the 10% significance level.It is negatively correlated with GDP growth at the 5% level, and with labor cost, political stability and the ease of doing business at the 10% significance level.The findings are in line with those related to the public debt, and the interpretation is thus similar.Financial sector liabilities are positively correlated with GDP growth at all levels and with the investments/GDP ratio at the 5% significance level.They are negatively correlated with the CPI, the GDP per capita and the corporate tax rate at all levels, with the labor cost and the pensions at the 5% level, and with gross fixed capital formation and the GDP at the 10% significance level.There is no statistically significant correlation with the other independent variables.The outcomes of the financial sector liabilities regressions indicate that the higher GDP growth and the investments/GDP ratio, the higher the percentage increase of financial sector liabilities, as the financial corporation sector can, apparently, access increased financing in countries that exhibit such conditions.On the other hand, the high CPI probably increases financing costs and thus leads to reduced rate of change of the financial sector liabilities.The high GDP per capita and high GDP potentially reduce the financing needs of financial corporations, as they most likely have other sources of income.The low corporate tax rate probably increases profitability and thus increases investments in assets issued by financial corporations, and thus their liabilities.The low labor cost and the low pensions as a percentage of GDP could mean increased profitability and thus again higher investments in assets issued by the financial corporations and therefore higher financial corporation liabilities.High gross fixed capital formation possibly implies reduced interest in the assets issued by financial corporations and thus leads to a drop in the rate of change of financial sector liabilities.
In addition, we ran a regression of financial sector liabilities against public debt to determine whether they are negatively correlated at all significance levels.This can be probably interpreted by the fact that high public debt implies reduced interest for the assets issued by financial corporations and thus a drop in the financial sector liabilities change.
Financial sector liabilities by subsector (as a % of GDP) are positively correlated with the labor cost, the GDP per capita, and the ease of doing business at all levels, and with the competitiveness index and the CPI at the 5% level.They are negatively correlated with the pensioners and the pensions as a percentage of GDP at all levels, the corporate tax at the 5% level and unemployment at the 10% level.The other variables show no explanatory significance.This means that the higher the competitiveness of a country, the more easily the financial sector can obtain financing.The same holds when the ease of doing business is perceived as high.Higher GDP per capita potentially means increased interest for the assets issued by financial corporations and thus increases their liabilities.The high labor cost could also mean that financial corporations are in greater need of covering this cost.As pensioners, pensions, and unemployment increase it is possible that there are limited funds to be directed to the financial corporations, thus decreasing their liabilities.The same is possible in regard to the impact of high corporate tax rates, which reduce profitability and thus the demand for the assets issued by the financial sector.
To make sure that our findings are valid when we combine all variables, we regressed public debt with GDP growth, GDP per capita and productivity, pensions as a percent of GDP, unemployment and corporate income tax rate to realize that these variables remain significant either for private or for public debt.More specifically, public debt is negatively correlated with GDP growth at the 5% level, positively correlated with the GDP per capita, the pensions as a% of GDP and the unemployment at the 10% level.The private debt is negatively correlated with the GDP growth at the 10% level and the pensions as a % of GDP at the 5% level, whereas it is positively correlated with the GDP per capita at all levels.The net external debt is negatively correlated with the GDP growth at the 10% level and with the GDP per capita at all levels.Financial sector liabilities are negatively correlated with the GDP per capita at the 10% level.Financial sector liabilities by subsector are positively correlated with the GDP per capita at all levels and negatively correlated with the income tax rate at the 10% level.The remaining variables in all cases show no statistical significance.The interpretation remains similar to the one presented in the aforementioned argumentation of the individual regressions.The results are presented in Table 3.
The relationships identified among the measures of the debt of a country and the determinants of its competitiveness indicate that a country (for example Greece) that wishes to contain its public debt (as measured by the general government debt and the net external debt) needs to attract increased investment as a portion of its GDP, secure GDP growth, and create conditions to increase its GDP per capita.In addition it needs to foster a friendly corporate environment with high perceived ease of doing business, affordable corporate income tax rates, and reasonable pensions (as a percent of GDP).All this is maybe well-known empirically, but has also emerged as a finding of our study.Private debt (as measured by financial sector liabilities as a percentage of GDP) is in the same direction with GDP per capita, the ease of doing business, labor cost, the competitiveness index, and the CPI.It moves to the opposite direction from pensions and pensioners, the unemployment and the profit tax.If private debt is viewed as a means of financing, then to attract it countries need to pretty much do what is needed in order to reduce public debt, due to the negative sign of the coefficient of the regression.Consequently, a consistent policy that increases the competitiveness of a country can work towards consolidating GDP growth, GDP per capita, and the perceived ease of doing business, and maintaining pensions, unemployment, and taxes at acceptable levels.
Conclusions
The competitiveness of a country is vital both for the public and private debt.It is therefore of great importance to identify the characteristics of economic activity that countries with low public debt exhibit and realize the implications to private debt.In this paper we were able to show that the public and private debt is definitely linked to the country competitiveness as measured by GDP growth, GDP per capita, ease of doing business, tax rate, pensions and unemployment, as evidenced by the regression analysis performed, comparing the relevant figures of our countries of interest.As we did not use panel data, but rather OLS on the averages per country, we leave for future research the investigation of our findings when we use the entire time series, this being a limitation of our research.
Ideally, we would like to gain access to the data of more countries, so as to have an even bigger set of countries to apply our findings.
Consequently, a country that wishes to reduce its public debt and attract funds for the private sector lending (as a source of financing) needs to pay attention to these figures and secure that they move in the appropriate direction.
As evidenced by the afore mentioned findings, this can be achieved by proceeding with the necessary reforms that will facilitate the entrepreneurship in the country, rationalize pensions, will create employment opportunities and contain taxes at affordable levels.All these require strong decision making and consistent implementation.The relevant actions are not necessarily conflicting as containing pensions could release resources that can be used to increase employment and stabilize taxes.At the same time fostering entrepreneurship, will also contributes to the same direction.Last but not least, they need to create the conditions that will increase GDP and GDP per capita growth.The previous actions also contribute to this direction as well.As a result, policymakers can concentrate at least on these five directions/metrics to secure that their country will remain or become competitive. | 8,680 | 2018-03-17T00:00:00.000 | [
"Economics",
"Political Science"
] |
Future Decreases in Thermospheric Neutral Density in Low Earth Orbit due to Carbon Dioxide Emissions
Increasing carbon dioxide causes cooling in the upper atmosphere and a secular decrease in atmospheric density over time. With the use of the Whole Atmospheric Community Climate Model with thermosphere and ionosphere extension (WACCM‐X), neutral thermospheric densities up to 500 km have been modeled under increasing carbon dioxide concentrations. Only carbon dioxide and carbon monoxide concentrations are changed between simulations, and solar activity is held low at F10.7 = 70 throughout. Neutral density decreases through to the year 2100 have been modeled using four carbon dioxide emission scenarios produced by the Intergovernmental Panel on Climate Change (IPCC). The years 1975 and 2005 have also been simulated, which indicated a historic trend of −5.8% change in neutral density per decade. Decreases in the neutral density relative to the year 2000 have been given for increasing ground‐level carbon dioxide concentrations. WACCM‐X shows there has already been a 17% decrease in neutral densities at 400 km relative to the density in the year 2000. This becomes a 30% reduction at the 50:50 probability threshold of limiting warming to 1.5°C, as set out in the Paris Agreement. A simple orbital propagator has been used to show the impact the decrease in density has on the orbital lifetime of objects traveling through the thermosphere. If the 1.5°C target is met, objects in Low Earth Orbit (LEO) will have orbital lifetimes around 30% longer than comparable objects from the year 2000.
• Thermospheric neutral density at 500 km altitude lowers by over 80% with a high ground-level carbon dioxide concentration of 890 ppm • Meeting the 1.5°C Paris Agreement target limits the reduction in neutral density at 400 km since the year 2000 to around 28% • Objects in Low Earth Orbit (LEO) will have orbital lifetimes around 30% longer at the 1.5°C target than comparable objects from the year 2000 with increased extreme ultraviolet emission which heats the thermosphere, causing oscillatory variation in neutral densities of an order of magnitude. These peaks also vary in magnitude from cycle to cycle, with the most recent (solar cycle 24) maxima having one of the smallest peak sunspot numbers observed since records began in 1749. There is a wide range of literature trying to predict the peak of the next solar cycle, with these predictions ranging from lower than the last, to being one of the largest recorded (McIntosh et al., 2020). The length of each cycle also varies, with an average period of around 11 years and the majority falling between 10 and 12 years. Part of this increased period can be attributed to the length of time taken for the Sun to start recovering from low solar activity to high, with the last 2 solar minima being particularly prolonged (Lockwood et al., 2012). Both of these minima were also signifcantly lower than previous historic minima, resulting in historically low neutral densities.
The secular decrease in thermospheric density caused by an increase in CO 2 concentration is of particular concern for all objects orbiting in the Low Earth Orbit (LEO) region. With decreasing atmospheric density, an orbiting object experiences less atmospheric drag. This becomes particularly relevant at altitudes below 500 km where drag is a dominant perturbing force and the effect of a secular density trend is substantial. The smaller drag force leads to a reduced rate of semi-major axis decrease, and hence a longer orbital lifetime. Observations of changes in the semi-major axis within the tracking data of historical LEO objects have been used to measure density trends (Emmert, 2015;Emmert et al., 2008;Keating et al., 2000;Saunders et al., 2011). Numerical atmospheric models have also been used to simulate historical time periods and estimate the magnitude of density trends associated with an increase in CO 2 concentration (Qian et al., 2006;Solomon et al., 2015Solomon et al., , 2018. Results from both groups of studies, at an altitude of 400 km, found under low solar activities are summarized in Table 1. All of these studies have found the historical secular trend to be negative, with values ranging from −2.5% to −7.2% per decade. While historical observations relied on tracked satellites, more recently satellites such as CHAMP, GRACE, and GOCE have been launched with accelerometers, allowing for higher resolution thermospheric density data (Doornbos, 2011;. Further improvements can be made to the data by bettering the drag models of these satellites, whether that be gas-surface interactions or the geometry and aerodynamic models, as detailed in . In the long term, this will lead to better estimations of the density trend over multiple decades. The magnitude of the trend is inversely proportional to the level of solar activity (Emmert, 2015;Solomon et al., 2019), so the largest secular changes in neutral density are seen during low solar activity.
Space debris in LEO also have their orbital lifetimes increased due to the declining thermospheric density. Made up of all the discarded components and collision fragments left over from human activity in orbit, space debris poses a substantial risk to operational spacecraft (ESA Space Debris Office, 2020). The number of trackable objects (greater than 10 cm in size) intersecting the LEO region continues to increase, reaching nearly 17,500 in 2020, of which around 2300 are active spacecraft. As the amount of debris increases, BROWN ET AL. (2015) changes depending on the period it is calculated over. b k q , CO 2 -O collisional deactivation rate, of ∼1.5 × 10 −12 cm 3 s −1 or 3.0 × 10 −12 cm 3 s −1 .
Table 1
Observations and Models of the Historic Density Trend at 400 km and for Low Solar Activities Only so does the probability of a collision which would create further debris. This poses further risk to active spacecraft and disruption to operations as spacecraft operators have to respond to possible conjunctions.
Space debris models have been created to investigate the evolution of the debris environment. However, the decreasing thermospheric density trend has not been included in the majority of these models. Simulations can run many decades, even centuries into the future, over which secular density trends will have an important cumulative effect. The models are also used to assess possible ways to reduce the amount of debris and the risk it poses. One method for operators to reduce the risk posed by space debris in the future is to follow the voluntary debris mitigation guidelines introduced by the United Nation's Committee on the Peaceful Use of Outer Space (UN COPUOS), which includes the limiting of orbital lifetime to 25 years once a satellite's mission is complete. Another method known as Active Debris Removal (ADR) is the launching of satellites with the aim of removing the pieces of space debris which pose the greatest risk to the environment.
The Intergovernmental Panel on Climate Change (IPCC)'s Fifth Assessment Report (AR5) published four Representative Concentration Pathways (RCPs), with each giving a CO 2 trajectory through to the year 2100. These are shown in Figure 1 and summarized in the Synthesis Report from the IPCC (2014). These are entitled RCP2.6, RCP4.5, RCP6.0, and RCP8.5, where the number refers to the radiative forcing in W/m 2 in the year 2100 for each scenario. While these are not meant to be predictions of the future, they provide a limited number of baseline scenarios and CO 2 concentration trajectories from which modeling can be performed and results across studies compared. The RCPs are used to simulate future density reductions and trends within this work. For more information on how four independent groups arrived at the CO 2 concentration profiles used within the RCPs, see van Vuuren et al. (2011).
Model Simulations
The Community Earth System Model (CESM) from the National Center for Atmospheric Research (NCAR) allows for simulation of the whole, coupled Earth climate, using separate modules for each major system (Hurrell et al., 2013). In this work, the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X) module is used (Liu et al., 2010). This models the atmosphere numerically from ground level through to 4 × 10 −10 hPa, which corresponds to an altitude of 350 km at CO 2 levels from the year 2000 and low solar activity. The model has a resolution of 1.9° in latitude and 2.5° in longitude (using a 96 by 144 grid), with 81 vertical pressure levels and a resolution of one-quarter scale height above 1 hPa. Solar and geomagnetic activity are parametrized in the model using established indices of activity such as the solar 10.7 cm radio flux, F 10.7 , and the planetary Kp index respectively. For a full description of the model, including the chemistry and radiative transfer within WACCM-X, see Liu et al. (2010) and Liu et al. (2018). For this work, CESM 1.2.2 was run on the University of Southampton computing cluster, Iridis 4.
There are only small variations in carbon dioxide concentration from ground level up to around 70 km where the atmosphere is well mixed. Above this altitude molecular diffusion takes over and the concentration reduces towards 0 ppm, as seen in Figure 2c. New initial conditions for WACCM-X under varying CO 2 concentrations were created by scaling the CO 2 values at each pressure level in the original initial history files (here chosen as the WACCM-X default files for the year 2000) by the relative increase in ground-level CO 2 concentration. At the higher altitudes, CO 2 and carbon monoxide (CO) exist in chemical equilibrium. To account for this, CO values are scaled similarly to CO 2 . This accounts for over 99.7% of the carbon in the thermosphere and minor constituents containing carbon such as methane (CH 4 ) were not scaled. However, BROWN ET AL. the effect of changes in methane on thermospheric density is expected to be much smaller than the effect of the increase in CO 2 concentration (Roble & Dickinson, 1989).
Nitric oxide (NO) also plays an important role in thermospheric cooling during solar maximum (Mlynczak et al., 2016), and could be increased by the anthropogenic emission of the greenhouse gas nitrous oxide (N 2 O). However, the large amount of Nitrogen (N 2 ) in the lower atmosphere acts as a reservoir, keeping NO in the thermosphere at a relatively stable level. To remove the effects of solar activity (and therefore also NO) on cooling and the secular density trend, the F 10.7 and Kp indices were held fixed at 70 sfu and 0.33 respectively in all simulations. While Kp values can be used as integers between 0 and 9, WACCM-X uses a Kp decimal value which provides a finer scale for geomagnetic activity. A Kp value of 0.33 is similar to the value of 0.3 used in Solomon et al. (2015), allowing for easier comparison between the historical trends. Other increases in gas concentrations such as O 3 , CH 4 , and H 2 O vapor and CFCs which would impact the stratosphere and mesosphere regions were not considered.
The Earth's magnetic field also changes over time, affecting the ionosphere and in turn the thermosphere (Cnossen, 2014). It was found that for the period 1908 to 2008, the historic changes in the magnetic field do contribute to cooling at 300 km, however, the increasing CO 2 concentration dominates the thermospheric cooling. A recent study by Cnossen and Maute (2020) confirmed the predicted changes in the Earth's magnetic field up to the year 2065 will result in at most a 1% to 2% increase in neutral density from 2015 to 2065. This is equivalent to an increase of 0.2% to 0.4% per decade over the next 5 decades, which is an order of magnitude smaller than the decreasing historical trends of −2.5% to −7.2% per decade summarized in Table 1. The impact of the changing magnetic field will therefore not be considered in the simulations for BROWN ET AL. this study. The magnetic field within WACCM-X, namely the International Geomagnetic Reference Field (IGRF-12) described in Thébault et al. (2015), is held fixed at the year 2000 level.
The CO 2 -O collisional deactivation rate (quenching rate), k q , has a major impact on the cooling within atmospheric models (Akmaev, 2003). This can be seen by the change in density trend of Solomon et al. (2015) from −4.9% per decade at k q = ∼1.5 × 10 −12 cm 3 s −1 to −6.8% at k q = 3.0 × 10 −12 cm 3 s −1 . Recent measurements of the value vary between 1.5 × 10 −12 and 8.0 × 10 −12 cm 3 s −1 and are summarized in Feofilov et al. (2012). The value of k q used for this study has been left as the default in WACCM-X, namely 3.0 × 10 −12 cm 3 s −1 as this was the value WACCM-X was calibrated with during development.
WACCM-X performed simulations of 10 different ground-level CO 2 concentrations, each for 16 model months total. These are the CO 2 concentrations of RCP8.5 at 10 years intervals starting from 2005 and ending on 2095, along with the year 1975 (for validation against previous studies). All simulations were performed as free runs, and hence the lower atmosphere (< ∼50 km) was not constrained by data. Lower boundary conditions were set following the Coupled Model Intercomparison Project (CMIP5) implementation of RCP8.5 (Taylor et al., 2012). Ground-level CO 2 concentrations were allowed to vary with season and propagate through the atmosphere. Therefore, annual mean CO 2 concentrations are stated through this work. The seasonal sinusoidal variation had a maximum amplitude of 1% of the annual mean. Numerical models (like WACCM-X) require time for the user-set, initial conditions of the modeled atmosphere to stabilize into a physical equilibrium. While other studies such as Solomon et al. (2018) allowed one year for minor chemical constituents to equilibrate, we found temperature and density appeared to equilibrate after one month. As a precaution, the first 4 months of each data set were ignored, leaving 12 model months for each CO 2 concentration modeled. Key values from the simulations such as temperature and chemical concentrations were stored with a temporal resolution of 3 hours.
Along with the 10 simulations stated earlier, an additional 64 month long simulation of the year 2000 has also been completed. This provided a more robust reference point against which the later simulations could be compared. 64 months was chosen as 12 months are simulated 5 times, with the end of one simulated year being used as the initial conditions of the next 12 months cycle. Again 4 months are added to the start of this for equilibration. Figure 3 plots the differences for each of five cycles from the overall globally averaged temperature and globally averaged density altitude profiles for the 64 months simulation of the year 2000 (with the first 4 months ignored). This shows the impact the initial conditions have on the simulation of each year. These longer simulations could not be performed for the other concentrations due to limited computing time.
Processing
A geopotential height, h, is output at each of the grid points of WACCM-X. This was converted into a geometric altitude, z, via where r E is the average radius of the Earth, 6,371 km. The geometric altitude is equivalent to a satellite's orbiting altitude. All interpolation between the 81 altitude levels of WACCM-X for each latitude, longitude pair was performed via 1-D monotonic cubic interpolation.
WACCM-X models the thermosphere down to a pressure level of 4 × 10 −10 hPa. This minimal pressure level varies in height, with the maximum altitude decreasing as the thermosphere cools. At high ground-level CO 2 concentrations the maximum model altitude is only 280 km. As the motivation of the work was to understand the reduction in density at commonly used LEO altitudes, the WACCM-X model data was extrapolated to an altitude of 500 km. It was found that the function that best fit the densities at points above 175 km for all cases was calculated by where ρ is atmospheric density and a, b, c, and d are coefficients fit to the modeled density with non-linear least squares. This allowed a neutral density profile as a function of altitude to be obtained for each latitude-longitude combination. It should be noted that from 175 km to the maximum modeled altitude, WACCM-X is dominated by atomic oxygen. Helium becomes the dominant species within the thermosphere above around 700 km, which would not be accounted for by this extrapolation method. Applying the extrapolation method to the NRLMSISE model (Picone et al., 2002) which does account for helium showed an increasing deviation with altitude, reaching an overestimate of 3% at 500 km. As the relative differences in densities was of primary concern in this study, and the overestimate was consistently applied, this extrapolation method proved acceptable when used up to 500 km. Temperatures in the thermosphere tend towards the exospheric temperature with increasing altitude. It is assumed the temperature at the highest modeled altitude is the exospheric temperature, and therefore this temperature is used for all higher altitudes up to 500 km.
To obtain global mean annual mean values of temperature and density, data was transformed from the model's pressure levels to geometric altitudes using the above methods, and then averaged temporally to calculate annual means at each altitude, latitude, and longitude. The global mean annual mean is then obtained by averaging over latitude (with cosine latitude weighting) and longitude.
BROWN ET AL.
Figures 4a and 4b
show the WACCM-X global mean temperature plotted against ground-level CO 2 concentration at the fixed pressure level of 2.9 × 10 −7 mbar (around 200 km altitude) during the March equinox and June solstice. This was done to compare the WACCM-X data at large CO 2 concentrations against three implementations of the Coupled Middle Atmosphere Thermosphere version 2 (CMAT2) model (Cnossen et al., 2009), where each implementation has different gravity wave parameterization schemes. While WACCM-X is cooler than all three implementations of the CMAT2 model, WACCM-X's temperature decreases with increasing CO 2 as expected, and at a similar rate to that of CMAT2.
Using the methods described in this study, the trend of decreasing neutral density due to increasing carbon dioxide for the period 1975-2005 has been calculated to be −5.8% per decade at 400 km altitude. This places it in the middle of the range predicted by other models and observations which were summarized in Table 1.
Stating trends for the reduction in neutral thermospheric density is useful for studies of historical periods, as the change in carbon dioxide concentration is fixed. However, for future reductions in density, CO 2 concentration will be variable and any future density trend will be dependent upon it. Figure Figure 6 shows the density change relative to the year 2000 for each RCP scenario. These data were generated by combining the data shown in Figures 1 and 5. Under the high emissions RCP8.5 scenario, the neutral density relative to the year 2000 reduced by 75% at 400 km by the year 2095. Under the RCP2.6 scenario, neutral densities at 400 km reach their largest change between the years 2040 and 2060 as CO 2 concentrations peak and begin to decline. This peak sees global ground-level temperature rise limited to 2°C or below and a 25% reduction in neutral density compared to the year 2000. Neutral densities recover to a 20% reduction by 2100 as the CO 2 concentration declines (see Figure 1). Regardless of scenario, the WACCM-X model shows that neutral densities have dropped by 17% at 400 km in 2020 relative to the year 2000.
Discussion
The targets and predictions set out within the Paris Agreement can provide some further context to this work's results. The Emissions Gap Report from the United Nations Environment Programme (2019) states that for a 50% probability of limiting global warming to 1.5°C, the carbon budget from 2018 onward is 580 GtCO 2 . Taking the 2017 globally averaged CO 2 concentration of 405.0 ppm (Le Quéré et al., 2018), this sets a target of 480 ppm above which there is higher than 1.5°C warming at ground level. This target is independent of time and is reached in different years in the RCP scenarios. By looking at the density reductions in Figure 5, it can be seen that the 1.5°C warming target is equivalent to a 32% drop in neutral density at 400 km relative to the year 2000. For a 66% probability of limiting warming to 1.5°C, there is a remaining budget from 2018 of 420 GtCO 2 . This is equivalent to a concentration of 459 ppm and a drop of 27% in neutral density at 400 km. The Emissions Gap Report also gives a prediction that under the current uncon- The empirical atmospheric model NRLMSISE-00 (Picone et al., 2002) is one of the thermospheric models used in space debris models and is calibrated with observational data up to the year 1997. The relative density drop seen in Figure 5 can therefore be used as a scaling factor for the neutral density output from NRLMSISE-00 to account for the density trends from increases in CO 2 . This has been done for a few objects in LEO in Table 2. A simple numerical propagator was used, with drag as the only perturbing force and NRLMSISE-00 as the density model. The changes presented here are to provide initial implications of the work for the debris environment. The lifetimes at 468 ppm was chosen as the closest modeled point using WACCM-X to the 1.5°C target CO 2 of 480 ppm. The orbital lifetimes of the chosen objects increase by between 26.9% and 32.6% relative to the year 2000. Under the highest modeled CO 2 concentration of 890 ppm, the orbital lifetime approximately triples when compared to the year 2000.
If these increases in orbital lifetime are experienced by all objects, they will have a substantial impact upon the space debris environment in at least two ways. First the number of orbiting objects will increase. The number of objects can only increase by adding new objects (most commonly via launches), or having orbiting objects collide and create collision fragments. Longer lifetimes lead to a greater cumulative chance of collison, resulting in further fragmentation events. Second, operators who meet the 25-year guideline by using atmospheric drag to passively remove their satellite from orbit will have to take the reduction in density into account by lowering the perigee of their final orbit or by using re-entry technologies such as drag augmentation devices. In both cases, further satellite mass has to be dedicated to the change.
These results have been computed under low solar activity only. Therefore, it is only appropriate to apply these density reductions at solar minima. There will still be a secular density reduction when looking at solar maxima, albeit smaller (see Emmert (2015)). It is unknown to what scale this will be and this will be the subject of future work. The density reduction is expected to scale with the solar activity between the minima and maxima, albeit the exact relationship is unknown. It is acknowledged that a number of assumptions have had to be made to allow for the modeling of future densities. These include the value of k q , extrapolation to higher altitudes and ignoring the density change due to the Earth's changing magnetic field. The initial state of each object was given by the two line element set on November 2, 2020 with use of the North American Aerospace Defense (NORAD) satellite catalog number. Coefficient of drag for all objects was set as Cd = 2.2. a Reference lifetime given is for the year 2000, equivalent to 379 ppm.
Conclusion
Increasing ground-level CO 2 concentrations result in decreasing thermospheric densities. These have been historically observed and modeled as summarized in Table 1. The impact on neutral densities under further increasing CO 2 concentrations have been modeled and presented within Figure 5. These neutral density reductions were also estimated for the four IPCC RCP scenarios in Figure 6. Density reductions reported throughout the paper have been given relative to the density in the year 2000 (under low solar activity) to provide a scaling ratio which can be applied to fast, empirical atmospheric models such as NRLMSISE-00. It has also been shown that limiting warming to the 1.5°C target of the Paris Agreement will still result in a 27% to 30% reduction in density relative to the year 2000 at 400 km, with orbital lifetimes increasing by around 30% as a result. Even under the low CO 2 emissions of the RCP2.6 scenarios, the drop in neutral density will have a substantial impact on LEO object orbital lifetimes, as well as the debris environment within this region. Any CO 2 concentrations higher than this will have an even more substantial impact on thermospheric densities and the space industry as a whole, particularly on constellations relying on atmospheric drag to passively remove their satellites from orbit. | 5,835.2 | 2021-04-08T00:00:00.000 | [
"Physics",
"Environmental Science"
] |
A method of partially overlapping point clouds registration based on differential evolution algorithm
3D point cloud registration is a key technology in 3D point cloud processing, such as 3D reconstruction, object detection. Trimmed Iterative Closest Point algorithm is a prevalent method for registration of two partially overlapping clouds. However, it relies heavily on the initial value and is liable to be trapped in to local optimum. In this paper, we adapt the Differential Evolution algorithm to obtain global optimal solution. By design appropriate evolutionary operations, the algorithm can make the populations distributed more widely, and keep the individuals from concentrating to a local optimum. In the experiment, the proposed algorithm is compared with existing methods which are based on global optimization algorithm such as Genetic Algorithm and particle filters. And the results have demonstrated that the proposed algorithm is more robust and can converge to a good result in fewer generations.
Introduction
With the development of the depth-sensing technology, such as Kinect and 3D LiDAR, the acquisition of 3D point cloud becomes more convenient. Furthermore, the 3D point cloud processing attracts more and more attention from research and industry fields [1][2][3][4][5][6]. Point cloud registration is one of the key technologies in 3D point cloud processing. The goal of registration is to obtain the spatial transformation between two different point clouds, which is quite useful in 3D reconstruction and object detection.
Numbers of registration methods are based on the iterative closest point (ICP) [7,8] algorithm as its high efficiency and accuracy. However, the classical ICP algorithm has some disadvantages which limit its usage in real world applications. Firstly, the speed and accuracy of convergence rely on the initial value heavily. Secondly, when the two point sets are partially overlapped, which means for some points in one set we cannot find corresponding points in the other set, the registration result becomes worse. And the algorithm may fail, if the overlapped portion is small. PLOS Trimmed Iterative Closest Point (TrICP) [9,10] algorithm has been proposed to handle the partially overlapping point sets registration problem. It estimates the rotation and translation between two sets as well ase the overlapping rate. Therefore, in each iteration it finds the correspondences only between overlapped points, and then updates the transformation using the corresponding point pairs. Accurately, when the overlapping rate nears one, the TrICP algorithm approaches the ICP algorithm. However, TrICP still need an appropriate initial value for iterative optimization procedure. Otherwise the algorithm would possibly converge to a local optimum. Moreover, TrICP is time consuming, because it needs to visit all possible overlap rate and search the one which get the best registration result.
The Differential Evolution (DE) [11] algorithm was proposed in 1997 by Rainer Storn and Kenneth Price on the basis of evolutionary ideas such as genetic algorithms. Substantially, it is a multi-objective optimization algorithm for obtaining the optimal solution in a multidimensional space. The source of differential evolution is the early proposed genetic algorithm (Genetic Algorithm, GA) [12], which simulates crossover, mutation, and reproduction in genetics to design genetic operators. Comparing with GA, the DE algorithm firstly generates the intermediate population based on the difference among the current population, and then obtain the new generation by competing between the intermediate population and the parent population. The DE algorithm has many advantages, such as high converging speed, fewer parameters.
To overcome disadvantages of traditional TrICP algorithm, the current paper proposed a global optimization method for TrICP based on DE algorithm. Through the appropriate design of the evolutionary operation, the population can be distributed widely, and increasing the probability getting the global optimal solution. It is efficient and accurate, even when the overlapping rate is low.
Related works
The original ICP algorithm relies heavily on the initial estimation of the transformation between two point clouds. And it also requires the two clouds should be close to each other. Moreover, the algorithm may fail when there the noise is significant or the number of outlier is large [13]. In the literature, numerous efforts have been made to tackle these problems.
Tsin and Kanade [14] proposed a Kernel Correlation algorithm which represented the point clouds as probability distribution, and the distance between the clouds was measured by the similarity of the distribution. However, the computation cost is very high as each point in one cloud should be compared with all points in the other.
The filter-based approaches have also been proposed to solve the local optimal solution problem. Unscented Particle Filter (UPF) is able to register small point clouds [15]. This method requires great number of particles to obtain accurate registration result. Thus, when the amount of points is large, the computational cost will be high. Although the Unscented Kalman Filter (UKF) could overcome this shortcoming, but it is constrained by unimodal distribution assumption of the state vector. Therefore, the algorithm would fail when the distribution is complex. Zhu, et al. proposed to use particle filter for rigid registration [16]. However, this algorithm is time consuming because it needs lots of particles to obtain accurate result.
TrICP introduces an overlapping rate into a least square function in order to improve the robustness to partial overlapping. However, the computation is slow. Phillips et al. [17] presented Fractional ICP (FICP) algorithm to speed up the process of registration. The algorithm computes the best correspondence and overlapping rate simultaneously. But FICP relies heavily on hyper-parameters which may lead registration to failure. Gold [18] proposed the Robust Point Matching (RPM) method, which applies the annealing algorithm to reduce the exhaustive search time. However, when noise is significant or some structural missing exist, RPM would fail.
Differential evolution algorithm
Similar to other evolutionary algorithms, the DE algorithm has several operations, including population initialization, mutation, crossover and selection. The whole process is shown in Fig 1.
Population initialization
The initialization operation aims to generate the first generation for the iterative process. If there is no priori knowlege about the optimum, the population can be initialized randomly. In this case, the individuals are widely distributed. Usually, the uniform distribution is used.
Mutation operation
In many evolutionary algorithms, the mutation operation generates new vectors via adding disturbance to the individuals in the current generation. In DE, the disturbance is ralated with the difference between two other randomly selected individuals. The generated vectors are called mutant vectors. This operation enhances the search capability, and it is the key characteristic of the DE algorithm.
Crossover operation
The crossover operation is used to increase diversity of the population. It reassigns new values to some components of the mutant vector. The components are selected randomly, and the probability is controled by a parameter, i.e. crossover rate. The result new vector is named as crossover vector.
Selection operation
The selection operation generates population of next generation from the crossover vectors and the original individuals in the current generation. Usually, the DE algorithm utilizes greedy algorithm to select new individuals according to the fitness.
As shown in Fig 1, the mutation, crossover and selection are performed iteratively. When the termination criteria is meet, the process stops. And the algorithm outputs the best individual of the last generation.
Point cloud registration based on differential evolution algorithm
The original TrICP algorithm estimated the rigid transformation and the overlapping rate using a iterative procedure. Such procedure could fall into a local optima easily. Therefore, it needs a good initial value. However, selection of the initial value is a difficult problem. In this paper, we turn to use a global optimization method. Due to efficiency and accuracy, the DE algorithm is increasingly popular in optimization field. Thus, it is adapted for registration partially overlapping point sets.
Formulation
ðd j 2 R n ; j ¼ 1; � � � ; N D Þ be the registration point set. The registration problem is to find the optimal rotation matrix R and the transform vector t to achieve the best alignment with two point clouds. Denot m c(j) as the corresponding point of d j in M. If the rotation R and the translation t between the two point sets can be obtained, the error between the two matched points can be computed as, Then, the registration process is to minimize total errors. In the overlapping case, only a part of D can be aligned with a part of M. Thus the overlapping rate r need to be estimated as well. Then the overlapped part of D can be defined as Then the TrICP algorithm find the optimal R, t and r by min R;t;r where N r is the number of points in D r , and λ is a preset parameter (in this paper, λ = 2).
In the iterative process of DE, the objective function in Eq 2 can be seen as the fitness function which measures the goodness of the individuals. Then, the whole process of registration with DE algorithm is shown in Fig 2. Initialization Let x i (g) represent the i th individual in the population of the g th generation. In this paper, each individual is a 7-dimensional vector, containing a 3D translation vector t, a 3D rotation vector and a trimming parameter. The rotation matrix R can be converted from the rotation vector. And the first generation can be computed using Eq (3).
where x j,i (0) is the j th gene in the i th individual, and x U j;i and x L j;i are the upper and lower bound of each gene. rand(0, 1) generates a random number which is uniformly distributed between 0 and 1.
Calculating transformation and fitness
The operations in following steps, such as mutation and selection, are based on the fitness of individuals. Moverover, we also perform optimization like what is done in TrICP, which is utilized to improve the fitness. Thus, the following operations will be performed on a population which has higher quality.
In this step, We first transform the cloud M to D by initial transformation, and find the correspondence between the points in two sets. Secondly, we discard the point pairs if the distance between corresponding points is out of scope defined by initialized upper and lower threshold. Thirdly, the errors of the left points is calculated and the overlapping rate can be obtained. Finally, we find the index with smallest overlap rate, and update the minimum overlap rate and previous overlap rate. We then replace the two point clouds by the trimmed ones. For new point clouds, the transformation matrix can be calculated. Then the rotation matrix R 0 and the translation vector t 0 can be obtained by singular value decomposition (SVD).
Mutation
In the mutation operation of original DE algorithm, the involved individuals are selected randomly. And the operation is performed as where r1 6 ¼ r2 6 ¼ r3 6 ¼ i are indices of individuals which are selected randomly, F is the mutation scale factor, v i (g) is the mutation vector in g th generation.
Obviously, the operation in the form of Eq 4 does not consider the evolutionary state of the current generation. It has same effect on all the individuals in spite of the fitness. Therefore, the best individual in this generation is introduced. Then the operation has a form as However, this operation has similar effect on all the individuals in spite of the fitness. Actually, the individuals which have good fitness, is more likely to trapped into a local optimum. We should add more disturbance. For the individuals, which has bad fitness, should be changed toward good ones. That is the mutation scale vectors in Eq 5 must adjusted according to the fitness of the individual. In this paper, we introduce a new operator shown in Eq 6 v i ðgÞ ¼ x r1 ðgÞ þ F � g 1 � ðx r2 ðgÞ À x r3 ðgÞÞ þ F � g 2 � ðx best ðgÞ À x r1 ðgÞÞ ð6Þ Here, F is the current scale factor. γ 1 and γ 2 are the weights, which adjusted according to the fitness of the individuals. They can be computed as where f is the fitness of the current selected individual, f best and f worst are the best fitness and worst fitness in the current generation respectively. Since the problem is minimization, f best is the smallest value. Therefore, when the individual is bad, i.e. its fitness value is large, the λ 1 will be greater than λ 2 . The mutation is more likely toward to the good individuals. Otherwise, when the individual is good, the operation is like the original one which has greater randomness. Moreover, to keep the population from early-maturing, we change the value adaptively as following, and, F 0 is the basic mutation scale factor, G is the number of generations, and g is the index of current generation.
Crossover
In this paper, the uniform crossover is used. For the individuals in the g th generation, the crossover operation is performed as follows.
where CR 2 (0, 1) is the corssover rate. It controls the proportion of the components where the crossover occurs. j rand is the index of randomly selected component. This insures that crossover occurs on at least one of the components. The generated vector is called crossover vector.
Selection
The DE algorithm applies greedy strategy to select individuals which have good fitness for the next generation.
where f(�) is the fitness of the individual. The fitness can be obtained by TrICP (Eq 2). This operation generates population for the g + 1 generation.
Experiment
In this section, the proposed algorithm was verified on a public and popular 3D range data set, i.e. the Stanford 3D Scanning Repositor [19]. And the proposed algorithm was compared with three related methods: the registration based Particle Filters (PF) [16], the registration based on GA [20], and the registration based on original DE. And we denote these approach as PF, GA, and DE respectively.
Convergence speed
For those global optimization based algorithms, the convergence speed is an important indicator of the algorithm's performance. Therefore, we selected two shapes from S1 Dataset for the experiment. One was the bunny shape and the other was the dragon shape. To generate data set, a part of the points in the shape were discarded. And after adding white noises to the position of points, the left points formed the data set. Then another part of the shape was cut down. And a randomly generated transformation (R r , t r ) was applied to the left part. The result point set was the reference set. Then we used the four methods to register the data set and model set.
To compare the performance on convergence speed, we fixed up the overlapping rate (r = 0.75) and varied the population size in different algorithms. We generated 10 pairs sets using the process mentioned in the last paragraph. Then, each algorithm was tested on all pairs. The average number of iterations of each algorithm is shown in Figs 3 and 4. From these results, one can notice that the proposed method need fewest generations than other three methods. This is because in the proposed method, the individuals were evolved according to their own state. So the search ability of the population is better than others. Also, comparing with the original DE, the proposed method can increase the efficiency greatly. 5. Registration results of the proposed algorithm for shape "Bunny". The first column is the initial position of two point sets. And the second column is the results after registration using the proposed algorithm. https://doi.org/10.1371/journal.pone.0209227.g005
Overlapping rate
Then we fixed up the population size for all the methods, and varied the overlapping rate between the data set and the reference set. In this experiment, the population size was set to 100 and the bunny shape from S1 Dataset is used. All the methods were tested with 5 different Fig 6. Registration results of the proposed algorithm for shape "Dragon". The first column is the initial position of two point sets.
And the second column is the results after registration using the proposed algorithm.
https://doi.org/10.1371/journal.pone.0209227.g006 overlapping rates. And the tests were performed for 30 trials. In this case, the successful rate and the number of iterations are concerned. The result is shown in Table 1. As shown by the results, the propose approach is more robust than other three methods. In summary, the proposed approach can find optimal result in fewer generations and is more robust for the registration between partially overlapped point cloud. Figs 5 and 6 gives some examples of registration results.
Conclusion
In this paper, we present a new variant of TrICP algorithm based on the differential evolution algorithm. In the proposed algorithm, the DE algorithm was used to obtain a global optimal solution. Via designing appropriate evolutionary operations, the population can be distributed widely. Therefore, it is difficult for the proposed algorithm to be trapped into local optima. The result of the experiment showed that the proposed algorithm can obtain accurate transformation between two point clouds, even when the overlapping rate is low. Meanwhile, the computational cost is relative low comparing with common algorithms such as genetic algorithm and particle filtering. | 4,006.8 | 2018-12-21T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Measuring the temperature and heating rate of a single ion by imaging
We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the anomalous heating rate. In contrast to other established schemes for measuring the heating rate, one does not have to switch off the cooling but the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.
Introduction
In many atomic physics and quantum optics experiments, the temperature of the atoms under investigation plays a critical role [1][2][3][4][5][6]. From fundamental tests to quantum information applications, cooling the atoms to ultra-low temperatures has become a prerequisite. To this end, laser cooling and trapping of atoms has become an indispensable tool in many labs. Furthermore, measuring the temperature of the cold atoms becomes important, for instance to understand the physics of the cooling mechanism, or to disclose additional sources of heating and thermal decoherence in the experiment. Depending on the type of the trapping and cooling method employed, several thermometry techniques have been developed.
In the case of trapped ions, the most common way to determine the temperature is to measure the sideband absorption spectrum [7,8]. This technique requires the ion to be cooled close to the motional ground state of the trap, and therefore is used in combination with ground state cooling schemes such as Raman sideband cooling [9] or cooling employing electromagnetically induced transparency (EIT) [10]. Outside the resolved sideband regime, various techniques exist. One way is to measure the Doppler broadening of the atomic transition due to the motion of the ion [11,12]. The accuracy of this approach relies on the ability to distinguish the Lorentzian spectrum of an atomic transition from the Gaussian spectrum. The Doppler broadening at sub-mK temperatures is small compared to the natural linewidth of the typically used transitions. Therefore, the statistical uncertainties in data evaluation prevent an accurate determination of the temperature close to the Doppler limit. Particularly, in the Lamb-Dicke Regime the first order Doppler effect is suppressed, and only the higher order Doppler shifts that are much weaker can be observed [13,14].
In order to enable fast and accurate determination of the temperature of a trapped ion at mK temperatures, thermometry by imaging the spatial extent of an ion has been demonstrated [15][16][17][18]. The accuracy of this method was limited only by the imaging resolution and the images' signal-to-noise ratio. In this article, we present the thermometry measurement of a single ion by imaging via a deep parabolic mirror. Our improved Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. resolution and high collection efficiency [19] allows us to determine the absolute temperature close to the Doppler limit more accurately in comparison to previous demonstrations of this technique. Furthermore, it opens up the possibility to measure temperatures below the Doppler limit, which has until now been possible only by the resolved sideband method or by similarly involved methods such as the one based on interference of fluorescence photons [20]. The high photon collection efficiency of our parabolic-mirror based set-up envisions the application of our method also for cooling processes in which only few photons are scattered, like e.g. EIT cooling.
In addition to the absolute temperature, the heating rate is another important figure of merit in thermometry of trapped ions [21,22]. In the resolved sideband regime, sideband thermometry is generally employed to measure the heating rate. Outside this regime, the heating rate is traditionally measured from the time-resolved fluorescence rate of the ion during the Doppler cooling process [23]. A similar technique combining the imaging approach and the time-resolved scattering method to determine the heating rate was recently demonstrated [24]. Both these techniques involve heating up the ion to temperatures at-least a few orders of magnitude above the Doppler limit, and therefore depend on several simplifying assumptions about the system. We present an alternative way to determine the heating rate of a single ion employing the imaging approach while varying the cooling laser power or its detuning. The advantage of our technique is that for every measurement point the ion is maintained in a state of thermal equilibrium during the entire measurement sequence. As detailed below, when varying the cooling laser power the effect of a finite heating rate is most evident at low powers, i.e. at low Rabi frequencies and hence low photon scattering rates. Here we again benefit from the collection efficiency of our setup which enables the acquisition of images with sufficient signal-to-noise ratio even from faint light sources.
Theory
The temperature T of an ion in an harmonic trap under weak confinement conditions can be approximated as T n k B w »¯, where n is the average excitation number of the harmonic oscillator, ω is the trap frequency and k B is the Boltzmann constant [17]. n in turn is related to the rms spread σ i of the ion in position space as where m is mass of the ion. In the experiment, we measure σ i by imaging the ion, and thereby determine n and T.
In order to determine the heating rate ζ induced by external factors, we use a simple model of laser cooling [25] which neglects additional heating or cooling due to micromotion. Since micromotion is well compensated in our experiment, this model is well suited to describe the cooling process. Cooling as well as heating induced by interaction of the ion with the cooling light is governed by scattering of photons from the near-resonant cooling beam. The steady state scattering rate of these photons is given by Γ·ρ ee , where Γ is the spontaneous emission rate of the cooling transition and 4 2 ) is the steady state excitation of the ion. Δ is the detuning of the laser from the atomic resonance and Ω is the Rabi frequency. Particles confined in harmonic traps can have anisotropic temperature, depending on the angle made by the cooling beam with the trap axes [16]. To include this effect in our model, we define an effective k-vector, k k cos , where α is the angle made by the cooling laser with a trap axis. The cooling rate along the chosen trap axis is given by The heating rate during the final stages of Doppler cooling can be approximated as The first term in the brackets corresponds to the momentum change along the trap axis due to absorption of a photon, while the second term corresponds to the momentum change due to spontaneous emission along this direction. ξ is a geometry factor that originates from the spatial emission characteristics of the scattered photons.
In our experiment, we use a J=1/2 to J=1/2 transition with a nearly isotropic emission pattern. Therefore, we use a geometry factor of ξ=1/3. In addition, we use a constant factor ζ to include any kind of heating other than photon scattering of the cooling light in the model. The equilibrium temperature is reached when the heating and cooling rates are equal: Below, we will measure σ i while either varying Ω or Δ. In both cases, we will obtain ζ by fitting our model to the experimental data.
Experiment
The schematic of our experimental setup is shown in figure 1. We trap a single 174 Yb + ion in the focal region of a deep parabolic mirror using a stylus like ion trap [26]. The trap is driven with a radio frequency (RF) signal at 2 5.2 MHz RF p W = · and an amplitude of 1 kV. The distance of the ion to the closest electrode is estimated to be 300 μm. Excess micromotion is compensated using a set of four electrodes [26] reducing residual electric fields to magnitudes below 0.45 0.08 V m 1 -.
The trap is mounted on a XYZ piezo translation stage (PIHera P-622K058) with a positioning accuracy of about±1 nm. With the aid of the piezo stage, the ion can be positioned and scanned in all three directions around the focal point of the mirror. A 370 nm frequency doubled diode laser (Toptica) is used for Doppler cooling the ion. The ion is repumped from the metastable D 3 2 state with a diode laser (Toptica) at a wavelength of 935 nm. The detuning of the lasers is set by using 200 MHz Accusto-Optic-Modulators (AOM), aligned in 'double-pass' configuration, and driven by the amplified signal of a Voltage Controlled Oscillator (VCO). The lasers are stabilized to a frequency comb (Toptica DFC). The frequency shifted beams are coupled into polarization maintaining single mode optical fibers, and focused onto the ion using a 400 mm focal length lens (L1). The optical power of the cooling beam can be tuned by varying the RF power supplied to the AOM using a Variable attenuator (VA). The parabolic mirror (focal length of 2.1 mm) collimates the fluorescence light scattered by the ion, and acts as an objective for our imaging system. The mirror covers 82% of a 4π solid angle, i.e. it collects 82% of the photons radiated by an isotropic emitter [19], neglecting the aluminum mirror's finite reflectivity of 0.9. A 300 mm focal-length lens (L2) along with a one-to-one telescope using lenses of focal length 50 mm (not shown in figure 1) is used to image the ion on an electron-multiplying charge-coupled device (EM-CCD) camera (Princeton Instruments PhotonMAX 512B) with a pixel size of 16 μm. A flip mirror (FM) directs the fluorescence photons instead to a Photo-Multiplier-Tube (PMT-A). The trap frequencies were measured to be 205 and 196 kHz in the lateral directions (X and Y), and 390 kHz in the axial direction (Z) by applying AC fields to one of the trap electrodes. The cooling beam has an angle α of 71°with both the lateral trap axes.
As introduced above, we measure the temperature of the ion by determining the width of the image recorded on the EM-CCD camera. Due to the geometry of the trap electrodes (see [19]), the lateral trap axes make an angle of 45°with respect to the edges of the pixel array of the camera. Therefore, we rotate the images by nearest neighbor interpolation to make the pixel array axis coincide with the trap axis 5 . For simplicity, we restrict the discussion to one spatial dimension.
First, we project the image onto the horizontal direction by summing over all pixels in each column. We then determine the rms image width σ from this projection by using a 1D Gaussian fit. The image recorded on the camera is a convolution of the imaging point-spread function (PSF) and the 'true image' of the ion. Assuming both the PSF and the true image to be Gaussian spots, the width of the recorded image can be approximated as In order to determine the temperature of the ion, we need to extract σ i from the measured σ. For this process the magnification M of the imaging system as well as the width PSF s of the imaging PSF need to be known. M is measured by moving the ion in lateral directions, and measuring the image shift on the camera as outlined in appendix A, yielding M=113±2. We use PSF s as a free parameter in the fitting procedure discussed below.
Several example images acquired at different Rabi frequencies Ω are shown in figure 2. The Rabi frequency is obtained by one calibration measurement at fixed power (see appendix D). All other values of Ω are then calculated from the power of the cooling laser and the power used in the calibration measurement. As expected, the width of the images in figure 2 varies with the Rabi frequency Ω.
We now turn to the determination of the heating rate ζ. We fit our model to a set of image widths σ by varying either Ω at fixed Δ or vice versa. The free fit parameters are ζ and PSF s . The result of the measurement and the fit for varying Ω at a fixed detuning 2 13MHz p D =are shown in figure 3. The increase of the image width and thus the ion temperature at very small Rabi frequencies indicates a non-zero excess heating. Here, the number of photon scattering events is too small to compensate for non-radiative heating processes. On the contrary, in the absence of such heating processes the spatial spread of the ion and hence the measured image width would remain at a low value also for Rabi frequencies approaching zero. Moreover, the smaller the heating rate the smaller will be the increase of the ion's spatial width and the smaller will be the Rabi frequency at which this increase may become recognizable. Therefore, the determination of low heating rates benefits from imaging optics with large collection efficiency.
The lowest Rabi frequency investigated in figure 3 corresponds to a saturation parameter of 3×10 −4 . For the life time of the excited state of the cooling transition (8.1 ns) and the used detuning this corresponds to about 6.5 × 10 3 photons per second scattered into the full solid angle. In view of inevitable losses in any practical detection beam path, the above number underlines the necessity of imaging optics covering a large fraction of the solid angle.
The heating rate as determined from the fit shown in figure 3 is 0.38±0.07 quanta ms −1 . The width of the imaging PSF is 6.6 2.7 m PSF s m = , which is in good agreement with the expected PSF of 7.1 μm determined from simulations including the interferometrically measured aberrations of our parabolic mirror [27] (see appendix C). The average phonon number n and thus the temperature of the ion for any Ω can now be determined using these parameters.
The lowest measured σ i is 0.166±0.013 μm, for a Rabi frequency of Ω=0.23 Γ. This corresponds to a mean phonon occupation number n of 97±15, and a temperature of 950±147 μK. In the Doppler limit, the temperature according to k T 2 Thus, the temperature of the ion is found to be about twice this Doppler limit, mainly due to a large angle between the cooling beam and the trap axis.
Recalling the finite amount of excess micromotion one could argue that the measured spatial width of the ion is enlarged in comparison to the prediction of a Doppler cooled harmonic oscillator. As detailed in appendix B, this contribution can be estimated to be not larger than 8.3±1.5 nm. This value is far below the smallest measured size and therefore neglected. Similarly, the effects of a time-dependent trapping potential have been shown to enlarge the ion's spatial spread by about only 5% for trap parameters comparable to the ones used here [28].
Furthermore, it can be seen that for the measured temperatures, the contribution of the PSF ( PSF s ) to the measured image width (σ) is much smaller than the contribution from spatial extent of the ion wavefunction (σ i ). Hence, this method can be used for measuring even lower temperatures. From the standard error estimates of PSF s and M, we estimate the minimum measurable temperature with a 50% relative error to be ≈200 μK 6 , which is well below the standard Doppler limit. An alternative way to measure the heating rate of the ion is to measure σ when varying the detuning Δ. We fix the cooling beam power such that Ω=0.2 Γ. The detuning is varied by using the VCO, and the image width is measured as a function of the detuning. The result is shown in figure 4. From a fit we extract a heating rate of 0.22±0.07 quanta ms −1 , which is in fair agreement with the previous measurement.
Conclusion
We have demonstrated a technique to measure the absolute temperature of a single ion and its heating rate by measuring its spatial probability distribution in the trap. The high resolution image of the ion obtained by using our parabolic mirror as imaging tool allows us to measure temperature close to the Doppler limit, indicating the potential to perform thermometry below the Doppler limit. This would be of particular interest for measuring the temperature of an EIT cooled ion. The feasibility of imaging EIT cooled atoms using photons scattered off the cooling beams has been demonstrated recently [29].
We have also measured the heating rate in our trap, while the ion is constantly maintained in a thermal equilibrium. Therefore, this technique might be useful for traps exhibiting high anharmonicity or temperature dependent heating rates.
where r k (k = x, y, z) represents the ion position in each spatial dimension, and a q 2 2 is the secular trap frequency. RF W is RF frequency which is 2π·5.2 MHz in our experiment. a k and q k are the trapping parameters with a k ≈0 by design in our trap, which leads to q q q , , 0.11, 0.11, 0.21 x y z » { } { }for our operating trap frequency. r k 0, is the amplitude of secular motion, and r k , is the shift in the position of the ion due to a stray field from the node of the pseudo-potential. The last term in equation (B.1) represents the broadening due to excess micromotion.
The shift due to a static electric field ò k is r Q m k k k , 2 w = ( )( )with ion charge Q and mass m. Using our imaging setup we measure this shift in x direction while varying the secular frequency ω x (see figure B1). We determine the stray electric field from a fit to be −0.45±0.08 V m −1 . At our operating trap frequency this would result in a shift of r 150 27 nm We can now determine the amplitude of excess micromotion to be 8.25±1.48 nm. Since this is small compared to the lowest measured rms ion width of 166 nm in our experiment, it appears reasonable to neglect the excess micromotion contribution in our theoretical model.
Appendix C. Imaging PSF
We simulate intensity distribution of a radially polarized doughnut mode focused by our parabolic mirror, including the interferometrically measured aberrations by a generalization of the method presented in [31]. We obtain a FWHM width of the intensity distribution of 148nm for our wavelength. Including the magnification M of our imaging system, this translates to an expected PSF 7.1 μm at the EMCCD camera.
Although also extractable from the fits presented in section 3, we give an independent estimate of the size of the PSF of our imaging system as a consistency check. We generate a collimated radially polarized doughnut beam at the wavelength of the P S 1 2 1 2 transition at 370 nm wavelength as described e.g. in [32]. This mode is focused by the parabolic mirror. The rediverging beam is collimated again by the paraboloid and also imaged onto the EM-CCD camera. It thus passes the same optical elements as the fluorescence photons detected during the temperature measurements. The rms width of the image on the EM-CCD chip is determined by 1D Gaussian fits as shown in figure C1, yielding a width of 12.3 0.5 m PSF s m = and 16.3±0.5 μm for the horizontal and vertical direction, respectively. Figure B1. Mean x-position of the ion determined from its image on the EM-CCD chip as a function of the trap frequency in x direction. The origin of the coordinate system is arbitrarily chosen, and the ion x-position for each data point is measured by a Gaussian fit. The solid (red) line represents a fit of the measured points to the function r x Qm , where x 0 is the node of the pseudo-potential of the trap in this coordinate system. The free parameters determined from the fit are x 0 =453±38 nm and ò x =−0.45±0.08 V m −1 .
The PSF s extracted from these measurements is also influenced by residual aberrations stemming from the optical elements used for preparing the doughnut beam. Moreover, this beam is reflected twice at the surface of the parabolic mirror. Thus, aberrations due to a non-perfect parabolic shape of the mirror [27,32] are imprinted twice onto this beam. The phase front of the fluorescence photons emitted by the ion carries these aberrations only once. Furthermore, the spatial mode of the laser used in that measurement is not the same as the average spatial emission pattern of a 174 Yb + ion emitting photons on the P S 1 2 1 2 transition. After collimation by the parabolic mirror, the intensity pattern of the ion's fluorescence is of Lorentzian shape [26]. Therefore, the width of the PSF obtained in this measurement can be considered as an upper bound for PSF s in the temperature measurements.
Appendix D. Determination of the Rabi frequency
In order to determine the temperature of the ion from the image size, it is essential to precisely measure the onresonance Rabi frequency Ω. We measure the effective Rabi frequency W¢ by performing a Hanbury-Brown-Twiss type experiment on the fluorescence photons. The detuning of the cooling beam is fixed at Δ=−Γ/2. The power of the cooling beam, as measured by a power meter (Ophir Nova II), is fixed at a calibration value of P = 50 μW. This value is chosen such that W¢ D , which makes it possible to observe Rabi oscillations in g (2) measurement within the decay time. The on-resonance Rabi frequency is then determined from W¢ and , 2 435 2 s . The fluorescent light from the ion is split using a 50/50 beam splitter, and detected using two Photo-Multiplier Tubes PMT-A and PMT-B. A Time-to-Digital Converter is used to measure a Start-Stop correlation histogram between the PMT clicks, with a timing resolution of 161 ps. The normalized correlation function (g (2) (τ)) shown in figure D1 oscillates with a period that corresponds to the Rabi frequency. Since Ω ∝ P , for subsequent measurements we determine Ω by measuring the cooling beam power P. | 5,289.2 | 2019-05-22T00:00:00.000 | [
"Physics"
] |
Historical Feature Pattern Extraction Based Network Attack Situation Sensing Algorithm
The situation sequence contains a series of complicated and multivariate random trends, which are very sudden, uncertain, and difficult to recognize and describe its principle by traditional algorithms. To solve the above questions, estimating parameters of super long situation sequence is essential, but very difficult, so this paper proposes a situation prediction method based on historical feature pattern extraction (HFPE). First, HFPE algorithm seeks similar indications from the history situation sequence recorded and weighs the link intensity between occurred indication and subsequent effect. Then it calculates the probability that a certain effect reappears according to the current indication and makes a prediction after weighting. Meanwhile, HFPE method gives an evolution algorithm to derive the prediction deviation from the views of pattern and accuracy. This algorithm can continuously promote the adaptability of HFPE through gradual fine-tuning. The method preserves the rules in sequence at its best, does not need data preprocessing, and can track and adapt to the variation of situation sequence continuously.
Introduction
With attacks becoming more prevalent, the traditional static passive defense and whole system consolidation are hard to keep up with the changing rhythms, which have huge amounts of investment and affect the network performance. In this case, the dynamic, proactive, and targeted defending measures have been presented, most of which rely on attack situation forecast, that is, network attack situation sensing (NASS) [1,2]. NASS aims at forecasting future evolution trend of network attack situation based on historical features and current attack indications, guiding dynamic defense, and allowing administrators to take corresponding measures in advanced, and effective manner to quickly respond to the complex and ever-changing attack threats [3,4].
Rarely studying attack situation forecast, previous researches mostly using existing methods, such as autoregressive moving average model (ARMA), grey model (GM), and radial basis function neural network (RBFNN) [5][6][7][8]. ARMA identifies the dependence relationship and autocorrelation of situation sequences and establish mathematical prediction model [9]. It requests that situation sequences or their certain step difference satisfies the steady suppose, which is too strict to increase suitable scope. As one of GMs, GM(1,1) firstly weakens the randomness of situation sequences by using accumulation, secondly fits the born sequence through index curve, and then does regressive restitution after prediction, which can embody monotonously and slowly changing trend but hardly reflect some characteristics such as random rove and periodic fluctuation [10,11]. Grey Verhulst is suitable to describe the situation sequences with swing development according to "S" or anti-"S" form [12], and the method dividing the changing line into several stages does not lack rationality, but the difficulty is how to predict the occurrence moment and lasting time of each stage [13]. RBFNN utilizes the nonlinear characteristic to describe the regulation contained in situation sequences [14]. However, evolving regulation of attack situation is infinite and changeable; a practical type neural network with small scale cannot solve well [15,16].
Situation sequence contains massive complex and inconstant evolution trends, beyond the expression and prediction 2 The Scientific World Journal capability of traditional methods only by some formulas, functions or via some training [17,18]. Most traditional methods suffer from the confliction among training samples, rely on data preprocessing and artificial intervention heavily, do not support incremental training, and need to rebuild model once situation sequence changes [19][20][21]. Therefore, a situation prediction method based on historical feature pattern extraction (HFPE) is presented. The method measures the similarity between historical feature from the aspects of pattern and accuracy and utilizes multiple order difference operation to discriminate trends. It searches similar indications from recorded historical situation sequence, measures the link intensity of occurred indication upon subsequent effect, and infers the recurrence possibilities of some effects according to current indication. An evolution algorithm is introduced to measure prediction deviation and improve the adaptability of prediction algorithm continuously via gradual fine-tuning.
This paper proceeds as follows: Section 2 discusses algorithm principle for HFPE. Section 3 clarifies algorithm establishment and analysis. Section 4 presents the experiment results and Section 5 concludes the paper.
Basic Definition.
Looking from mathematical form, the continuous time-varied curve, = ( ), is commonly applied to describe the evolving process of attack situation. This curve is carried out by computer through sampling method, that is, to sample situation values with time interval , and then obtains discrete time sequences composed by ( , ), where represents the situation value at moment . To facilitate the research, a basic definition is made as follows: let ( , ) be the segmental subimage with neighboring segments from moment , let be the segmental gradient, let ( , ) be the gradient sequence, let ( , +1 , . . . , + −1 ), ( , ) be the characteristic spectrum of ( , ), let be zero vector; then (1) For the th component product of ( , ), + , the angle of inclination, + , can be defined as The stretch rate from ( , ) to ( , ) can be calculated by ( , , ), which is defined as [ , , ] is utilized to adjust the stretch rate, where is the prediction steps.
Prediction Principle.
Looking from probability theory and statistics, similar situation curve shapes are more probably derived from similar origin, mechanism, and impact, subsequently resulting in a similar subsequent effect. From the point of view of statistics, when the precedence relations of sequences in time appear frequently, it usually meant that the logical causal relationship exists in a certain degree.
It is supposed that ( , ) and ( , ) are known historical feature subpatterns, from the same pattern, < , and the further trend after > + is unknown and needed to be predicted. If ( , ) is similar with ( , ), then it can be deduced that the origin, mechanism, and impact in [ , + ) are similar with those in [ , + ), and the history after + may be repeated after + with some differences. According to this principle, the slope of the line segment behind can be forecasted bŷ+ is utilized to control the predicting steps. When = 0, 1, 2, . . . , − 1, the trend prediction curve can be recurred by and̂+ + .
Measurement System
2.3.1. Fitting Degree. Firstly calculate the angle cosine similarity between slope vectors, secondly introduce more order difference operators to obtain the trend difference of qualitative change and quantitative change, and then acquire the narrowing fitting degree by the difference of similarity degree and trend difference.
The trend differences of qualitative change and quantitative change are denoted by 1 ( ) and 2 ( ), respectively, and the former of which stands for the pattern difference, The Scientific World Journal 3 and the latter stands for the accuracy difference. The above two parameters can be derived by Thus the composite trend, ⊥ ( ), can be defined by Let ∇ represent backward difference operator, and define and then the order differential recursive equation can be obtained by in which is a positive integer, and (9) meets Let ∇ ( , , ) denote the trend difference between the feature patterns ( , ) and ( , ); then The fitting degree function, ( , , ), can be defined by where the large value of ( , , ) represents a fine fitting, and for −1 < ( , , ) ≤ 1 and 0 < ( , , ) ≤ 2, it can be derived that The occurrence probability of ( , , ) > 0 may be 50% statistically, which is too big. Therefore, it is necessary to subtract the penalty term, ∇ ( , , ), and filter ( , , ) by the threshold (0 < < 1) to narrow the fitting degree.
Universality Degree.
Divide the attack situation subsequence into two parts, that is, occurred indication and subsequent effect; the values of the domination intensity of the former to the latter (or call link intensity between the two parts) may be high or low, some of which have a far-ranging representative, and some just have rare earth especially instance. If all the values are treated evenly, then the prediction accuracy will be affected seriously, so it is important to outstand inevitable link of the high intensity and weaken accidental link of the low intensity.
Let [ , , ] be the universality value of ( , + ) in the historical feature pattern (0, ), where max can be derived by The value of max will be updated with the change of [ , , ] and can be accessed directly without waiting to calculate. The universality value can be shined upon to universality degree in (0, − ] by function ( , , ), which is shown as follows: The larger value of universality degree reflects finer representativeness of ( , ) and its extension and more exact patterns predicted by ( , + ). Otherwise, ( , + ) is just a special example, and the prediction effect is worse.
Contrast Degree.
The predication results of situation are usually impacted by link intensity of several different weights. The function mechanism often changes; that is, sometimes they work with a community decision and sometimes with an individual domination. Therefore, it is necessary to trace and adjust between outstanding statistics effect and showing individual advantage. It is supposed that̃1,̃2, . . . ,̃are not normalized weights, which can be adjusted tõ1,̃2, . . . ,̃by sensitization index ( > 0). Then the standardized weight can be derived by and comparison degree / can be obtained by =̃.
Algorithm Establishment and Analysis
As shown in the figure, the preparation part circularly promotes the sliding window ( , ), selects poor values of fitting degree ( , ) to reject, and sensitizes the product of universality degree ( , , ) and fitting degree ( , , ), which is assigned to . The prediction part first checks whether historical feature pattern set has record. What calls for special attentions is that the value of ( , ) in the sliding window or the fitting degree value of it with ( , ) in the occurred indication cannot be too small, because the smaller the above value, the poorer the contribution to prediction valuê+ .
Evolution Algorithm.
Evolution algorithm is introduced to measure predicting deviation from the views of pattern and accuracy, which can be fine-tuned to raise the adaptability of prediction algorithm.
The accuracy of adjusting to × can be derived by which is based on current weight set and (18) As shown in Figure 2, the evolution algorithm carries on the variables and results of the prediction algorithm and works to promote adaptability after acquiring measured value. Δ is an adjustment variable for and meets − −1 ≤ Δ ≤ −1 . If rises or the distance between | | and ln drops, then the adjustment amplitude becomes lower, else becomes higher. If | | < ln , then decrease the threshold to soften the terms, else increase the threshold. Δ is calculated , then the prediction according to ( + , ) is accurate, and the value raising can be large. To determine , select the best one among value lowering by 5%, current value, and value rising by 5%, and restrict it by a reasonable range to prevent passivating or sharpening. Figure 3 gives an example of pre-dictinĝ (13,2) according to the historical feature pattern Table 1. When = 5, the slope becomes larger at = 7 and smaller at = 12, which are reflected through ∇ 1 7 > 0 and ∇ 1 12 < 0 derived by (9), and the relative penalty value is recorded by ∇ (5, 10, 3). And through normalization process, the elements of set are and so forth, and step trend can be predicted. It can be seen that this scheme has the ability to identify multiple long-range correlation contained in the same situation sequence.
6
The Scientific World Journal This part is analyzed according to evolution algorithm. Assuming that 13 = −0.86 and 14 = 0.00, so | | = 2, which is smaller than ln 13; thus, the value of needs to be lower, and once | | > 2, then raise the value of . It can be known that the changing value of universality degree [0, 3, 2] is 1.00 × 1.00, and raising this degree can strengthen the role of vector (0, 5). The changing value of [5,3,2] Table 2 shows that (5, 3, 2) becomes smaller, and becomes larger with continued evolution, which results in rapid rise of 0 / 5 , and approach between prediction value and measured value.
With the passage of time, and keep unchanged, grows linearly, and the algorithm can delete stale data, save recent data, and correct fitting threshold and universality degree. The above process can be complicated not only by autonomous evolution, but also by artificially modified parameters.
Experiment Results Analysis
The traditional indexes utilized to measure the prediction accuracy include mean absolute error (MAE), standard deviation error (SDE), and mean absolute percentage error (MAPE) [21] derived by This section selects MAPE to obtain the relative error between prediction pattern and measured pattern, which is denoted by . The standard deviation of relative error components is denoted by std . Figure 4 is a critical subsequence selected from actual network attack situation records, which includes various features such as ascent trend, saturation trend, decline trend, periodic fluctuation, and stochastic disturbance. From the view of the experimental prediction results, the relative errors of HFPE, ARMA, GM(1,1), and RBFNN are 3.28%, 5.89%, 7.18%, and 16.11%, respectively. As shown in Figure 5, in the experiment, ARMA, GM(1,1), and RBFNN need to be artificially identified and protected against cyclical situation fluctuations. The difference transformation utilizes 12 as the distance and is restored after prediction to prevent poor prediction effect; otherwise, the relative errors of GM(1,1) and RBFNN may reach 59.67% and 73.99%, respectively. However, the above method is special, cannot be spread for that data preprocessing of these algorithms does not exist in universal law. On the contrary, HFPE can maintain adaptation to complicated and changeable trends but does not need data preprocessing or artificial cognition.
Experiment 2.
This experiment is to randomly choose subsequences with similar parts, repeat 20 times, and then calculate the average value.
From the view of the experimental prediction results, the relative errors of HFPE, ARMA, GM(1,1), and RBFNN are 8.09%, 20.89%, 44.89%, and 34.75%, respectively. If the situation sequence selected does not exist in any principle, then the relative errors will be 3.96%, 21.72%, 37.47%, and 53.54%, respectively. Figure 6 shows one group of data, in which = 42 is a boundary for historical feature pattern and prediction feature pattern.
If put all groups of the historical feature patterns into a new long sequence, and repeat above prediction, then the performance of ARMA and GM(1,1) drops rapidly, and that of HFPE does not change much for that longer sequence containing more correlation is benefit to prediction.
Experiment 3.
To compare differences among four algorithms, random data are utilized to simulate situation sequences. First, extract random data with bits from the entropy pool of Windows 7 system. Then randomly gather subsequence with 16 bits, the former 8 bits of which are occurred indication and the latter 8 bits are subsequent effect. Thirdly, splice occurred indication behind the random sequence to form a historical feature pattern and treat the subsequent effect as a prediction feature pattern. Let us make 100 groups of experiments to test each algorithm's capacity in resisting random interference and in identifying the correlation with far distance. The average results are listed in Table 3.
It can be found from the table data that HFPE has the best performance among the four algorithms. When the scale of experiment is large, this conclusion can be repeated well. And ARMA and RBFNN cannot deal with the random sequences with long bits, while HFPE can perform smoothly.
Conclusion
This paper proposes a prediction method based on historical feature pattern, that is, HFPE. The main principle of this algorithm is shown as follows. Fitting degree is introduced to measure the similarity among subsequences from the views of pattern and accuracy. Universality degree is utilized to test the representation of subsequence and its epitaxy. Contrast of the weight system is adjusted by sensitized index, which gives prominence to statistical effect in passivation | 3,855.6 | 2014-04-27T00:00:00.000 | [
"Computer Science"
] |
Social Cost of Leptospirosis Cases Attributed to the 2011 Disaster Striking Nova Friburgo, Brazil
The aim of this study was to estimate the social cost of the leptospirosis cases that were attributed to the natural disaster of January 2011 in Nova Friburgo (State of Rio de Janeiro, Brazil) through a partial economic assessment. This study utilized secondary data supplied by the Municipal Health Foundation of Nova Friburgo. Income scenarios based on the national and state minimum wages and on average income of the local population were employed. The total social cost of leptospirosis cases attributed to the 2011 disaster may range between US$21,500 and US$66,000 for the lower income scenario and between US$23,900 and US$100,800 for that of higher income. Empirical therapy represented a total avoided cost of US$14,800, in addition to a reduction in lethality. An estimated 31 deaths were avoided among confirmed cases of the disease, and no deaths resulted from the leptospirosis cases attributed to the natural disaster. There has been a significant post-disaster rise in leptospirosis incidence in the municipality, which illustrates the potential for increased cases—and hence costs—of this illness following natural disasters, which justifies the adoption of preventive measures in environmental health.
Keywords: disaster assessment; cost of illness; health care costs
Introduction
When communities struggling with social, environmental, or health vulnerabilities are affected by extreme events such as hard rains, the effects may worsen enough to cause disasters that could lead to a wide range of material, environmental and human loss. These events may eventually lead to an increased occurrence of some diseases [1][2][3], such as leptospirosis, which is often connected to episodes of heavy rainfall. In the State of Rio de Janeiro (Brazil), the uncontrolled urban growth in naturally vulnerable areas, the urban soil compaction, and the deficits in basic sanitation services increase the frequency and severity of environmental disasters caused by extreme events [4]. The State of Rio de Janeiro has some regions that are seriously vulnerable to extreme events, including the Mountain Region that comprises 14 municipalities.
Barata et al. [5] demonstrated that the municipalities of Nova Friburgo, Petropolis and Teresopolis, located in the Mountain Region, were among the most susceptible to extreme climate-related events due to their geomorphology and human occupation, with a high potential for human, material and environmental damage [6]. Indeed, on the night of January 11, 2011, heavy rainfall in the Mountain Region caused one of the worst mass movement disasters ever recorded in Brazil [7], ranked by the United Nations as the world's 8th largest landslide in the last 100 years, as reported by Busch and Amorim [8]. The death toll amounted to more than 900, and another nearly 35,000 people either lost their homes or were displaced in the affected municipalities of the Mountain Region [8], illustrated in Figure 1. Note: Source-Archive of authors, 2012. Produced from the database of the Brazilian Institute of Geography and Statistics (IBGE) [9]. Nova Friburgo, highlighted in Figure 1, was one of the most severely affected counties, where 3,000 landslides were recorded [8], along with damage to water, power, transport, telecommunications and health services. In this municipality alone, 429 people were killed, and 3,220 were left homeless [10]. The disaster entailed costs to the health sector and society at large, some of which have been ignored, such as the social cost of leptospirosis cases attributed to the calamity.
Leptospirosis was one of the diseases that demonstrated a sharp rise in occurrence after the disaster; in Nova Friburgo, the county was targeted with specific measures of epidemic control and notification. The real cost of these cases to the municipality of Nova Friburgo has not yet been measured. Underestimated costs may hinder the development of both disease control and disaster prevention strategies because factual analysis remains limited to the immediately visible environmental, material, and human damage.
Analysis of the financial and social impact is important for disaster-related diseases, such as leptospirosis, because the results may signal how much an extreme event can increase the cases-and hence the costs-of the illness. Therefore, the aim of this paper is to estimate the social cost of leptospirosis cases attributed to the disaster that struck Nova Friburgo (State of Rio de Janeiro, Brazil) in 2011.
Experimental Section
This study includes cost-of-illness analyses for confirmed leptospirosis cases, and avoided cost analyses for syndromic measures adopted in the county. The term "social cost" refers to the total costs and includes both society and health care system costs (i.e., represents not only a portion of costs allocated to the population, but integrates the sum of all costs of a disease).
Scope
Nova Friburgo keeps records of past health response actions that were adopted, which provided ground for the economic assessment as described in this article. All confirmed cases of leptospirosis attributed to the disaster by the local health authorities were included in this study. These cases had onsets of symptoms between 12 January and 22 March 2011. The recommendations contained in the Guide to Epidemiological Surveillance from Brazil [11] were adopted for confirmation of the cases. These recommendations included the procedures for epidemiological research and conducting laboratorial tests and clinical research for suspected cases.
The laboratory method of choice depended on the developmental stage of the disease in the patient, and the two most used in Brazil are the Enzyme Linked Immunosorbent Assay (ELISA) and Microscopic Agglutination Test (MAT) [11]. The number of laboratory tests performed by each suspected case was variable in Nova Friburgo. The criteria for confirmation were either clinical-laboratory-when the laboratorial test results and the signs and symptoms presented were compatible with the disease-or clinical-epidemiological-when presented symptoms were associated with epidemiological antecedents (such as contact with flood), and for some reason, samples were not available for laboratory tests or a single sample collected before the 7th day of the illness did not have a positive result. In the medical records, there was only information if the case was confirmed or discarded, without information on probable cases.
Source of Data
The study used secondary data supplied by the Health Surveillance sector and the Primary Health Care sector of the Municipal Health Foundation (FMS) of Nova Friburgo. Several of these data are not openly available. Pertinent data were obtained from reports of epidemiological surveillance, financial and management reports, medical charts of leptospirosis notifications, and charts of empirical therapy. Data collection was conducted between December 2012 and April 2013. Furthermore, data on county characterization were obtained from the Brazilian Institute of Geography and Statistics (IBGE) [12], the Brazilian Support Service for Micro and Small Enterprises (SEBRAE) [13], the Federal Ministry of Health [14], and the National Registry of Health Establishments (CNES) [15].
Costs to the Health System
The Unified Health System (SUS) defrays public health services in Brazil, and its expenses are named direct costs, which include medical costs and non-medical costs. The direct medical costs consist of health system expenses, including both inpatient and outpatient procedures. The expenses incurred from patient companion care (i.e., follow-up of patients in hospital) represent direct non-medical costs. Data on direct medical costs were gathered from financial and epidemiological surveillance reports, as well as records of leptospirosis notifications. These records are maintained by the Municipal Health Foundation (FMS).
The costs from patient companions were calculated on the basis of the companion per diem values listed in the Management System of Table of Procedures, Drugs, Orthotics, Prosthetics and Special Materials of the SUS (SIGTAP) [16]. Nevertheless, this cost was only included for those cases in which the SUS allows for the permanent companions, specifically for patients under 18 years of age or aged 60 and over [17].
Information about diagnostic tests was retrieved from the medical charts to record the disease. Information on the type and quantity of performed exams was recorded from the patient medical charts, and the costs were accessed from SIGTAP [16] and the Outpatient Information System (SIA) [18]. However, both databases showed zero cost for all the diagnostic tests for leptospirosis. A possible explanation is that specific kits for leptospirosis tests are usually made available to the public health system laboratories, so no additional costs would result from testing. The Central Laboratory Noel Nutels (LACEN-RJ), a major reference to Nova Friburgo for diagnostic tests, was consulted on the matter, and the organization informed that the State Network of Public Health Laboratories typically request the Federal Ministry of Health for the Leptospira ELISA kit, containing 96 individual tests. Because no other types of test kits are used by this institution [19], we could only estimate the cost of this particular diagnostic test.
Costs to the Society
Society has to bear some of the costs related to a disease. In this study, the costs to society were represented by productivity loss (PP), which consists of the labor input that the patient failed to apply to their job activities due to absenteeism relative to the disease. This burden is imposed on the employer because the employee still gets paid for the missed work days. This cost was calculated using Equation 1, based on Motta [20]: [ ' worker s salary social charges PP days off days in month Because no records on absenteeism in the city were available, productivity loss had to be estimated. The recovery period from leptospirosis may last from one to two months, and urinary elimination of Leptospiras may persist for months after symptoms have disappeared [11]. Absenteeism is therefore expected among patients stricken with the disease, due to either the illness recovery period or reasons of sanitary impediment.
Considering that the PP represents the burden imposed on the employer, who pays only for the first 15 days of employee absence, we could exclude those cases in which absence from work was extended for longer periods. The maximum limit for productivity loss was set at 15 missed work days. This number is justified by the analysis of the statistical yearbooks of the Brazilian Ministry of Social Security [21]. The data shows that the monthly average of benefits granted due to leptospirosis under both the Welfare Illness Aid and Accident-related Illness Aid categories in 2011 was low-26.25 benefits per month for the entire country. The data demonstrates that most reported cases of leptospirosis resulted in absences from the workplace for periods not longer than 15 days and are therefore not included in these statistics. The Brazilian social security system only pays benefits from the 16th day of absence.
Two different scenarios were adopted in the calculation of total productivity loss: one refers to the minimum known period of absenteeism, in which lost productivity is equal to the number of hospitalization days; the other refers to the maximum possible period of absenteeism, which occurs if both outpatient and hospital patients are absent for the period most costly to the employer (i.e., 15 days). Finally, PP was considered as the range of values set between the parameters calculated for the two scenarios.
The reference wage values adopted in the calculations included the national minimum monthly wage in 2011 [22,23], the lowest minimum monthly wage in the State of Rio de Janeiro in 2011 [24], and the average monthly wage in the municipality of Nova Friburgo [25].
Empirical Therapy and Avoided Cost Analysis
Empirical therapy adopted in Nova Friburgo consisted of the administration of specific medication for leptospirosis treatment even if there was no diagnostic confirmation, a procedure in which the presence of three characteristic symptoms of the disease was required [10]. The major symptoms to define an eligible case for empirical therapy were fever, myalgia and headache, but the other symptoms of the disease were also considered. This measure aimed to prevent worsening of the patients' condition before their diagnoses were confirmed and avoid increased social costs caused by the disease. The drugs recommended in the Guide to Epidemiological Surveillance were the following: doxycycline (the main drug used in Nova Friburgo), amoxicillin, ampicillin and penicillin. In Brazil, empirical therapy is also called the syndromic approach.
The necessary information for calculating the avoided cost of treatment was obtained from charts used for syndromic surveillance, namely the medications administered, duration of treatment, and dates of procedures. The cost of the syndromic approach comprised drug expenses, as well as the cost of the health care team performing the procedure.
As reported by the Epidemiological Surveillance Service of the municipality, the State of Rio de Janeiro Health Department professionals performed the first procedures and interventions at the calamity site. After leaving, the City staff continued the job. Because there was no accurate information about who actually implemented the measures or how many man-hours were employed in the work, each intervention was attributed the value of US$26.98, which corresponds to 15-minute work by a team consisting of a physician, a nurse, and a community health agent. The calculated value was based on the average wages for these professionals in the region [26][27][28][29]. Drug values were obtained from the Drugs Price List from 2011, which was available on the National Health Surveillance Agency (ANVISA) website [30].
To assess the health sector avoided costs (with not having a local parameter for the pre-disaster period), the ratio of inpatient and outpatient cases in Nova Friburgo was compared to that observed at the national level. These cases were estimated by research conducted about cases of leptospirosis that occurred throughout Brazil during the year 2008 [31], the latest year for which assessment of this type was held in the country. Although this calculation is an estimate of a period other than the period analyzed in this study (2011), it is the most current available parameter. To use this estimate, we assumed that no major changes in the behavior of the disease that could alter this parameter occurred between 2008 and 2011. The number of prevented deaths by empirical therapy was estimated by using the average disease lethality recorded in Nova Friburgo between 2001 and 2010.
Ethical Criteria
This study was approved by the Ethics Committee of the National School of Public Health Sergio Arouca-ENSP/Fiocruz and by the Ethics Committee of the Oswaldo Cruz Institute-IOC/Fiocruz, under CAAE 907112.2.0000.5248. FMS Nova Friburgo signed a Term of Consent for the conduction of the study and collection of secondary data. Additionally, the researchers signed a Confidentiality Agreement.
Results and Discussion
In Nova Friburgo, approximately 182,000 people live within a 933.4 km 2 area, which corresponds to a population density of 195 people per km 2 [12]. This area is one of the three most populous municipalities in the Mountain Region of the State of Rio de Janeiro, concentrating nearly 20% of its entire population [14]. The Human Development Index (HDI) for the municipality is 0.810. The main economic activities are food and beverages services (service sector), clothing and accessories retail (commerce), underwear manufacturing (industrial sector) and cattle raising (agricultural sector). Most households (29%) fall under C1 class, in which the monthly family income is approximately US$889.28 [13].
Of all current health facilities in the city, 65.5% are private; the other establishments (34.5%) belong to the municipal public service [12]. The core public facilities comprise [15]: one Psychosocial Care Center (CAPS), 19 Basic Health Units and Family Health Strategies, one specialized clinic, one Specialized Hospital (Maternity), one General Hospital, three Polyclinics, one Emergency Unit (UPA) and two Terrestrial Mobile Units.
In the post-disaster period between January and March 2011, 525 suspected cases of leptospirosis were treated in public health units, and 177 of these cases received diagnosis confirmation (98 by clinical/laboratory criteria, and 79 by clinical/epidemiological criteria). According to information from the Epidemiological Surveillance Service, the disaster caused an environmental imbalance in Nova Friburgo that changed the leptospirosis behavior previously observed in the county. Therefore, all cases recorded until March 2011 were attributed to the disaster. Indeed, there was an atypical number of confirmed cases in the county in 2011, as shown in Table 1, which displays information obtained from the Brazilian Case Registry Database (SINAN) [32]. This table contains only reported cases with a confirmed diagnosis. Descriptive statistics of outpatient cases are presented in Table 2, and those of hospitalized cases in Table 3. According to the data from these two tables, the majority of cases of leptospirosis attributed to the Nova Friburgo disaster were addressed in outpatient care, and most patients were male. The mean and median ages of hospitalized patients were higher than those of patients receiving outpatient care. Also based on the two tables, the most performed diagnostic test among both hospital and outpatient cases was the Enzyme Linked Immunosorbent Assay (ELISA), which can offer faster results than the Microscopic Agglutination Test (MAT) test, currently the gold standard for leptospirosis diagnosis [33,34]. Among the other tests applied were: indirect immunofluorescence test for leptospirosis and tests for hepatitis A and C.
Most of the cases were cured, although the data on the disease progression of two patients is unavailable. The City Epidemiological Surveillance Service confirmed that no deaths due to leptospirosis were recorded among the cases assigned to disaster. The costs associated with confirmed cases are presented below.
Direct Costs to the Health Sector
The costs to the health system reported in this section include outpatient and hospital expenses. The cost of the 149 confirmed cases treated in outpatient care was nearly US$1,500 in total. This amount includes costs for diagnostic tests and specialist medical consultations expenses. The median outpatient cost was US$9.79. For the 28 confirmed cases that required hospital care, the total cost was nearly US$10,700. The total hospital care cost includes the costs of diagnostic tests, professional services, hospital services and companion care per diems. The median hospital cost was US$346. 44. In summary, the 177 confirmed cases of leptospirosis cost US$12,200 in expenses by the Health Care System, which was considered as direct costs by the Department of Health. The median costs of leptospirosis were higher than the costs of dengue fever, another disease strongly associated with the Nova Friburgo disaster. Among the confirmed dengue fever cases also related to the 2011 disaster, the median hospital cost was US$274.18, and the median outpatient cost was US$6.35 (data calculated based on statistics provided by the FMS-Nova Friburgo).
Costs to Society
Together, the 28 leptospirosis patients who were hospitalized stayed for 179 days in health facilities. Of these cases, 26 patients were of working age and were absent from work for 173 days, which corresponds to a PP of US$3,300 based on the national minimum wage of 2011 [22,23]. This value reaches US$3,700 when the lowest minimum wage in the State of Rio de Janeiro in 2011 is considered [24], and US$5,700 when calculated according to the 2010 average wage in Nova Friburgo [25].
Among the 149 cases treated in outpatient clinics, 129 patients were at an economically active age. The estimated loss for this group ranged from 129 to 1,935 workdays. The estimated PP for outpatient cases ranged from US$2,700 to US$39,800 based on the national minimum wage in 2011 [22,23]; US$3,000 to US$44,800 when considering the lowest minimum wage in the State of Rio de Janeiro in 2011 [24]; and US$4,600 to US$68,700 if using the employee's average wage of Nova Friburgo [25]. The total loss of productivity, considering both hospital and outpatient cases, was estimated for two different scenarios: the first assumed only the minimum known amount of missed work days, which is equal to the total days of hospitalization; and the second considered the maximum possible loss, which would result from patients being absent from work for as long as possible (i.e., 15 days according to the adopted criteria). Based on the 2011 national minimum wage [22,23], the total PP ranged from US$3,300 to US$47,800. Using the lowest minimum wage in the State of Rio de Janeiro in 2011 [24], the total PP varied between US$3,700 and US$53,800. Total PP reached values between US$5,700 and US$82,600 based on average worker wages in Nova Friburgo [25].
Empirical Therapy
Empirical Therapy charts were recovered for 157 (88.70%) of the 177 confirmed cases. The remaining 20 cases (11.30%) had no information. For cases that used the syndromic approach, costs were estimated to be US$4,400 for the health care team that applied the measures and US$1,600 for pharmaceutical expenditures. In total, the estimated cost of the syndromic approach in the county was US$6,000. The cost of the syndromic approach was absorbed by the local health service. The median cost of the syndromic approach among confirmed outpatient cases was US$26.98 and US$46.35 for hospital-confirmed cases.
Avoided Cost Analysis
Empirical Therapy substantially reduced the severity of cases and avoided deaths due to leptospirosis. In Nova Friburgo, only 28 of the 177 confirmed cases required hospitalization. Moreover, there were no deaths among the leptospirosis cases that were attributed to the disaster.
Among the confirmed cases of leptospirosis in the county, the treatment ratio was one hospital case to 5.32 outpatient cases. Based on the estimated ratio for episodes that occurred throughout Brazil during 2008 [31]-0.90 outpatient cases to each hospital case-and considering no major changes in the behavior of disease occurred until 2011, the analysis of avoided cost was based on this national estimate.
Assuming that the empirical therapy (syndromic approach) reduced the ratio of hospital cases in the county and Nova Friburgo would present the same rates assessed in the 2008 national research data, the number of confirmed hospital cases would be 93 (instead of 28), and 84 outpatient cases (instead of 149) would have been recorded. This calculation would result in a total of 177 cases, which was the number of confirmed cases actually recorded. If so, the confirmed cases alone would have cost US$33,000 to the health system. In reality, this cost was US$18,200 (treatment costs and empirical therapy). Therefore, under these circumstances, the syndromic approach avoided US$14,800 in costs to the Health System.
The syndromic approach may have also reduced the costs to society. Between 2001 and 2010, seven deaths due to leptospirosis in Nova Friburgo were reported to the Mortality Information System (SIM) [35]. Considering the total number of leptospirosis cases in the municipality reported in SINAN [32] for the same period, the average lethality of the disease equals 17.95%. In 2011, when empirical therapy was applied, no deaths due to leptospirosis attributed to the natural disaster were recorded. If this reduction in mortality is assumed to be a result of the syndromic approach, then 31 deaths were avoided among the 177 confirmed cases of the disease.
Total Cost of Illness
The total costs incurred by the health system, arising from professional services, outpatient and hospital services, diagnostic tests and empirical therapy, was US$18,200. Because the costs to society, represented by lost productivity, varied according to each scenario-from US$3,300 to US$47,800 in the lowest wage scenario, from US$3,700 to US$53,800 in the intermediate wage, and US$5,700 to US$82,600 in the highest wage scenario-the total social cost of leptospirosis cases in Nova Friburgo due to the disaster of January 2011 may have had various different values: from US$21,500 to US$66,000 in the scenario displaying less productivity loss; from US$21,900 to US$72,000 in the intermediate productivity loss scenario; and US$23,900 to US$100,800 in the larger productivity loss scenario. Table 4 Notes: * Off work period ranging from one to 15 days for outpatient cases. ' Average income of the local population in the amount of US$591.98 [25]. " It was considered the lowest value of 2011, equivalent to US$386.13 [24]. # Value between January and February 2011: US$343.01 [21]. Value effective as of March 2011: US$346.19 [23].
Because no deaths occurred in Nova Friburgo, there were no lost years of potential life in the cases of leptospirosis associated to the disaster. The average hospitalization cost was higher in the study by Souza et al. (US$538.55) whereas in Nova Friburgo, the average cost was US$383.43. The average loss of productivity was also greater in the study by Souza et al. (US$770.86) whereas in this study, the highest average was US$221.31. In Brazil, not all cases are related to disasters, and the search does not always enough active to start the treatment in the early stage of the disease. Most cases in Brazil are moderate or severe, with underreporting of cases in the early stage [11]. Because Souza et al. intended to study the cases that died, the costs of their study may have been higher because these cases may have been the most serious and complex, required longer treatment, and demanded more health services, which would generate a higher cost for both the health care system and society.
Another study about leptospirosis was performed in New Caledonia [37] where an epidemic of human leptospirosis after heavy rainfalls and floods occurred in 2008. The disaster resulted in 135 cases of leptospirosis and five deaths. Eighty eight patients were hospitalized, generating a direct medical cost of 622,894 € (US$989,100). The remaining 47 patients not hospitalized generated a cost of 14,486 € (US$23,000). The total number of lost workdays was estimated to be 1,431 days, corresponding to a loss of 86,340 € (US$137,100). Altogether, the total cost for the 135 cases was estimated to be 723,720 € (US$1,149,200). The average cost of hospitalization was also higher for the New Caledonia study (US$11,239) compared with this study. The average cost of non-hospital treatment was also higher (US$489). The New Caledonia study presented a single value for the loss of productivity, perhaps by having tracked the cases and obtained more accurate responses. Despite the uncertainty in this estimate for the Nova Friburgo study, it surpassed the New Caledonia loss of productivity (when highest wage scenario is considered). Despite the differences in the estimates, both of these studies illustrate the effect of extreme rains on increasing leptospirosis cases and the cost of illness.
In their review of recent literature on the causes, consequences and responses to natural disasters, Freitas and Ximenes [38] emphasized that leptospirosis has had a major effect on health, especially in flooding episodes. In fact, in Nova Friburgo, an average of 3.9 confirmed leptospirosis cases per year were reported to SINAN between 2001 and 2010, whereas in the first three months after the disaster, 177 cases of the disease were confirmed, which was 45.38 times the amount of cases as the municipality's average. Climate scenarios that have been developed for Brazil indicate a probable increase in the number of extreme hydro-meteorological events in the coming years, especially in the South and Southeast regions [39].
Because climate is considered to be a determining factor for the occurrence of infectious diseases such as leptospirosis, which is sensitive to climate variability and extreme events such as floods [40], a higher frequency of cases in these areas can be expected. Despite this connection of leptospirosis with floods, there are other factors that may precipitate its emergence, even during dry seasons. A study developed in Aracaju (State of Sergipe, Brazil) on leptospirosis cases during 2001 to 2007 provided a clear illustration of this situation: the authors found no correlation between rainfall and cases of the illness in the city, concluding that occurrence may increase with rainfall, but even in the absence of rain, a certain amount of cases of the disease will occur [41].
Fensterseifer [42] explained the effects of environmental injustice and social inequalities in increase the number of vulnerable groups to the negative effects of environmental degradation and disaster. In the specific case of the health in Nova Friburgo, poorer social groups were not more affected by the disaster than wealthier groups. Many leptospirosis cases were observed in the municipality's main district and in places that actually represent high economic activity and income concentration levels. The very center of the city, which was heavily impacted, is a good example. Perhaps inequalities have surfaced in access to emergency and response services because those places distant from the urban center and with rugged topography were more difficult to reach, due to barriers in access routes.
Fensterseifer also discussed the extent to which the government should be responsible for damage caused by extreme events. He stressed that the State must seek ways to compensate those affected and meet their basic rights, especially if their vulnerability results from state failure to prevent damage due to climate change. In most cases, the poorest segment of the population comprises the people most affected, who have low autonomy and capacity to respond to the impacts of a disaster [42]. Therefore, the state must act on the resilience of these people, preventing vulnerability and risk situations when everyday life activities resume.
However, aid measures implemented by the State may not adequately incorporate the costs to society caused by the disaster because economic assessments are not routinely performed to support public action. In Nova Friburgo, the estimated cost to society of leptospirosis ranged between US$3,300 and US$82,600, without considering other possible social impacts, such as material losses.
Adopting economic assessments of social costs could lead to more coherent compensation, consistent with the magnitude of losses.
The Health Sector expenses with the empirical therapy may have avoided costs to society because no deaths were recorded. External costs were internalized by the health sector through the syndromic approach. In this approach, drugs prescribed by the Federal Ministry of Health [11] for the treatment of leptospirosis were used, including doxycycline, which is recommended for treatment of the early phase of the disease.
A cost-effectiveness analysis [43] of five different strategies for treating mild febrile illness in patients hospitalized with suspected leptospirosis was performed using a hypothetical cohort of patients over 14 years of age, based on another clinical study conducted by the same authors. The strategies analyzed were: (a) non-performance of diagnostic test or use of antibiotic treatment, (b) empiric treatment with doxycycline, (c) use of doxycycline in cases confirmed through the lateral flow test, (d) use of doxycycline in confirmed cases through the MCAT test, and (e) use of doxycycline in cases confirmed by latex test. The empirical treatment had the lowest direct cost and higher effectiveness compared with the other four strategies. As effectiveness was measured by productivity loss by considering the number of days of hospitalization, the empirical treatment resulted in shorter stays for the patients [43]. The empirical treatment described in this study is similar to the syndromic approach adopted in Nova Friburgo, and it corroborates the potential of such measures to avoid costs to society and to health sector as a preventive measure.
Extreme events are recurrent in Nova Friburgo, some of which result in both human and material damage. As reported by Freitas et al. [44], flash floods hit Nova Friburgo, Teresopolis and Petropolis in 1988, resulting in 227 deaths and leaving 2,000 homeless. In 2000, floods in the same cities led to five deaths. In 2007, according Barata et al. [5], heavy rainfall in Nova Friburgo, Sumidouro, Petropolis and Teresopolis resulted in 23 deaths, 11 of which occurred in Nova Friburgo. Barata et al. [5] also reported that flash flooding in 2005 caused one death in Nova Friburgo. This history, coupled with the impact from the 2011 disaster, justifies the adoption of preventive measures because extreme events have sharply increased the incidence of leptospirosis in the municipality.
The issue of the Service of Epidemiological Surveillance needs to be addressed because the success of such measures depends on how their team is strengthened and capable to play their role. The knowledge of the municipality's epidemiological profile will allow the assessment of existing health risks and provide guidance on what action must be taken to avoid negative impacts to the population. Fostering an epidemiological surveillance system that is sufficiently trained and organized to assess the population's risks and vulnerability, and also capable of quick response, offering documents and records that will guide the work in the region, is paramount [45]. In Nova Friburgo, despite the team's strong effort to record activities and a systematized record of all actions, a lack of support and engagement to structure and strengthen this sector is lacking. This support is vital to good health sector performance in disaster management. Undeniably, the work conducted by the team-at the time of disaster comprising five members, currently only four-was successful. Still, management culture needs to emphasize the importance of systematic work in prevention and active work in disaster response. This goal may be developed by the Epidemiological Surveillance.
Leptospirosis is a disease that can be prevented by improved urban and sanitation conditions, and although natural hazards cannot be avoided, the vulnerability of the population can be reduced.
Leptospirosis cases related to disasters exert a negative social impact that can be avoided, as well as the economic burden imposed on the health sector and to society in general. This value represents the price that is paid for not spending money on measures of disaster prevention, risk management, urban planning, and vector control.
Conclusions
There were 177 confirmed cases of leptospirosis in Nova Friburgo that were attributed to the 2011 disaster. The total social cost of these cases ranged between US$21,500 and US$66,000 in the scenario of lower productivity loss, until between US$23,900 and US$100,800 in the scenario with higher productivity loss. The syndromic approach represented a total avoided cost of US$14,800, in addition to a reduction in lethality. These measures proved to be good preventive strategies against the worsening of cases in the municipality, and they also represented savings to the health sector and society. There has been a significant post-disaster rise in leptospirosis incidence in the city, which illustrates the potential for increased cases-and hence costs-of this illness following natural disasters.
It is important to know the full extent of the social costs of health-related outcomes that can be attributed to disasters, such as increased cases of leptospirosis, because only considering the costs of treating the disease can lead to an underestimation of the true impact of these events. The measurement of the economic and social burden of a disease is a useful tool for health and environment management to decide where and how to apply their resources. Furthermore, assessments of the social cost of disasters can subsidize the state on providing aid measures to affected populations.
The authors hope this work will encourage research on the impacts of leptospirosis and social cost of disasters, especially in Brazil, that will engage in practical studies that can be applied in everyday public management of environmental health.
Author Contributions
Carlos Pereira conducted the bibliographic research, data collection and analysis and wrote the manuscript's first draft. Martha Barata participated in the study's conception and design, recommended bibliography and assisted in writing the paper. Aline Trigo participated in the study's conception, recommended bibliography and helped write the paper. Both authors revised and approved the version for publishing. | 8,048.6 | 2014-04-01T00:00:00.000 | [
"Economics",
"Environmental Science",
"Medicine"
] |
Observable Proton Decay in Flipped SU(5)
We explore proton decay in a class of realistic supersymmetric flipped $SU(5)$ models supplemented by a $U(1)_R$ symmetry which plays an essential role in implementing hybrid inflation. Two distinct neutrino mass models, based on inverse seesaw and type I seesaw, are identified, with the latter arising from the breaking of $U(1)_R$ by nonrenormalizable superpotential terms. Depending on the neutrino mass model an appropriate set of intermediate scale color triplets from the Higgs superfields play a key role in proton decay channels that include $p^+ \rightarrow (e^{+},\mu^+)\, \pi^0$, $p^+ \rightarrow ( e^+,\mu^{+})\, K^0 $, $p^+ \rightarrow \overline{\nu}\, \pi^{+}$, and $p^+ \rightarrow \overline{\nu}\, K^+ $. We identify regions of the parameter space that yield proton lifetime estimates which are testable at Hyper-Kamiokande and other next generation experiments. We discuss how gauge coupling unification in the presence of intermediate scale particles is realized, and a $Z_4$ symmetry is utilized to show how such intermediate scales can arise in flipped $SU(5)$. Finally, we compare our predictions for proton decay with previous work based on $SU(5)$ and flipped $SU(5)$.
I. INTRODUCTION
Proton decay is rightly considered an important observable and discriminator for models of Grand Unified Theories (GUTs). The current lifetime bounds on various proton decay channels by Super-Kamiokande (Super-K) [1][2][3][4][5][6], and the anticipated experimental results from the next generation experiments such as JUNO [7], DUNE [8], and Hyper-Kamiokande (Hyper-K) [9] should provide valuable information for comparing the proton decay predictions by GUT models. In this regard proton decay induced by the dimension five operators in supersymmetric GUTs has been a subject of great interest. The expected dominant decay mode, p → K + ν, in minimal supersymmetric SU (5) has been under intense scrutiny [10,11].
In a recent paper [29] an exciting possibility of observable proton decay from a supersymmetric SU (4) c × SU (2) L × SU (2) R (4-2-2) model mediated by color triplets of intermediate mass range was identified. This 4-2-2 model nicely implements shifted hybrid inflation, as shown in [30]. These studies have prompted the present paper where we consider a supersymmetric hybrid inflation model [31][32][33] based on the flipped SU (5) gauge symmetry, supplemented by a global U (1) R symmetry and Z 2 matter parity. In order to study the contributions to proton decay from the color triplets of 5-plet and 10-plet Higgses, we employ two models of light neutrino masses. The first model utilizes an inverse seesaw mechanism with extra gauge singlets, while the second model assumes R symmetry violation at nonrenormalizable level in the superpotential and employs the type-I seesaw mechanism. These two models lead to proton decay modes in the observable range from color triplet mediation of either Higgs multiplets. The distinctive predictions of various branching fractions and comparison with SU (5) are presented. Especially, a unique prediction for p → K + ν decay is found to serve as an additional discriminator between the present model and previous models of flipped SU (5) [28,34,35] where this mode is highly suppressed. An additional Z 4 symmetry can naturally generate intermediate scale masses for the color triplets from the Higgs 5-plets. This is in contrast to another R-symmetric model recently considered in [34] where one of the color-triplets in Higgs 5-plet becomes naturally light and contributes only to the charged lepton channels. Lastly, in the present model a successful realization of gauge coupling unification is achieved in the presence of intermediate mass color triplets.
The layout of this paper is as follows: In Sec. II we briefly describe the flipped SU (5) model including its field content, the R-symmetric superpotential and some of its uniquely attractive features. Two models of neutrino masses are described in Sec. III. One is mostly based on R-symmetric interactions, and the second model assumes R-symmetry violation in the superpotential at nonrenormalizable level. In Sec. IV we discuss proton decay in Rsymmetric flipped SU (5) model mediated via both color triplets and the superheavy gauge bosons. We mainly focus on mediation by the color triplets which occurs via the chirality nonflipping operators of type LLRR from the renormalizable interactions. The estimates for the proton partial lifetimes for the various channels are presented in the observable range of Hyper-K along with the lower bounds on the color triplet masses and relevant couplings.
The role of an additional Z 4 symmetry for naturally realizing intermediate mass for the color triplets is briefly highlighted.
The issue of gauge coupling unification in the presence of these intermediate color triplet masses is mentioned in Sec. V. In Sec. VI we allow R-symmetry breaking terms at nonrenormalizable level to generate the right handed neutrino masses and also study their impact on proton decay. We identify the dominant contribution of color triplets from the 10-plet Higgses lying within the observable range of Hyper-K. Finally we conclude in Sec. VII.
II. SUPERSYMMETRIC FLIPPED SU (5) MODEL
The Flipped SU (5) gauge group is defined as F SU (5) ≡ SU (5) × U (1) X [21][22][23][24][25][26][27]. The MSSM matter superfields including the right handed neutrino superfield (N c ) belong in the 10 1 , 5 −3 and 1 5 representations of F SU (5). Here and later, if necessary, the U (1) X charge, q(X), of F SU (5) representations are labeled with superscripts. In contrast to SU (5), the right handed neutrinos are required by the gauge symmetry in F SU (5 Table I. It is clear from the table that we can obtain the MSSM decomposition of F SU (5) mutliplets by flipping U c ↔ D c and E c ↔ N c in the corresponding multiplets of the standard SU (5) model [23].
The superpotential suitable for supersymmetric hybrid inflation in F SU (5) with the additional U (1) R × Z 2 symmetry listed in Table-I is given by [31][32][33] where λ, λ and κ are real and positive dimensionless couplings. The SU (5) gauge indices will be suppressed. 2 h ) do not acquire mass from these terms. This ultimately provides the solution of doublet-triplet splitting problem via the missing partner mechanism [25]. The significance of U (1) R symmetry is quite evident here as it forbids the 5 −2 h 5 2 h term to all orders while keeping the electroweak Higgs doublets massless, and by also avoiding dimension five proton decay mediated via the expected 5 −2 h 5 2 h mass term [31]. The MSSM µ term, however, is assumed to be generated by the Giudice-Masiero mechanism [36]. Note that the U (1) R symmetry also forbids the quadratic and cubic terms of S for successful realization of susy hybrid inflation.
The Yukawa couplings, y ij , in third line of Eq. (1) provide the Dirac masses for all fermions. The discussion of tiny neutrino masses and its possible connection with proton decay is included in the next sections. Some additional terms such as, S10 −1 and 10 1 H 5 −2 h 10 1 i , appear at the renormalizable level. Although U (1) R symmetric these terms are forbidden by Z 2 matter parity. The key feature of Z 2 matter parity lies in making the lightest supersymmetric particle a dark matter candidate while forbidding the dangerous dimension four proton decay terms. The last term, W HN , in Eq. (1) is responsible for generating the heavy Majorana neutrino masses necessary for the implementation of seesaw mechanism as described in the next section.
III. NEUTRINO MASSES
In order to accommodate the light neutrino masses responsible for solar and atmospheric neutrino oscillations [37,38], we can employ a inverse seesaw mechanism [39][40][41] with the help of extra gauge singlet superfields S a which have odd matter-parity with R(S a ) = 1. This allows us to include the following additional term in the superpotential at renormalizable level, where i, a = 1, 2, 3. Other terms at the nonrenormalizable level relevant for proton decay are S a 10 1 H 10 1 10 15−3 and S a 10 1 H5 −35−3 1 5 . However, their contribution to proton decay rates is highly suppressed. To implement a double seesaw mechanism we also need a mass term for the gauge singlet superfields S a . However, an explicit mass term, µ ab S a S b , is not allowed due to R-symmetry. We, therefore, include a spurion gauge singlet superfield Σ through the Kähler potential term, y ab where we adopt a basis in which both m (u,ν) = y (u,ν) υ u and µ are real and diagonal, m (u,ν) diag(m u , m c , m t ) and µ = diag(µ 1 , µ 2 , µ 3 ). Applying the inverse seesaw mechanism with µ a |γ ja M |, we obtain the light neutrino mass matrix, which is diagonalized by a unitary matrix U N , namely m diag ν = U * N m ν U † N . This is in contrast to the double seesaw mechanism where µ a |γ ja M | is assumed. See Refs. [42,43] for a recent analogous treatment of double seesaw mechanism in an inflation model based on In general for a given matrix γ ia , the mixing matrix U N can be determined as a function of µ a . However, for numerical estimates we will assume normal-ordered (NO) light neutrino masses with U N equal to a unit matrix. This also allows us to write the mixing matrix This enables us to estimate all relevant proton decay rates mediated by the color triplets in the Higgs 5-plets as discussed in the next section.
An alternative interesting possibility for generating light neutrino masses can be realized by allowing explicit U (1) R symmetry breaking terms at the nonrenormalizable level [44].
As U (1) R is a global symmetry it could be broken in the hidden sector while mediating breaking effects to the visible sector via gravitational interactions. We will assume that the R-symmetry breaking occurs in such a way that it only allows terms with R = 0 charge in the superpotential at the nonrenormalizable level. With Z 2 matter parity present only even number of matter superfields appear with the 10-plet Higgs fields. Therefore, to leading order the following terms are allowed in the superpotential, where γ k , with k = 0, 1, 2, 3, are the dimensionless matrices with family indices suppressed.
As we will see in Sec. VI, these terms play a crucial role in the estimates of proton decay mediated by the color triplets in the Higgs 10-plets.
A neutrino mass matrix in the (N, N c ) basis can now be written as where the third term in the superpotential W II HN provides the mass matrix, M ν c = γ 2 M 2 m P , for the right handed neutrinos. The light neutrino mass matrix is obtained via the standard seesaw mechanism [45], and is diagonalized by a unitary matrix U N as m diag For numerical estimates in this second model of neutrino masses we adopt the basis where (γ 2 ) ij is real and diagonal, 16 GeV, we obtain M ν c diag(5.1 × 10 10 , 1.7 × 10 11 , 6.0 × 10 14 ) GeV for γ 2 diag(6.3 × . These values of the right handed neutrino masses are significantly larger than the corresponding estimate of heavy neutrino masses obtained in the inverse seesaw mechanism described above. This scenario can be naturally incorporated in hybrid inflation models with successful reheating and nonthermal leptogenesis [46]. Proton decay in F SU (5) mediated by the superheavy gauge bosons has been extensively studied in the past [47][48][49][50][51][52] mostly in comparison with the unflipped SU (5) model. In a recent paper [28] this is discussed in a no-scale supersymmetric F SU (5) inflation model with an approximate Z 2 symmetry and modified R parity. In this section we will explore proton decay in an R-symmetric F SU (5) model suitable for susy hybrid inflation model. As emphasized earlier the U (1) R × Z 2 symmetry plays an important role in suppressing various operators that mediate rapid proton decay. For example, the dimension four rapid proton decay mediated through the color triplet, D c ⊂ 10 1 , can appear at nonrenormalizable level via the following operators, Without the S field and with no U (1) R symmetry these operators can lead to fast proton decay incompatible with the experimental observations. The presence of S is required by the U (1) R symmetry which makes these operators highly suppressed as the S field is expected to acquire a vev of order TeV scale from the soft susy breaking terms [53]. Note that these operators are also forbidden by the Z 2 matter parity even if we allow R-symmetry breaking operators at nonrenormalizable level as discussed in the previous section. The GUT scale mass terms for Higgs 5-plets, 5 h 5 h , and Higgs 10-plets, 10 H 10 H , are also not allowed due to U (1) R symmetry and which may otherwise mediate dimension five rapid proton decay.
For proton decay via dimension five and dimension six operators we mainly focus on the mediation by color triplets in the conjugate pairs of Higgs superfields, In general, these color triplets can contribute to proton decay via operators of chirality types LLLL, RRRR and LLRR, as discussed in a recent paper on 4-2-2 model [29]. In our model R symmetry with renormalizable interactions only allows the chirality nonflipping modes which reduce to the following four Fermi operators of LLRR chirality generated via color triplet exchange from Later we also discuss the proton decay mediation by the color triplets from 10 H , 10 H by allowing explicit R-symmetry breaking terms with R-charge zero at the nonrenormalizable level.
The Yukawa terms in the superpotential W (Eq. (1)) relevant for proton decay mediated by the color triplets can be expressed in terms of mass eigenstates as with the diagonal Yukawa couplings, y D , given by The F SU (5) supermultiplets are expressed in terms of the following mass eigenstates [28,48] where V is the Cabibbo-Kobayashi-Maskawa (CKM) matrix and P = diag(e iϕ 1 , e iϕ 2 , e iϕ 3 ) is the phase factor matrix with the condition i ϕ i = 0 [28]. As the amplitude of dimension five diagrams involves loop factors their contribution is generally expected to be suppressed as compared to dimension six diagrams. Therefore, we will include the contribution of color triplets only from dimension six diagrams which are generated from a combination of the Yukawa terms in the Lagrangian d 2 θW and their Hermitian conjugates. Similarly, the gauge boson exchange diagram (2a) is generated from the following part of the Kähler potential [28], where X is the SU (5) gauge vector superfield. The combined effects of the superheavy SU (5) gauge boson and color triplet mediation below their mass scales are described by the dimension six effective operators, where the Wilson coefficients C ijkl 6(1,2) are given by Here the color triplet masses are written as M λ = λ M and Mλ = λ M . The first term in C ijkl 6(1) is the contribution from the gauge boson exchange diagram (2a) which has been studied recently in [28] for an inflation based model. The contribution of the first term in C ijkl 6(2) arises from the D h color triplet exchange diagram (2b). This contribution has been studied more recently in an R-symmetric flipped SU (5) model [34] which naturally predicts M λ to be of intermediate scale. With Mλ of order M G only the charged lepton channels are predicted to lie in the observable range of future experiments at Hyper-K [9]. The contribution of the second term in C ijkl 6(1) arises from the D h color triplet exchange diagram (2c) and is crucial for making a nonvanishing prediction for the K +ν decay channel which is usually assumed to be suppressed. The present model with an additional Z 4 symmetry, as described in the next section, naturally predicts both M λ and Mλ to be of intermediate scale. This leads to distinctive proton lifetime predictions especially for the neutral lepton decay channels as described below.
The Wilson coefficients C ijkl 6(n) (n = 1, 2) in Eqs. (19) and (20) are run down to low energy scales using the Renormalization Group Equations (RGEs) given in [54]. The effect of oneloop RGE between the GUT scale M G and the electroweak scale M Z are encoded in the renormalization factors, A Sn , [55,56]: where c ) are the coefficients of one-loop RGEs for Wilson coefficients C ijkl 6(1,2) above (below) the SUSY scale, M SUSY , and are given as The one-loop beta coefficients, b i , b (2) i and b (1) i , of the gauge couplings α i = g 2 i /(4π) 2 are given by ). Therefore, the decay rates for charged-lepton channels with l + i = (e + , µ + ) become, where m p , m π , m K and m l i = (m e , m µ ) are the masses of proton, pion, kaon and charged leptons l i respectively. The MSSM parameters are υ u = υ sin β and υ d = υ cos β with electroweak vev, υ = 174 GeV. Finally, the k-and the C-factors are respectively defined as Decay channel T ml = Matrix element (GeV 2 ) Super-K bound [38] Hyper-K sensitivity [9] (10 34 years) (10 34 years) For convenience, the recently updated values of hadronic matrix elements T ml from lattice computation [58] and the corresponding Super-K bounds [1-6, 38] and the Hper-K sensitivities [9] are given in Table II.
With an additional Z 4 symmetry these relatively tiny values ofλ = λ can be boosted by a factor (m P /M ) 2 ∼ 10 4 as discussed in the subsection below. prediction for this scenario is depicted in Fig. (4). As expected from the M λ contribution in Eqs. (26) and (27), the weak dependence on tan β in the range 2 ≤ tan β ≤ 60 does not exhibit any spread in the proton lifetime predictions shown in Fig. (4). In this case the Super-K bound for the decay channel p + → e + π 0 with Eq. which is somewhat smaller than the corresponding estimate of M λ contribution quoted in Eq. (30). However, a potentially observable range of this bound, with M T 10 11 GeV, is in contradiction with Super-K bounds on neutral lepton channels described below.
The proton decay rates for neutral lepton channels, π +ν i and K +ν i , based on the neutrino model described in W I HN (Eq. 5), are expressed as Apart from the gauge boson contribution in the π +ν i channel [28] the contribution of color triplet with mass M λ has been ignored so far. The numerical results are displayed in Figs. (5a) and (5b) where we have used the recently updated values of U P M N S parameters from [37] with U N equal to the unit matrix. In the large M T limit the proton lifetime of the first channel is dominated by the gauge boson contribution whereas for the second decay channel lifetime increases without bound due to the absence of the gauge boson contribution.
For neutral lepton channels the Super-K bound for the decay channel p + → ν K + with Eq. (33) gives the following lower bound, This is the largest bound among the neutral and charged lepton channels with a naturally accessible value with Z 4 symmetry. This bound also allows the charged lepton channels, shown in Fig. (3) with λ 2.2 × 10 −4 > λ 1 + tan 2 β 3.24 × 10 −6 , to lie within the observable range of Hyper-K whereas the prediction of π +ν channel lies far beyond the Hyper-K reach.
In order to make a comparison of proton partial lifetime predictions among various GUT models the estimates of branching fractions play a pivotal role. For this purpose a variation of various branching fractions with respect to color triplet mass M T = Mλ = M λ for tan β in the range 2 ≤ tan β ≤ 60 is shown in Fig. (6). We particularly include the corresponding predictions from the unflipped SU (5) model recently presented in [28] by ignoring the dimension five contribution of color triplets with large sfermion masses of order 100 TeV [12][13][14][15][16][17][18][19]. For a comparison with 4-2-2 model see [29] and for SO(10) models see Refs. [59][60][61].
As is obvious from Fig. (6) the present F SU (5) model makes a very distinctive predictions of various branching fractions within the observable range of Hyper-K. Especially the branching fraction of ν K + channel plays a key role in making distinctive comparison of the current model with the other models of flipped SU (5) [28,34] where this channel is highly suppressed.
A. Z 4 Symmetry and Color Triplet Masses
An additional Z 4 symmetry can be employed to make the color triplets naturally light for observable proton decay. This is achieved with the following Z 4 -charge assignments: with all other fields carrying zero Z 4 -charge. This modifies the superpotential in Eq. (1) as follows: (Γ ν _ π + /Γ e + π 0 ) SU (5) (Γ e + K 0 /Γ e + π 0 ) SU (5) This superpotential can be employed to realize smooth hybrid inflation [62]. Also see [35] for a relevant model of inflation. The Z 4 symmetry is spontaneously broken during smooth hybrid inflation and the domain wall problem is therefore avoided.
It is important to note that both color triplets are now naturally light relative to M G with M λ = λM (M/m P ) 2 and M λ = λM (M/m P ) 2 , and the couplings, γ ai , relevant for the realization of light neutrino masses via a double seesaw mechanism have also been enhanced by the factor, (m P /M ) 2 . The explicit mass term, µ ab S a S b , for the gauge singlet fields S a , generated effectively from the Kähler potential, K ⊃ y ab Σ † m P S a S b + h.c, still remains intact. Note that we do not consider this symmetry in the second model of neutrino masses based on the standard seesaw mechanism arising from the explicit R-symmetry breaking terms at nonrenormalizable level. The relevant superpotential terms for these additional multiplets are In this section we assume that the U (1) R symmetry is enforced at the renormalizabe level in the superpotential and its violation is allowed at the nonrenormalizable level with operators of zero R-charge (Eq. (5)). The effective Yukawa terms in the superpotential W II HN (Eq. (5)), relevant for proton decay mediated by the color triplets (D c H , D c H ) from (10 H , 10 H ), can be expressed in terms of mass eigenstates as The additional terms arising from the effective Yukawa interactions of W II HN modify the Wilson coefficients C ijkl 6(1,2) of Eq. (17) as In chirality nonflipping mediation via dimension six operators only the last term utilizes the coupling responsible for assigning superheavy Majorana masses to right handed neutrinos. With U E c = U † L this term becomes related to the PMNS mixing matrix. A similar connection of proton decay with the right handed neutrino masses and the CKM mixing matrix is built in the so called new dimension five proton decay via the chirality flipping mediation discussed in an SO(10) model [59,60,63]. Assuming all γ matrices to be real and diagonal with U E c = U † L , the above Wilson coefficients lead to the following dimension six proton decay rates, for the charged lepton channels and [29] and also from the predicted estimates in the gauge boson domination limit [28]. The predicted values of proton partial lifetime for the neutral lepton channels show a trend similar to what has been already shown for the color triplets from Higgs 5-plets in Fig. (6). Here again the K + channel plays a discriminating role in differentiating the present model from the other models of F SU (5) considered in [28,34]. | 5,728.8 | 2020-10-04T00:00:00.000 | [
"Physics"
] |
River Channel Forms in Relation to Bank Steepness: A Theoretical Investigation Using a Variational Analytical Method
: Riverbanks vary considerably in anti-scourability and consequently take various profiles. By using an isosceles trapezoid as the generalized form of river channel cross-sections and then incorporating the e ff ects of bank angle into the variational analytical approach developed by Huang and Nanson (2000), this study presents a detailed theoretical investigation of the self-adjustment of alluvial channel forms. It is demonstrated that when alluvial channel flow achieves stable equilibrium, a significant decrease in riverbank steepness leads to a slight decrease in maximum sediment (bedload) discharge, and yet results in a significant increase in optimal channel width and a considerable decrease in optimal channel depth. The hydraulic geometry relations, theoretically derived for bank steepness to vary across a wide range, show that among the multivariant controls, the roles of bed sediment size, channel roughness, flow discharge and sediment (bedload) discharge are independent of bank steepness. While the e ff ects of bank steepness illustrated in the theoretically derived hydraulic geometry relations are highly consistent with the results of threshold theory and previous empirical studies, limitations on using bank angle to reflect the anti-scourability of natural riverbanks are also highlighted.
Introduction
Rivers are self-adjusting systems and able to reach a dynamic equilibrium state of neither erosion nor deposition through adjusting their channel geometry and gradient [1,2]. The dynamic equilibrium state of rivers is a very important concept in fluvial geomorphology and river engineering for it embodies the physical mechanism governing the complex interactions among river flow, sediment transport and channel forms. Although rivers in many circumstances can deviate from the state of dynamic equilibrium, the state determines the adjusting direction of river channel forms as it acts as an attractor in river systems [3][4][5]. In recent decades, many rivers encounter intensive human disturbances, such as riverbank reinforcement, dam construction, floodplain occupation for urbanization and agricultural development, logging practices and many more, and so it is urgent to know to what an extent these rivers deviate from dynamic equilibrium, or if they are capable of regaining dynamic equilibrium. Hence, determination of the state of dynamic equilibrium in river channel flow not only helps to deepen our understanding on how rivers function properly, but can also offer valuable guides to the practices of preservation and restoration of river systems [6].
In the process of developing equilibrium theory for understanding the behaviors of river systems, there is a scientific problem that needs to be solved: three basic equations governing river channel flow (flow continuity, friction and sediment transport equations) in contrast to four unknown variables (channel width, depth, slope and flow velocity). To solve the mathematically nonclosure problem, many hypotheses have been put forward largely in the way of developing an additional flow equation, typically the so-called stability theories and extreme hypotheses. In the early stages, stability theories were concentrated on the development of "threshold theory", which assumes that sediment on the entire channel boundary is in the critical state for incipient motion in order to make channel flow maintain stability [2,7]. Later on, stability theories were focused on the conditions that make flow achieve stability in alluvial channels with equilibrium banks and a mobile bed [22][23][24][25]. Although stability theories provide a reasonable physical explanation for river channel-form adjustment, the analytical methods they provided in terms of Newtonian formulations are very difficult to use, and the results they produced are not very satisfactory in many cases [26].
Similar to stability theories, the approach of extremal hypotheses tries to adopt an extremal condition as an additional flow equation, such as minimum energy gradient [27][28][29][30][31][32][33][34], maximum sediment transport capacity [35], minimum energy loss rate [36][37][38][39][40][41][42][43][44][45], etc. Although this approach is relatively easy to apply, its applications have led to considerable controversies. The main reasons of the opponents against using extremal hypotheses are: (1) river channel width calculated by using extreme hypotheses is always smaller than the observed; and (2) all extreme hypotheses are not based on sufficiently convincing physical mechanisms [46,47]. On the contrary, the supporters argue that extremal hypotheses are based on generally applicable physical principles, such as the principles of minimum work, maximum entropy, etc. [48][49][50]. In addition, Eaton and Millar (2004) deem that the opponents applied the extremal approach in an incomplete form and did not consider the impacts of riverbank anti-scourability on river channel forms [49,51]. On the basis of a series of studies, Eaton and Millar (2017) developed a so-called UBC model by incorporating the repose angle of bank sediment into their extremal hypothesis-based framework. Since the incorporation makes the UBC model able to reflect the effects of riverbank anti-scourability, the model provides acceptable computations of alluvial channel forms in many situations [26].
Different from stability theories and extremal hypothesis approach, Huang and Nanson (2000) developed a variational analytical approach, which elucidates the physical mechanism governing the self-adjustment of river channel-forms in an easily understandable way. By using channel width/depth ratio as a variational variable to reflect the shape of river channel cross-sections, it can be found that the number of independent variables in the basic relationships governing alluvial channel flow, i.e., relationships of flow continuity, resistance and sediment (bedload) transport, can be reduced and the response of sediment discharge to the variation of channel width/depth ratio, illustrated simply with a curve-drawing method. As a result, stable equilibrium state is identifiable where sediment transport discharge reaches a maximum or energy gradient achieves a minimum. Importantly, the conditions of maximum sediment transport discharge and minimum energy gradient have been demonstrated to be the different realization forms of the general physical principle of least action in river systems [3][4][5][6][52][53][54][55].
Although the variational analytical approach developed by Huang and Nanson (2000) is physically sound and able to provide acceptable calculations of river channel forms in many circumstances [53][54][55][56], it has not taken into account the impacts of riverbank anti-scourability. So far, the variational analytical approach has been applied only to river channels that take a rectangular cross-section, with the angle of 90 • between riverbanks and riverbed. It is well known that the anti-scourability of riverbanks is related closely to the angle of riverbanks or bank steepness in many situations [51,[57][58][59][60], and so it is necessary to examine the applicability of the variational analytical approach to the determination of the impacts of bank steepness on alluvial channel forms. Aiming at this objective, this study deploys an isosceles trapezoid as the generalized cross-sectional form of alluvial channels, and then incorporates the effects of bank angle into the variational analytical approach developed by Huang and Nanson (2000) [53]. Consequently, conditions that make alluvial channel flow achieve stable equilibrium can be defined and theoretical hydraulic geometry relations derived. Finally, the effects of bank angle on alluvial channel forms are elucidated in detail, and the applicability of the theoretically derived hydraulic geometry models is evaluated in comparison with the results from previous studies.
Basic Flow Relations in an Open Channel with Bedload Transport
Riverbanks are normally composed of various materials, and thus they differ significantly in anti-scourability, consequently taking considerably different bank profiles. To study the effect of riverbank anti-scourability on channel forms, many generalized models have been adopted to reflect the variation of channel bank profile [12,13,26,49]. In terms of previous studies by Eaton and Millar [26,49,51], this study adopts an isosceles trapezoid as the generalized cross-sectional form of river channels at bankfull level as shown in Figure 1, and so the steepness of channel banks, or the angle of channel banks θ, can be regarded as the main factor reflecting the anti-scourability of the banks.
For flow to maintain continuity in an alluvial channel, the following one-dimensional relationship is applied: where Q, V and A are the flow discharge, average flow velocity and cross-sectional area of the channel at bankfull level, respectively. For uniform and turbulent flow in an open channel, the following Manning formula has been widely applied to determine flow resistance: where n, R and S are the roughness coefficient, hydraulic radius and channel slope of the study channel, respectively. approach to the determination of the impacts of bank steepness on alluvial channel forms. Aiming at this objective, this study deploys an isosceles trapezoid as the generalized cross-sectional form of alluvial channels, and then incorporates the effects of bank angle into the variational analytical approach developed by Huang and Nanson (2000) [53]. Consequently, conditions that make alluvial channel flow achieve stable equilibrium can be defined and theoretical hydraulic geometry relations derived. Finally, the effects of bank angle on alluvial channel forms are elucidated in detail, and the applicability of the theoretically derived hydraulic geometry models is evaluated in comparison with the results from previous studies.
Basic Flow Relations in an Open Channel with Bedload Transport
Riverbanks are normally composed of various materials, and thus they differ significantly in anti-scourability, consequently taking considerably different bank profiles. To study the effect of riverbank anti-scourability on channel forms, many generalized models have been adopted to reflect the variation of channel bank profile [12,13,26,49]. In terms of previous studies by Eaton and Millar [26,49,51], this study adopts an isosceles trapezoid as the generalized cross-sectional form of river channels at bankfull level as shown in Figure 1, and so the steepness of channel banks, or the angle of channel banks θ , can be regarded as the main factor reflecting the anti-scourability of the banks.
For flow to maintain continuity in an alluvial channel, the following one-dimensional relationship is applied: where Q , V and A are the flow discharge, average flow velocity and cross-sectional area of the channel at bankfull level, respectively.
For uniform and turbulent flow in an open channel, the following Manning formula has been widely applied to determine flow resistance: where n , R and S are the roughness coefficient, hydraulic radius and channel slope of the study channel, respectively. The shear force of flow has been widely regarded as the main driving factor for bedload movement [61][62][63][64][65] and the resultant numerous bedload transport formulas take the generalized form of: In many circumstances, the following simplified form of Equation (3) has been demonstrated capable of yielding acceptable results: The shear force of flow has been widely regarded as the main driving factor for bedload movement [61][62][63][64][65] and the resultant numerous bedload transport formulas take the generalized form of: where q b is the rate of bedload transport on the unit width of channel bed, c b is a coefficient, τ b is the average shear stress of flow acting on the entire cross-section of the channel (τ 0 = γ RS), τ c is the critical shear stress for the incipient motion of bed sediment, and i and j are exponents. In many circumstances, the following simplified form of Equation (3) has been demonstrated capable of yielding acceptable results: where q * b , τ * 0 , τ * c are, respectively, the dimensionless bedload transport rate on unit width of channel bed, the dimensionless average flow shear stress, and the dimensionless critical flow shear stress, which separately take the following specific expressions: In Equation (5), P b is the wetted perimeter of channel bed (equivalent to the width of channel bed as shown in Figure 1), on which bedload transport takes place, Q s is the sediment discharge in the form ofthe rate of bedload transport over the whole channel bed P b , γ s and γ are the specific weight of sediment particles and water, respectively, ρ s and ρ are the density of sediment particles and water, respectively (2650 kg/m 3 and 1000 kg/m 3 , respectively), g is the gravity acceleration (9.8 m/s 2 ), and so γ s = ρ s g and γ = ρg.
In Equation (4), c b , τ * c and j have been given considerably different corresponding values in various studies [61,64,65], among which, Huang (2010) argued based on a solid theoretical analysis of the interactions among channel geometry, bedload transport and flow resistance, that j should take a value of 5/3. Consequently, fitting Equation (4) with a wide range of laboratory observations yields the most suitable values of c b and τ * c to be 6 and 0.047, respectively, leading Equation (4) to take a specific form of:
Variational Analysis of the Effect of Channel-Form Adjustment on Bedload Transport
According to the variational analytical method developed by Huang and Nanson [53], the crosssectional shape factor of river channels, i.e., width-depth ratio ζ, needs to be treated as a variational variable, which for the trapezoid-form channel shown in Figure 1 is defined as: where W and D are the width and depth of the channel, respectively. For the channel form shown in Figure 1, the following geometric relationships maintain: By incorporating the channel geometrical relationships in Equations (7) and (8) into the relationships of flow continuity and resistance presented in Equations (1) and (2), channel width W, depth D and flow shear stress τ 0 can be written as the functions of channel roughness coefficient n, flow discharge Q, channel slope S and width-depth ratio ζ in the forms of: Consequently, by combining the bedload transport relationships presented in Equations (5) and (6) with Equation (9) and the relationship of Q s = q b P b , bedload discharge Q s can be written as the function of width/depth ratio ζ and angle of riverbank slope θ in the form of: Water 2020, 12, 1250 5 of 18 where coefficients K 0 and K 1 take the following separate expressions: Assuming that flow discharge at bankfull Q takes a value of 1600 m 3 /s, channel slope or energy gradient S is 2/10,000, sediment size d is 0.3 mm, and n is 0.03, the variations of Q s with a change in width-depth ratio ζ from 10 to 1000 are computed according to Equations (10) and (11) for bank slope θ to take each of the specific values of 0 • , 30 • , 45 • and 60 • . Figure 2 and Table 1 present the computed results. It can be seen from Figure 2 that for each of the specific values of θ, an increase in channel width-depth ratio ζ from 10 to 1000 makes Q s increase gradually at the early stage, then reach a maximum and afterwards decline gradually. Importantly, it is seen clearly that in the situation of Q s < Q smaxm , a given Q s Q s can be satisfied with two values of channel width-depth ratio ζ and only when Q s equals the maximum, or Q s = Q smaxm , does channel width-depth ratio ζ take a unique value of ζ m .
where coefficients 0 K and 1 K take the following separate expressions: / 13 8 / 3 16 / 3 8 / 3 2 3 1275 . 24 (11) Assuming that flow discharge at bankfull Q takes a value of 1600 m 3 /s, channel slope or energy gradient S is 2/10,000, sediment size d is 0.3 mm, and n is 0.03, the variations of s Q with a change in width-depth ratio ζ from 10 to 1000 are computed according to Equations (10) and (11) for bank slope θ to take each of the specific values of 0°, 30°, 45° and 60°. Figure 2 and Table 1 present the computed results. It can be seen from Figure 2 that for each of the specific values of θ , an increase in channel width-depth ratio ζ from 10 to 1000 makes s Q increase gradually at the early stage, then reach a maximum and afterwards decline gradually. Importantly, it is seen clearly that in the situation of , flow has no excessive power or energy to expend, and so can take only a unique channel which is neither very narrower and deeper nor very wider and shallower [3][4][5][6]. In contrast, flow has excessive power or energy to expend in the situation of smaxm s Q Q < and so can take either a much narrower and deeper channel or a much wider and shallower one, because the channels of the two shapes can yield much larger boundary resistance. Hence, in theory, the situation of As investigated in detail by Huang et al. (2004) and Nanson and Huang (2008, 2017, 2018, the physical mechanism underlying the results presented in Figure 2 is that in the situation of Q s = Q smaxm , flow has no excessive power or energy to expend, and so can take only a unique channel which is neither very narrower and deeper nor very wider and shallower [3][4][5][6]. In contrast, flow has excessive power or energy to expend in the situation of Q s < Q smaxm and so can take either a much narrower and deeper channel or a much wider and shallower one, because the channels of the two shapes can yield much larger boundary resistance. Hence, in theory, the situation of Q s = Q smaxm reflects the most stable equilibrium state of river-channel flow and is the objective for flow to adjust channel geometry in the situation of Q s < Q smaxm . That is to say, when a river channel possesses a fully adjustable boundary, it can achieve the most stable equilibrium state after a self-adjusting process from the situation of Q s < Q smaxm . Therefore, the state of Q s = Q smaxm reflects the equilibrium state of all fully adjustable river channels (e.g., Huang et al., 2004;Nanson and Huang, 2008, 2017, 2018 [3][4][5][6]. If a river channel possesses only a partially adjustable boundary, it is not possible to adjust the channel to the most stable equilibrium state of Q s = Q smaxm when flow is in the situation of Q s < Q smaxm . As a result, the given conditions of channel slope, sediment size and straight single-channel planform have to change to some degrees. In the situation of Q s > Q smaxm , there is no mathematical solution of channel width-depth ratio because flow is short of sufficient energy to transport sediment load. Thus, aggradation becomes necessary, making not only channel geometry but also the given conditions of channel slope, sediment size and straight single-channel planform change to some degrees. These changes are generally in very complex forms and have been addressed largely in empirical manners (e.g., Schumm, 1971) [9].
Furthermore, it can be noticed from Figure 2 and Table 1 that when bank angle θ takes values of 0 • , to 30 • , 45 • and finally 60 • , the maximum values of Q s or Q smaxx , become smaller and smaller, with the corresponding values of 0.08733, 0.08708, 0.08670 and 0.08601 m 3 /s, respectively, while the corresponding optimal values of the width-depth ratio, or ζ m , become larger and larger, with the corresponding values of 101, 113, 128.7 and 168.5, respectively. When θ= 30 • is taken as a reference level, it can be found from Table 1 that with θ taking respective values of 0 • , 45 • and 60 • , ζ m varies in the wide range of from −10.62% to 49.12%, while Q smax varies in the narrow range of from -1.23% to 0.29%. This demonstrates clearly that bank slope θ exerts a much more significant influence on optimal width-depth ratio of river channels, or ζ m , than on the maximum sediment (bedload) transport discharge Q smax . Table 1. Values of maximum sediment transport rate Q smax and optimal channel width/depth ratio ζ m under different values of bank angle θ. When n, Q, S, and θ are taken as given constants, the following differential equations can be derived from the relationships presented in Equation (9) where coefficients F and E are determined separately by: E = (−3ζ − 10 sec θ + 8 tan θ)(ζ + 2 sec θ − 2 tan θ); Taking into account the relationship of Q s = q b P b = q b (W − 2D tan θ) and the bedload transport relationship presented in Equation (3), the following differential relationship of Q s against ζ can be derived: When bedload discharge Q s reaches a maximum, the following condition needs to be satisfied: which, in combination with the relationships in Equations (12) and (14), yields the following condition: where parameters F 1 , B, B 1 , C and C 1 take the following respective expressions: When Equation (6) is adopted to determine the rate of bedload transport, i and j take respective values of 0 and 5 /3, and consequently Equation (16) becomes: which is equivalent to: It can be seen from Equation (19) that to satisfy the condition that bedload discharge Q s reaches a maximum as defined in Equation (15), there is a lower threshold in the shear stress when τ 0 = τ c . At the threshold, it can be found from Equation (19) that it requires B 1 = 0, which, according to the expression of B 1 in Equation (17), can be satisfied with the condition of either B = 0 or ζ − 2 tan θ = 0. Although B has a very complex relationship with θ and ζ as shown in Equation (17), it can be found that the condition of B = 0 can be satisfied when ζ = tan θ or ζ = 2 sec θ. As a whole, there are three conditions that can make B 1 = 0 in Equation (19). Nevertheless, only the condition of ζ = 2 sec θ can be regarded as reasonable because when θ = 0, the isosceles trapezoid cross-section of the study channel becomes a rectangle as shown in Figure 1, which yields ζ m = 2 as what has been demonstrated in previous studies (e.g., Huang and Chang, 2006) [52]. Hence, the reasonable condition at the lower threshold of τ 0 = τ c is: When bank angle θ takes respective values of 0 • , 30 • , 45 • and 60 • , it can be computed from Equation (20) that the optimal width-depth ratio at the threshold, or ζ mc , takes values of 2, 2.3094, 2.8284 and 4, respectively. Clearly, the optimal width-depth ratio of the study channel at the lower threshold increases significantly with an increase in bank angle θ or a decrease in bank steepness.
Equilibrium Channel Relations at the Lower Threshold
When river flow is at the critical state for the incipient motion of bed sediment, i.e., τ 0 = τ c , combining Equation (20) with Equation (9) yields the following threshold equilibrium channel relations: where coefficients a, b and c are determined respectively by the relationships of: Table 2 presented the computed results and it can be seen that with θ taking different values, the coefficients in the relations change in complex forms. Specifically, coefficient a increases significantly with an increase of θ, while coefficients b and c vary in complex forms within very small ranges and maintain the relationship of b · c ≈ 4.6 · 10 −5 . This demonstrates clearly that when flow in a river channel reaches the lower threshold, a decrease in riverbank steepness can result a wider and shallower channel cross-section, while channel depth and slope remain almost unchanged.
Averaged Equilibrium Channel Relations
When flow in a river channel is in the state of τ 0 > τ c , it can be seen from Equations (18) and (19) that there is no upper limit for Equation (15) to be satisfied or for sediment (bedload) discharge Q s to reach Q smax . Hence, when Q s = Q smax , combining Equations (18) and (17) with Equations (7) to (9) and the relationship of Q s = q b P b = q b (W − 2D tan θ), and then eliminating channel slope S such that the optimal channel width-depth ratio ζ m can be expressed as a function of flow discharge Q, sediment discharge Q s , sediment size d, roughness coefficient n and the angle of channel banks θ in the form of: Consequently, the following relationships can be derived by combining Equation (23) with Equations (18), (17), (6) and (9) to determine equilibrium channel slope S m , width W m and depth D m as: Equations (18) and (19) show clearly that theoretically there is no upper limit in the variation of ζ m , that is ζ m can take any value in the range of ζ mc to +∞ under the given conditions. However, Water 2020, 12, 1250 9 of 18 the width-depth ratios of actual river channels rarely exceed 1000, and so we assume that the maximum value of ζ m is 1000. Nevertheless, Equation (18) shows that bank angle θ has a significant influence on ζ m and when θ takes a value of 60 • , letting ζ m vary from ζ mc to 1000 requires τ 0 /τ c to change in the range of from 1 to 195.70. By assuming that when θ takes values other than 60 • and letting τ 0 /τ c vary in the range of from 1 to 195.70 in all cases, the potential varying range of ζ m for each given value of θ can be calculated from Equation (18). Table 3 presents the calculated results, with the potential varying ranges of ζ m being defined in integers approximately. Since the equilibrium channel relations presented in Equations (23)- (26) are in very complex forms, typically the terms containing ζ m . By allowing θ to take a value of 0 • and ζ m vary from 3 to 625 with an increment of 1 in terms of the results presented in Table 4, regression analyses are conducted and the complex terms containing ζ m in Equations (23)-(26) can be expressed approximately in the averaged forms respectively as: where K W , K D and K S are coefficients.
It is seen clearly from Equation (32) that although bank angle θ takes significantly different values of 0 • , 30 • , 45 • and 60 • , the exponents of sediment size d, channel roughness coefficient n, flow discharge Q and sediment discharge Q s in channel width, depth and slope relations all vary in very narrow ranges. Hence, these exponents encounter almost no influences from bank angle or bank steepness and so can be regarded as constants.
The variations of coefficients K W , K D and K S in Equation (32) When S is regarded as an independent variable and Q s a dependent variable, Q s is replaced in terms of the relationship for determining S m in Equation (31). As a result, the averaged equilibrium channel relations derived from Equations (31) and (1) In a similar way, the averaged hydraulic geometry relationships for θ to take respective values of 30 • , 45 • and 60 • can be obtained. Table 5 presents the equilibrium channel relations for all of the four cases when bank angle θ takes respective values of 0 • , 30 • , 45 • and 60 • and it is seen clearly that the four independent variables of sediment size d, channel roughness coefficient n, flow discharge Q and sediment discharge Q s all play very important roles in shaping river channel forms. To examine if bank angle θ affects the performance of the four variables, the varying ranges of the exponents of the four variables in four sets of equilibrium channel relations for bank angle θ to take significantly different values of 0 • , 30 • , 45 • and 60 • are summarized from Table 5 as: (34) where K W , K D and K V are coefficients.
Equation (34) shows clearly that although bank angle θ takes significantly different values of 0 • , 30 • , 45 • and 60 • , the exponents of sediment size d, channel roughness coefficient n, flow discharge Q and sediment discharge Q s in hydraulic geometry relations vary all in very narrow ranges. Hence, bank angle or bank steepness exerts almost no influences on these exponents and so they can be regarded as constants.
Equilibrium Channel Relations at the Lower Threshold
When the equilibrium channel relations at the lower threshold presented in Equation (21) are compared with those from classic "threshold theory" (e.g., Lane, 1952) [66], a perfect agreement is achieved in the reflection of the roles of flow discharge in determining river channel width, depth and slope, as shown in Table 6. However, there is a considerable difference between width/depth ratios. This is because the classic "threshold theory" assumed that sediment at every point on the wetted perimeter of the cross-section is in a state of impending motion. This embodies a very idealistic case because the banks and bed of natural river channels commonly differ significantly in the states of motion such that the width-depth ratios of the channels can take values of as low as 2 (e.g., Nanson et al., 2010) [67]. Because our study is concerned with river channels that possess different states of motion on channel banks and bed, the theoretical results of width-depth ratios obtained in our study are much closer to those of natural river channels as observed by Nanson et al. (2010) [67]. Table 6. The lower threshold channel relations in comparison with "threshold theory".
Averaged Equilibrium Channel Relations
It has long been identified that flow discharge Q is the predominated factor determining alluvial channel forms, with "regime theory" developed empirically from field measurements in stable canals in India, Pakistan, and the USA in early 20th century gaining worldwide recognition [10,67]. However, studies on natural river channel forms have shown that the roles of flow discharge in the one-variant hydraulic geometry model of W ∝ Q b , D ∝ Q f and V ∝ Q m vary considerably not only from one river to another, but even from one reach to another on the same river, with exponents b, f and m taking values ranging respectively within 0.3-0.6, 0.2-0.5 and 0.0~0.2 most frequently (Rhodes, 1987) [68]. As a result, the development of multivariant models has been practiced in recent decades. In particular, through examining the applicability of a relationship developed based on flume experimental observations between shear stress distribution on channel banks and bed with channel width/depth ratio in a wide range of stable canals and natural river channels, Huang and Warner (1995) established the following multivariant hydraulic geometry model [69]: where coefficients C W , C D and C V are determined by bank strength. Using the hydraulic geometry model presented in Equation (35), Huang and Nanson (1998) performed a detailed analysis of worldwide observations on river channel forms and bank compositions, and identified that bank strength in relation to bank compositions can produce a three-fold change in channel width and about a two-fold change in depth, or 2 ≤ C W ≤ 6.5 and 0.33 ≤ C D ≤ 0.63, respectively [13].
Equation (35) shows clearly that besides flow discharge Q channel slope S, channel roughness coefficient n and bank strength also play very important roles in shaping river channel forms. Nevertheless, the hydraulic geometry relations theoretically derived in this study as presented in Table 5 shows that sediment size d is also a very important factor that needs to be taken into account in determining river channel forms. In fact, the influence of sediment size on channel forms has long been recognized [68]. Hence, our theoretical results provide a more comprehensive hydraulic geometry model. Importantly, when the effects of the other factors including channel slope S, sediment size d, channel roughness coefficient n and bank scourability are not very significant and can be ignored without causing significant errors as they are in the simple case of stable canals, Table 7 presents the comparison of the one-variant hydraulic geometry relations theoretically derived in this study with those summarized by Rhodes (1987) and developed by Huang and Warner (1995) [68,69]. It can be noticed that the exponents of flow discharge Q obtained in our theoretical study fall into the most frequently occurred ranges given by Rhodes (1987), and are almost identical with the results obtained in the semi-theoretical study of Huang and Warner (1995) [69]. Table 7. Comparison of the hydraulic geometry relations obtained in this study with the studies by Rhodes (1987) [68] and by Huang and Warner (1995) [69].
Hydraulic Geometry
Although it is generally known that bank strength or scourability can exert significant influences on river channel forms, there have been no appropriate methods to directly quantify bank strength. As a result, many qualitative indices are adopted, such as noncohesive sand, gravels, cohesive sand, tree size and more. In very detailed forms, Huang and Nanson (1998) adopted these indices in their quantification of the influences of riverbank strength on channel forms and found that bank strength can produce a three-fold change in channel width and about a two-fold change in depth [13]. For convenience to conduct mathematical analysis, this study uses bank angle to reflect bank strength and our theoretical results show clearly in Figures 3 and 4 that with a change in bank angle from 0 • to 60 • , channel width can increase by 34.84%, while channel depth declines by 13.29%. While the trends of the influences of bank strength on channel width and depth illustrated in our theoretical results are consistent with the semi-theoretical study of Huang and Nanson (1998), large differences occur in the ranges of the influences. This is because bank angle deployed in our study can reflect bank strength of natural river channels only in the simple cases where alluvial channel banks are composed of noncohesive sand to cohesive sand. Indeed, Huang and Nanson (1998) also identified that the effects of bank strength are in the small ranges of increasing 62.2% on channel width and decreasing 26.7% on channel depth [13]. Table 8 presents a comparison of the theoretical results obtained in this study with the semi-empirical results by Huang and Nanson (1998) for the situations in which alluvial channel banks are composed of noncohesive sand to cohesive sand [13]. While it is seen clearly from Table 8 that the theoretical analysis of this study produces results highly consistent with field observations, it also highlights the need for a more detailed study on how to accurately embody the complexity and influences of bank strength on river channel forms. Table 8. Comparison of riverbank steepness effects on river channel forms between the theoretical results of this study and the semi-empirical results by Huang and Nanson (1998) [13].
Conclusions
Although it is well known that bank anti-scourability or bank strength exerts significant impacts on river channel forms, there has been lacking a suitable method to determine the impacts. In light of the recent advancement on understanding the self-adjusting mechanism governing river channel-form adjustment, this study applies the variational analytical approach developed by Huang and Nanson [53] to investigate the influence of bank anti-scourability on alluvial channel forms. Riverbanks are normally composed of various materials and take considerably different profiles, and as such, this study uses an isosceles trapezoid as the generalized cross-sectional form of river channels. Taking the angle of channel banks θ as the main factor to reflect the anti-scourability of riverbanks, our detailed mathematical analysis of the variation of sediment (bedload) discharge with changes in the variational variable of channel width/depth ratio and bank angle θ yields the following results: (1). For a given bank angle θ, flow achieves stable equilibrium in alluvial channels when sediment discharge reaches a maximum at a width-depth ratio which is not very large nor very small. With a change in bank angle θ from 0 • to 60 • to reflect a decrease in the steepness of channel banks, maximum sediment discharge declines slightly while optimal width/depth ratio increases very significantly. This is because the change in bank angle, while the channel bed remains unchanged, can result in a significant change in channel width and width-depth ratio, while the hydraulic radius changes only slightly.
(2) When flow in alluvial channels is at the critical state for the incipient motion of bed sediment, the roles of flow discharge in our theoretically derived equilibrium channel relations are in a perfect agreement with those from classic "threshold theory", and the width-depth ratios obtained in our study are much closer to those of natural river channels.
(3) When flow in alluvial channels has excessive shear to transport sediment (bedload), our theoretical analysis shows that equilibrium channel relations are determined by multiple variables, including flow discharge, bed sediment size, channel roughness coefficient, sediment (bedload) concentration or channel slope and bank angle. Importantly, this study finds that only when the effects of the other variables on channel forms are so small as to be ignored, such as in irrigation canals, are the roles of flow discharge in shaping channel forms highly consistent with the results of empirically based studies. Hence, the hydraulic geometry model developed in this study not only has a sounder physical base, but also takes a more comprehensive form than the other models developed previously.
(4) When bank angle changes from 0 • to 60 • , no significant responses can be found in the roles of flow discharge, sediment size, channel roughness coefficient and sediment discharge or channel slope in the averaged hydraulic geometry relations, and yet an increase of 34.84% in channel width and a decrease of 13.29% in channel depth take place.
Rivers have a self-adjusting character in shaping channel forms and the variational analytical approach developed by Huang and Nanson has been proven physically sound and robust in uncovering the character in many circumstances [5,6,52,53,62]. Using this approach, this study successfully develops a hydraulic geometry model in which the effects of riverbank anti-scourability on channel forms gain reasonable quantifications. However, this study is conducted with an assumption that the cross-sections of river channels can be illustrated with an isosceles trapezoid. In reality, however, this assumption is valid only in very limited circumstances and so care needs to be taken when applying the theoretical results of this study in practical problems solving.
Conflicts of Interest:
The authors declare no conflict of interest. | 8,953 | 2020-04-28T00:00:00.000 | [
"Engineering"
] |
Tuning the optical response of a dimer nanoantenna using plasmonic nanoring loads
The optical properties of a dimer type nanoantenna loaded with a plasmonic nanoring are investigated through numerical simulations and measurements of fabricated prototypes. It is demonstrated that by judiciously choosing the nanoring geometry it is possible to engineer its electromagnetic properties and thus devise an effective wavelength dependent nanoswitch. The latter provides a mechanism for controlling the coupling between the dimer particles, and in particular to establish a pair of coupled/de-coupled states for the total structure, that effectively results in its dual mode response. Using electron beam lithography the targeted structure has been accurately fabricated and the desired dual mode response of the nanoantenna was experimentally verified. The response of the fabricated structure is further analyzed numerically. This permits the visualization of the electromagnetic fields and polarization surface charge distributions when the structure is at resonance. In this way the switching properties of the plasmonic nanoring are revealed. The documented analysis illustrates the inherent tuning capabilities that plasmonic nanorings offer, and furthermore paves the way towards a practical implementation of tunable optical nanoantennas. Additionally, our analysis through an effective medium approach introduces the nanoring as a compact and efficient solution for realizing nanoscale circuits.
Scientific RepoRts | 5:09813 | DOi: 10.1038/srep09813 is devised by removing small bits of material from around the center of a nanobar. In both cases, the structure modification creates an effect equivalent to that of an electrically small circuit that loads and tunes the impedance response of a nanoantenna. An alternative type of tuning mechanism has been documented in [16], where the loading volume of a plasmonic nanodipole was filled with photoconductive material. In this case the material operates as a nanoswitch which enables either the coupling or decoupling of the two nanodipole arms. From the preceding analysis it becomes evident that one of the great challenges for the realization of effective tuning schemes at the nanoscale is the development and fabrication of nanodevices than can effectively load and tune a nanoantenna configuration.
In this paper through experiments and numerical simulations we investigate the feasibility of tuning the optical response of a nanodimer using plasmonic nanorings. It has been well-documented that the resonance properties of plasmonic nanodimers are primarily determined by the gap distance between their two constituent particles [17][18][19]. Herein we demonstrate that a plasmonic nanoring can function as an effective nanoswitch that enables the dual mode operation of the loaded nanodimer structure. Plasmonic nanorings are ideal candidates for this type of functionality since their electromagnetic properties are inherently characterized by a switching response due to the two distinct hybridized dipole moments that this geometry can support [20][21][22][23][24]. It should be noted here that this manuscript can be considered as a companion to our previously published work in [25]. In that paper it was theoretically demonstrated how the response of a nanodipole can be custom engineered using plasmonic core-shell particles. In the current manuscript a planar version of that nanoantenna configuration is studied where the cylindrical nanodipole is substituted by a circular disk dimer, while the core-shell load is represented by a nanoring. Our analysis reveals that if the geometrical characteristics of the nanoring are carefully chosen then its two dipole moments can be spectrally arranged so that the loaded dimer exhibits a dual mode operation. The radiation properties of these modes correspond to the states where the two particles of the dimer radiate either independently or collectively.
Results
Geometrical considerations for choosing the base nanoantenna structure. At the first stage of this study it was required to determine through numerical simulations the geometrical characteristics of a nanodevice that would facilitate demonstration of the switching functionality under investigation. This stage was of paramount importance because the final design should correspond to a realizable structure taking into consideration the constraints of available nano-fabrication facilities. After extensive numerical experimentation it was decided that our baseline structure should be the nanodimer shown in Fig. 1(a). We define the baseline structure as one whose optical response can be tuned to enable its dual mode operation. The dimer is comprised by two equal in size gold parallelepipeds with a height of 30 nm. The cross-section of each parallelepiped is 120 nm-by-120 nm, while its corners have been blended at a radius of 50 nm. Also, the distance in between the two particles is equal to 120 nm. In order to be consistent with the actual measurement set-up, the structure is modeled to reside on an infinite glass substrate with permittivity equal to 2.09. The dielectric properties of gold, shown in Fig. 1(b), are defined according to measurements performed on fabricated gold samples. Now, given that the separation distance between the two disks is comparable to their radius, it is expected that upon illumination by a plane wave, there will be insignificant coupling between the two elements. It should be emphasized here that in this study we are interested in "structure modes" as opposed to individual particle resonances. Therefore, unless it is stated otherwise, the structures under study are illuminated by a plane wave polarized parallel to their center-to-center vector. This is the proper polarization required in order to excite the structure modes which are of interest in this work. Due to the minute coupling between the two particles comprising the dimer, the scattering signature of the compound structure corresponds to the superposition of the scattering response from the two individual disks, and therefore they exhibit the same resonance wavelength as shown in Fig. 1(c).
Given that in this particular case the size and spatial arrangement of the two disks is fixed it is expected that the structure will need to be appropriately loaded in order to tune its optical response, or equivalently it should be structurally modified. In this case we adopt a loading scheme analogous to that of a radio frequency (RF) wire dipole antenna [26,27], which suggests treating the space in between the two disks as the nanodimer's "loading volume". It should be emphasized that in principle the loading volume of a radiating element is electrically small which obviously is not the case for the baseline nanoantenna structure. However, as it will be demonstrated later in our analysis, even in this extreme case electrical responses that resemble those of a tuning circuit load can still be realized, which is advantageous from a nanofabrication perspective.
As mentioned previously the objective is to devise a loading particle that permits the dual-mode operation of the nanodimer. This can be realized if we choose a load for our structure whose electromagnetic properties resemble those of a tunable wavelength dependent nanoswitch. Essentially, the nanoswitch regulates the coupling mechanism between the particles comprising the dimer thereby allowing the desired optical response to be achieved. The engineering of a custom wavelength dependent response for the nanoswitch is primarily determined by two design parameters: its material properties and its geometrical characteristics. Given that, material customization is difficult to achieve at the nanoscale, the proposed design solely relies on customizing the geometry of the nanoswitch. To this end, nanorings were selected as the most promising candidate geometry in order to enable the desired switching capability.
There are two main advantages offered by the nanorings: first, since structure modes are strongly dependent on the coupling mechanism between the dimer and the load particle, the spacing between them is a critical parameter in the design. This by itself imposes great fabrication limitations since it is not that straightforward to maintain nano-meter scale accuracy during the fabrication process. A nanoring however allows the interparticle distance to be maintained, by keeping its outer radius constant (or within some acceptable tolerance), while its electromagnetic properties can be tuned by modifying its more forgiving inner radius. Second, although the electromagnetic properties of plasmonic nanorings are traditionally explained in terms of mode hybridization models, it can be shown that nanorings may be considered as homogeneous disks characterized by effective dielectric properties similar to those of a medium governed by the Maxwell-Garnett mixing rule. In other words, by modifying the geometrical characteristics of the nanoring we essentially create disks characterized by effective material properties that could not otherwise be easily achieved at optical wavelengths.
In order to demonstrate the previous statement let us consider the ring geometry shown in Fig. 2(a). Its outer radius is equal to 50 nm while for its inner radius r in we examine the following values: 10 nm, 25 nm, 30 nm, 35 nm, and 40 nm. The height of the nanoring is set equal to 30 nm. The structure is immersed in free space, with the ring comprised of gold and the void volume filled with free space. The nanoring is excited by a plane wave polarized parallel to its diameter. For each simulation performed, which corresponds to a different value of the inner ring radius, the following quantity was computed: In the preceding formula ⋅ r P and ⋅ r E are respectively the polarization and electric field intensity components that are parallel to the incident plane wave's polarization vector r. Also, ε 0 is the permittivity of free space while the integration is performed over the volume of the nanoring. This volume averaging based formula yields a rough albeit indicative approximation of the nanoring's effective dielectric properties. The corresponding results for the calculated effective permittivity are illustrated by the solid lines in Fig. 2(b,c). In the same figures, the dashed lines represent the effective permittivity as predicted by the Maxwell-Garnett mixing rule for a mixture comprised of infinite-in-length circular cylinders, or where in this case the permittivity of the host material ε h is gold (ring constitution), and the permittivity of the filler material ε f is free space (void constitution). The area fraction in the preceding formula is defined as = ( ) f r r in out 2 . First, it can be seen that as the inner radius increases the effective dielectric properties of the ring red-shift with respect to the dielectric properties of gold. Second, there is good agreement between the Maxwell-Garnett model and the calculated effective permittivity values as given by (1). In other words, there is clear indication that the nanoring can be characterized by its internal nano-mixture properties, where the material of the void (free-space) is diluted in the material of the host (gold). The effective material is Lorentzian in nature and its properties are solely dependent on the value of the area fraction, given that the constituents of the mixture are fixed. It should be noted that the observed discrepancies are attributed to the fact that (2) assumes infinite in length circular cross section cylindrical fillers, while in this case the height of the mixture is finite and equal to 30 nm. Another reason for the observed discrepancies is that (2) is applicable when the mixture's area fraction is low, and additionally when the size of each cylinder is electrically small. It should be mentioned here that given the direct relationship between the admittance and material properties of a structure, the nanoring under study corresponds to a device characterized by tunable admittance properties where the tuning parameter is solely dependent on the geometrical characteristics of the structure. As a result it is expected that by changing the value of the inner radius, the ring's effective material properties will be altered, and subsequently this will tune accordingly the way the ring couples with the dimer.
Having established a qualitative framework to explain the electromagnetic response of a plasmonic nanoring, we proceed with the investigation for a suitable nanoring geometry that will enable the desired dual-mode response of the baseline dimer. Fig. 3(a) shows the corresponding geometry and, as explained previously, it is excited by a plane wave polarized parallel to the vector defined by the dimer's center-to-center distance. The backscattered response corresponding to the five different values of the inner radius is shown in Fig. 3(b). From Fig. 3(b) it can be clearly seen that for the spectrum of interest the scattering response of the trimer exhibits two resonance peaks. The features of these peaks vary as a function of the nanoring's inner radius. In particular, it can be seen that the width of the long wavelength resonance decreases and the width of the short wavelength resonance increases. This behavior can be justified as follows: the short wavelength resonance corresponds to the scattering resonance of each half of the dimer. As the ring's inner radius becomes smaller the coupling between the left and right particle decreases. In the limit where the inner radius is equal to the outer radius the ring vanishes, and consequently the width of the short wavelength resonance is maximized, which can be observed in the dimer scattering simulation results shown in Fig. 1(c). In contrast, the long wavelength resonance corresponds to the case where the three particles scatter as a longer effective homogeneous particle. Now, as the inner radius of the ring increases the effective volume of the structure decreases, and therefore the bandwidth of the resonance increases. More insight into the coupling mechanism between the three particles will be given in a later section. In conclusion, from the previous parametric study it is evident that for the given structure an inner radius between 25 nm and 35 nm is required in order to provide a clear demonstration of the coupling/decoupling phenomenon for the trimer, thus exhibiting its dual mode operation.
Experimental setup and measurements. Fabrication of the nanoring with the desired dimensions as described in the previous section (25 nm inner radius and 50 nm outer radius) was a very challenging task. The details of this process are described in the Device Fabrication subsection of the Methods section. Now, the objective of this study was to systematically demonstrate the effects of the loading particle in the baseline dimer's optical response. For this reason three different structures were fabricated, corresponding to three different loading scenarios, and subsequently their optical response was measured. In particular, first we measured the optical responses of the unloaded dimer. Following, we examined the cases where the dimer is loaded by a solid circular disk, and then finally by a nanoring. The SEM images of these fabricated nanostructures are shown in Fig. 4(a-c).
The longest diameter of the two particles comprising the dimer shown in Fig. 4(a) is 116 nm which is slightly shorter than the desired length, which is 120 nm. Moreover, for the case of the solid disc load shown in Fig. 4(b), the length of the gap between the solid load and the dimer particles is 1 nm longer than the targeted length, which is equal to 20 nm. Finally, for the nanoring loaded dimer shown in Fig. 4(c), one discrepancy between the fabricated and the desired geometry concerns the length of the two gaps defined between the three particles. In particular, with respect to the image in Fig. 4(c), the left and right gap lengths are equal to 14 nm and 16 nm, respectively, while the desired length would be 10 nm. Additionally, the left and right particles of the trimer have slightly different diameters: the diameter of the left one is 121 nm, while that of the right one is 123 nm. Finally, the length of the fabricated nanoring's outer diameter is 10 nm longer than the desired value, while the diameter of the inner circle is equal to approximately 61 nm. All of the aforementioned geometry discrepancies were taken into account for the development of the numerical models presented in the next section.
A series of far-field scattering measurements were performed in order to characterize the optical response of the three fabricated nanostructures, as described in the Optical characterization subsection of the Methods section. The optical response of the three nanoantennas, measured under identical conditions, is shown in Fig. 4(d-f). The dimer structure exhibits only one resonance peak around 630 nm. The trimer configuration corresponding to the dimer loaded with a solid circular disk, as expected exhibits a red-shifted resonance compared to the response of the dimer, while the width of this resonance is slightly wider. The resulting red-shift is a direct consequence of the coupling that is introduced between the solid load and the dimer. Finally, in Fig. 4(f) it can be clearly seen that when the dimer is loaded by the nanoring the compound structure exhibits two resonances around 650 nm and 870 nm respectively. This behavior is in accordance with the numerically predicted results reported in the previous section, where the response of the trimer was studied as a function of the nanoring's inner radial length.
Numerical validation. The experimentally obtained optical response of the three fabricated nanostructures was validated through a series of numerical simulations. This not only allows the accuracy of the experimental procedure to be assessed, but also helps to reveal the underlying physics behind the coupling mechanism that enables the switching functionality of the nanoring, and thus the dual mode operation of the loaded dimer. In order to achieve computationally meaningful and realistic results, the geometrical characteristics of the numerically modeled structures were chosen to be as close as possible to those of the actual fabricated prototypes. These characteristics were described in the previous section, but for clarity and convenience we further summarize them in Fig. 5. All numerical simulations were performed using the Comsol Multiphysics full-wave electromagnetics solver. As mentioned previously, this effort is focused on investigating the antenna mode of the nanostructures under study.
This mode is typically excited when the nanoantenna is illuminated by a plane wave polarized parallel to its long dimension. However, in order to obtain a more comprehensive understanding of the structures' scattering response, we simulated two additional cases for the polarization of the plane wave excitation. In summary, the three scenarios examined correspond to linearly polarized plane waves, propagating in a direction perpendicular to the plane containing the nanostructure. The polarization of the three incident plane waves is 0°, 45°, and 90° with respect to the long dimension of the structure. The first case, denoted as "parallel polarization, " is responsible for the antenna mode excitation; the third case, denoted as "vertical polarization, " primarily results in the individual excitation of each particle. Finally, the 45° polarized plane wave closely resembles the "un-polarized incident light" scattering scenario, and Scientific RepoRts | 5:09813 | DOi: 10.1038/srep09813 naturally it results in the average scattering response of the structure, when the latter is stimulated simultaneously by both a parallel and a vertical excitation.
The lowest row of Fig. 4 summarizes the extinction cross section predictions for the three nanostructures subject to the aforementioned illumination scenarios. A cursory examination of the responses shown in Fig. 4(g) reveals that the coupling between the two particles is minute since its optical response is nearly independent of the incident plane wave's polarization. As a matter of fact a progressive, albeit slight, red-shift is observed as the transition is made from the vertical to the parallel excitation. Despite this minor variation, the three responses primarily correspond to the superposition of the extinction cross-section of the two particles. Finally, it should be emphasized that very good agreement is observed between the numerically predicted response and the experimental measurements, as shown in Fig. 4(d). Note here that the documented measurements have been obtained after exciting the nanostructures with unpolarized light. Therefore, the obtained results correspond to the superposition of all linear polarizations at angles from 0° to 180° (not 360° due to symmetry). Therefore, the numerical predictions and the measurements should be compared in an average sense rather than by making a direct one-to-one comparison. This last remark holds for all three of the scattering scenarios examined here. Now, the optical response of the dimer drastically changes when it is loaded by the solid circular disc, as is evident from Fig. 4(h). In particular, a pronounced red-shift is observed when the trimer is excited by the parallel polarized plane wave. Evidently, the three particles couple constructively and thus the trimer scatters as an effective nanobar. The effective length of the latter is longer than the size of the individual particle, and thus the supported antenna mode occurs at a longer wavelength. In contrast, the vertically excited structure does not support any structure mode, and the observed resonances correspond to the individual plasmon resonances of the trimer's component particles. Finally, the optical response that corresponds to the 45° polarization clearly exhibits the combined characteristics of the obtained optical response due to the parallel and the vertical excitations. Again, very good agreement is observed between the numerically predicted response and the experimentally obtained measurements, which are shown in Fig. 4(e).
Before proceeding with the analysis of the nanoring loaded dimer's extinction response, it is worth mentioning that the aforementioned loading scenarios (no load and solid disc load) correspond to the two limiting scattering states that such a structure can support. In particular, the "no load" case represents the state where the dimer particles are decoupled and scatter individually. On the other hand, upon insertion of the solid disc load the "coupled state" of the particles is established and the compound structure exhibits a red-shifted resonance. Note here that the solid disc load used in this study was not chosen so that a maximum coupling effect could be achieved. Its geometrical characteristics were rather chosen so that, to a certain degree, the concept of coupling could be demonstrated. The objective now becomes the selection and implementation of a wavelength dependent switching particle, where in this case it is the nanoring, so that both of the aforementioned scattering states can be enabled. Indeed, as can be clearly seen in Fig. 4(i) for the parallel excitation, the structure exhibits two distinct resonances. Moreover, from the wavelengths at which these resonances occur, as well as from their linewidth, they can be attributed to the coupled and decoupled states of the trimer. It should be emphasized here that the nature of these two resonances should by no means be confused with the two resonances that the extinction spectrum exhibits, when the structure is vertically excited. As explained previously, these are the resonances of the individual particles, and cannot be categorized as antenna modes. Finally, the experimentally obtained spectral response for the unpolarized excitation shown in Fig. 4(f) could be considered as a superposition of the optical responses created by a collection of polarization excitations that span from parallel to vertical. This experimental response is in very good agreement with the numerically obtained response illustrated in Fig. 4(i). In what follows, we further elucidate the origin of the multi-resonance response of the nanoring loaded dimer by examining the electric and magnetic field distributions as well as the polarization charge distribution of the resonating structures.
Electric field, magnetic field, and polarization charge distributions.
In what follows we present the electromagnetic fields as well as the polarization charge distributions for the three nanoparticle configurations, shown in Figs. 6,7, under parallel excitation, computed at the resonance wavelengths. Note here that for the field quantities their normalized absolute value is displayed, while the imaginary part is plotted for the surface polarization. First, all the surface plots for the unloaded dimer are computed at 632 nm. It can be clearly seen that each particle exhibits the typical electric field distribution of a resonating dipole (high field intensity around the poles of the particle). Additionally, the magnetic field circulates around the two particles (in and out of the paper), while it exhibits its maximum along the particles' equator. The field distribution is symmetric with respect to the symmetry plane of the particles indicating that there is minute coupling between them, and thus they radiate independently. However, since the two particles are identical their resonances occur at the same wavelength and thus the structure's overall optical response exhibits a single resonance peak. The fact that the two particles function as two decoupled dipoles is further supported by the surface polarization charge shown in Fig. 7(a). It can be clearly seen that positive and negative charge is symmetrically distributed with respect to the particle's equator. Note here that for a charge balanced dipole, the electric field vector is directed from positive to negative charge, while the magnetic field attains its maximum value along a plane perpendicular to the vector that connects the two charges. For the second particle arrangement, which corresponds to the circular solid disk load, we first examine its polarization surface charge plots. For this loading scenario all surface plots are computed at 705 nm. Evidently, at resonance the induced charge on the three particles resembles that of three aligned dipoles. Now, from the distribution of the magnetic field intensity it is evident that a circulating magnetic field has been established around all three particles. In addition, the circulation of the magnetic field around each particle is synchronized so as to create the equivalent effect of a magnetic field circulating around an effective nanobar. As a matter of fact the strong electric field created between the middle and the outer particles affects the charge balance distribution on the latter. In particular, the charge is not evenly distributed on the outer particles and therefore, the magnetic field distribution around them is not symmetric with respect to their equator, but rather it squints towards the center particle. The two squinted magnetic field distributions, along with the center particle's magnetic field distribution, create a combined effect that resembles the effective nanobar response mentioned previously. Consequently, due to the structure's longer effective length it resonates at a red-shifted wavelength, longer than that of the individual particles.
For the nanoring loaded dimer, the field and charge distributions were computed at the two resonant wavelengths of the nanostructure, namely at 622 nm and at 845 nm. At the longer wavelength resonance of 845 nm, where the three particles function collectively, the field distribution closely resembles the one observed in the previously discussed case of the solid disc load. In particular, from Fig. 6(c) we can see that the strong electric field established within the structure's gaps creates unbalanced charge distribution on the outer particles, as illustrated in Fig. 7(c). Consequently, similar to what was described previously, the magnetic field circulating around the outer particles squints towards the center particle, thus creating the effect of a magnetic field circulating around an effective nanobar. Obviously, due to the increased effective length of this nanobar, its resonance occurs at a red-shifted longer wavelength as shown in Fig. 4(i). It should be emphasized here that the coupling achieved in this case is considerably stronger than that created by the solid disc load and this is the reason why the resonance peak shifts to 845 nm, which is at a much longer wavelength than that corresponding to the solid disc loaded structure.
A totally different field and charge distribution is observed at the short wavelength resonance, at 622 nm. First, from Fig. 7(d) it is evident that the nanoring has opposite charge distribution with respect to that established on the outer particles. Because of this charge distribution the electric field vector around the center particle is directed oppositely with respect to the electric field vector established around the outer particles. Consequently, the sense of the magnetic field rotation around the center particle is also opposite to the rotation around the two outer particles. In addition to that, the magnetic field that circulates around the center particle is weaker than that corresponding to the outer particles. This is also evident from the electric field distribution shown in Fig. 6(d), where more electric field is concentrated around the outer particles rather than the center one. As a consequence, the electromagnetic response of the three particles decouples, and the trimer's response is dominated by the contribution from the two outer particles. This is further justified by the short wavelength resonance of the structure which is very close to the one expected by the outer particles.
Discussion
In conclusion, the feasibility of devising tunable dimer type nanoantennas has been demonstrated using plasmonic nanorings. Nanorings constitute a class of wavelength dependent nanoswitches whose electromagnetic properties (e.g. the two distinct dipole moments) can be tuned as desired by modifying their geometrical characteristics. It was shown that any modification of the nanoring geometry can be directly translated to an effective material property governed by an appropriate mixing rule. The latter is of paramount importance because it signifies that nanorings inherently exhibit tunable nanocircuit characteristics, and therefore it is expected that their applicability and utilization can be extended far beyond that of a two-state nanoswitch. For the nanoantenna configurations examined in this paper it was successfully demonstrated both numerically and most importantly experimentally, following a high accuracy fabrication process, that a dimer which is typically characterized by a single extinction resonance, can exhibit a dual mode operation. This was enabled by loading the dimer with a switching nanoring that permits its two component particles to either couple or decouple, and therefore to radiate either separately or collectively.
Methods
Numerical full wave simulations. All numerical simulations were performed using the COMSOL Multiphysics software package. For the simulations where the structure was excited with either a parallel or a vertical polarization the structure's symmetry planes were exploited to reduce the computational load. For the 45° cases (unpolarized light) the entire structure was modeled.
Device fabrication. Optimized ring-loaded and unloaded dimer nanoantennas were fabricated using a conventional top-down electron-beam lithography and metal lift-off process. First, a 150 nm thick electron-beam resist layer (Nippon Zeon ZEP 520A diluted by 50% with Anisole) was spun on a cleaned fused silica wafer at a speed of 5000 revolution per minutes (RPM) for 45 sec. The resist was soft-baked at 180 °C for 3 min, and the features were exposed at a dose of 190 μC/cm 2 (Vistec EBPG 5200, spot size 7 nm and beam current 1 nA). The electron beam resist layer was developed at −10 °C in n-Amyl Acetate for 2 min and then MIBK: IPA = 8:1 for 1 min to remove n-Amyl Acetate. Cold development increased the contrast of the resist, which was required to reproducibly fabricate the ring-loaded nanoantenna structures with sub-10 nm control over the feature dimensions. After lithographic patterning, the nanoantenna structures were completed by electron-beam evaporating the Ti/Au (1 nm/30 nm) metal and lifting-off the deposited metal film by dissolving the resist in Microposit Remover 1165 (Rohm & Hass).
Optical characterization. Unpolarized white light, generated by a tungsten-halogen lamp using an oil dark-field condenser with (NA = 1.2-1.43), was shined on the optical nanoantennas in the transmission mode. The scattering spectrum was collected using an upright microscope (Nikon TE 200U). The scattered light from the nanoantenna was collected with a 100 times magnifying lens. The spectrum of the scattered light was subsequently analyzed with an imaging spectrometer (Andor, Sharmock 303). The contribution from the substrate was removed by subtracting the spectra from adjacent unpatterned regions of equal size from the nanoantenna scattering spectra. The intensity variation of the light source was also accounted for by normalizing the corrected spectrum to the spectral intensity of the light source. | 7,232.4 | 2015-05-11T00:00:00.000 | [
"Physics"
] |
Rotationally inelastic processes of C2− ( 2Σg+ ) colliding with He (1 S) at low temperatures: ab initio interaction potential, state changing rates and kinetic modelling
We discuss in detail the quantum rotationally inelastic dynamics of an important anion often discussed as a possible constituent of the interstellar medium (ISM) and in different environments of circumstellar envelopes: the C2− molecular ion. Its interaction forces with one of the most abundant atoms of the ISM, the neutral helium atom, are obtained for the first time using ab initio quantum chemistry methods. The overall angular anisotropy of the potential energy surface is analysed in order to link its features with the efficiency of transferring energy from the abundant He atoms to the internal rotational levels of this molecular anion. Calculations of the corresponding rotational state-to-state inelastic cross sections, for both excitation and de-excitation paths are obtained by using a multichannel quantum method. The corresponding inelastic rates at the temperatures of interest are determined and their role in distributing molecular states over the different populations of the rotational levels at the temperatures of that environment is discussed. These computed rates are also linked to the dynamical behaviour of the title molecule when confined in cold ion traps and made to interact with He as the common buffer gas, in preparation for state-selective photo-detachment experiments.
Introduction
The diatomic carbon anion -C 2 is one of the most widely studied molecular anions which are stable in the gas phase.
The high electron affinity (EA) of neutral C 2 of around 3.3 eV [1,2] results in the anion having well bound electronically excited states, of which two have been observed ( P A u 2 and S + B u 2 ) [3] and are close in energy to the ground S + X g 2 state. The spectroscopic properties of -C 2 have been studied for a long time in order to provide detailed information on its possible subsequent sighting in different environments of the interstellar medium (ISM). Absorption spectra for the S + B u 2 -S + X g Lagerqvist [4] who suggested it was due to the anion of the neutral C 2 molecule. Subsequent work by other researchers confirmed this suggestion [5][6][7] and since then many other spectroscopic and photodetachment experiments have been performed on this molecule [1,2,[8][9][10][11][12] with the expressed aim of providing supporting information on its possible existence in diffuse molecular clouds. Many high level theoretical studies of the -C 2 anion have also been carried out. Examples include calculations of the spectroscopic constants [13][14][15][16][17], potential energy curves [3,14,15,17,18], transition probabilities [14,17,18] and radiative lifetimes [18]. Recently Shi et al obtained impressive agreement between theory and experiment for spectroscopic parameters of six electronic states of the molecule and spin-orbit coupling constants for the P A u 2 state [19]. The neutral molecule C 2 is abundant in interstellar space [20] and comet tails [21]. It is also a common component of carbon stars [22,23]. Combining these confirmed features of the neutral species with the fact that C 2 has indeed a large and positive EA, and that the -C 2 anion has strong absorption bands [7] which could specifically identify it, led to the expectation that the anion would then be rather likely to be detected in space [24]. Unfortunately, as yet no conclusive evidence of its presence has been found however, despite searches in carbon rich stars [25,26] and diffuse molecular clouds [27], with only upper limits given to justify the lack of observation.
The interaction, and possible reaction, of -C 2 with other molecules of astrophysical interest has also been investigated to include its possible presence within more extended molecular networks to model molecular clouds. Barckholtz, Snow and Bierbaum [28] found that -C 2 (and longer -C n chains) are unreactive with H 2 at room temperature, while it is however rather reactive with atomic hydrogen in the process: -C 2 + H C 2 H +e . Experiments in our group by Endres et al [29] also found that -C 2 is essentially unreactive with H 2 at room temperature but at 12 K some reactivity is observed with the most abundant molecule of the ISM.
The -C 2 anion is also of interest for ion trap experiments where, due to the anion's low lying electronic states with favourable Franck-Condon factors, it has been proposed as a candidate for laser cooling [30][31][32]. The simulations of Comparat et al has shown that -C 2 , initially cooled to tens of kelvin (using for example helium as a buffer gas [30]) could then be laser cooled to temperatures of milikelvin in ion traps. Laser cooled -C 2 could then be used to cool other negatively charged species in the same ion trap such as other anions [31] or even antiprotons [32] via sympathetic cooling. Very recently, Kas et al carried out a theoretical investigation of collisions of -C 2 with Li and Rb atoms [33], the latter of which is used in hybrid-trap experiments. By considering the anionic and neutral potential energy surfaces (PES), Kas et al concluded that the associative electron detachment (AD) process is not important for the ground electronic states of the involved partners but should be important for their interactions within their excited states. The authors also calculated the cross sections and corresponding thermal rate constants for rotationally inelastic collisions of Li and Rb with - covering a low-energy range for the cross sections and obtaining the related rates up to 100 K. In this paper we report inelastic scattering calculations for collisions of -C 2 in its ground electronic state ( S + g 2 ) with helium since the rotational state-changing collisonal processes of the molecular anion might be likely to occur with the He atom as a partner, given the diffuse presence of the latter in many different ISM environments. In particular, in the circumstellar envelope (CSE) around carbon rich stars where -C 2 could possibly be detected, He is around one fifth as abundant as H 2 and so is an important species for collisions in such environments. The rotationally inelastic cross sections which we calculate are in turn used to obtain the relevant thermal rate constants for rotational excitation (increasing angular momentum quantum number j) and de-excitation (lowering j) processes expected to occur in the range of temperatures of the molecular clouds and CSE envelopes where other carbonrich anions have also been observed.
The state-changing rates obtained here for the first time can in turn be included within different chemical networks and databases (for example within the Basecol ro-vibrational collisional excitation database [34]) to improve on the modelling of their possible contributions to the populations of rotationally excited states of this anion reached via collisions with He occurring in diffuse interstellar clouds. Furthermore, the rates can be used to model cooling of -C 2 in ion traps (where helium is often used as a buffer gas) and to model the rotational population dynamics during photodetachment experiments [35]. Both aspects of the above possible processes involving the title molecular anion will be discussed later in the present work.
The paper is organised as follows. In section 2 we give the spectroscopic parameters of the -C 2 anion obtained from the literature. In section 3 we then present in some detail our new ab initio calculations of the interaction of -C 2 with He and report the representation of the interaction through the expansion of the PES in analytical form using a multipolar description of the latter in Legendre polynomials. This allows us to assess the spatial features of its overall anisotropy, linking it to the expected behaviour of the quantum statechanging cross sections. In section 4 we discuss our present quantum scattering calculations for the system which we have carried out using a coupled-channel (CC) description of the inelastic dynamics. In section 5 we present our results giving inelastic cross sections and rates, with the -C 2 molecule treated both as a doublet and pseudo-singlet target, a simplified coupling scheme that we shall explain further. Section 6 presents dynamical calculations which model the relaxation of -C 2 in an ion trap with helium buffer gas cooling and give specific suggestions about the expected behaviour of the initial rotational population collisional relaxation of the molecular anion under well specified trap parameters. Such quantities are obviously also of interest for preparing experimental setups which can describe the subsequent photodetachment processes involving the same initial anion. However, we will discuss and analyse this aspect of the problem in a separate paper currently under preparation. Finally, we offer conclusions in section 7.
Spectroscopic properties of the C À 2 molecule
For the sake of completeness, we give in table 1 the experimental Dunham expansion spectroscopic constants of the -C 2 in its ground ( S + g 2 ) electronic state. Values for excited electronic states are given by Mead et al [8] and Rehfuss et al [9].
It is worth noting that since -C 2 is a homonuclear diatomic molecule, it does not exhibit a pure ro-vibrational spectrum and thus infrared adsorption or emission cannot be used for its detection. As discussed in the Introduction, transitions to and from the well characterised relatively low lying excited electronic states could however allow for the direct detection of the anion in different ISM environments.
Ab initio calculation of the PES
The interaction energy between -C 2 ( S + g 2 ) and He ( 1 S) was calculated ab initio on a Jacobi grid with R (the distance from the centre of mass of -C 2 to the He location) ranging from 2.8 to 20 Å and θ (the angle between R and the -C 2 internuclear axis) from 0°to 90°in 5°intervals. The -C 2 anion bond length was frozen at its equilibrium value of 1.268 Å [19]. Energies were calculated using the CCSD(T) method [36,37] applied to unrestricted Hartree-Fock wavefunctions. All ab initio calculations were carried out using the Gaussian09 programme suite [38]. Before selecting the basis set, it is customary to check the convergence of results. In order to show this convergence of CCSD(T) results for the -C 2 -He surface, we present an example in table 2 for the basis set superposition error (BSSE) corrected (using the counterpoise procedure [39]) and uncorrected potential energy values at θ=90°and R=4.2 Å. Correcting the BSSE using the counterpoise procedure in CCSD(T) calculations with our final basis set (the last row in table 2) was not computationally prohibitive and we have used this basis to calculate the presently employed PES. BSSE corrections obviously tend to diminish as the basis sets are increased; however, it is still not negligible at the level used in our PES calculations. The augcc-pV5Z basis on helium was necessary to reduce the BSSE to an acceptable level. For small values of R<3 Å where the potential is repulsive, some calculations did not converge.
Energies for these geometries were obtained by fitting a Morse type function to the energies for each angular cut and extrapolating to small R. In total a grid of 551 ab initio energies were calculated.
The PES was analytically represented by expanding it using a Legendre polynomial series as where, because -C 2 is a homonuclear target and thus symmetric around θ=90°, only even terms of the Legendre series are required with integer label λ. Using a nine term expansion, i.e. with λ max =16, gave a root mean square error (RMSE) to the ab initio data of 0.78 cm −1 . The expansion parameters l V r R eq ( | ) are provided in the supplementary information and are available online atstacks.iop.org/JPB/ 53/025201/mmedia. The convergence of this fit with respect to the ab initio grid was checked. Carrying out the fit using a smaller grid with 10°intervals resulted in a less than 1% change for the most important V 0 and V 1 terms and RMSE of 2 cm −1 , hence our ab initio grid is sufficiently dense for an accurate PES fit.
The radial coefficients for λ=0, 2, 4, 6 are plotted in figure 1. The V 0 term has a minimum of around −25 cm −1 at 4.5 Å while the other coefficients are mostly repulsive: the interaction of the anion with a He atom is thus found to be chiefly repulsive with only a weak attractive region due to the interplay of dispersion and polarisation effects. It is interesting to compare the present findings with recent calculations involving the same molecular anion but interacting instead with open-shell, highly polarisable systems. For these systems, there is a far stronger interaction of the same -C 2 molecular partner with Li and Rb, with the V 0 terms having minima of around 12 000 (1.5 eV) and 8000 cm −1 (1.0 eV) respectively, as discussed in detail by [33]. It should be noted however, that the crucial feature of the present PES is the extent and strength of its spatial anisotropy around the anionic target. It will be shown below that rotational excitation/deexcitation collisional efficiency is mainly linked to the overall spatial torque applied to the rotating molecule by the incoming He partner during the quantum dynamics which samples that feature of the interaction.
An overview of the PES is given as a contour plot in figure 2. The PES is relatively isotropic but becomes repulsive at slightly further distances for linear geometries versus perpendicular. The attractive interaction is relatively weak with the minimum in energy of around −30 cm −1 (relative to zero at infinite separation) at about 4.5 Å. The PES presented here can also be compared to the C 2 H − ( 1 Σ)-He ( 1 S) system which we have recently investigated [35]. They show, in fact, nearly the same well depth at around 4.5 Å, although the C 2 H − -He PES has its minimum occurring off the perpendicular (T-shaped) configuration, a feature due to the lower symmetry of the former anion compared with the present case.
Scattering calculations at low temperatures
Quantum scattering calculations for the collision of -C 2 and He were carried out using our in-house quantum scattering computational code ASPIN [41]: in the present application the anion was treated as a rigid rotor (RR), since we are interested in the behaviour of rotational state-changing collisional processes. The validity of the RR approximation for the calculation of cross sections and rates of rotationally inelastic transitions for collisions energies of up to thousands of wavenumbers has been justified many times. The rotationalvibrational coupling has been shown to be small for + H 2 -He collisions [42] and essentially negligible for SO + He [43] and CS + He [44]. Lique even showed that including the reactive channels in H + HCl collisions had very little effect on the rotationally inelastic cross sections [45].
The ground electronic state of - , a doublet state. The scattering of a structureless particle from a 2 Σ state target [46] is also implemented in our scattering code ASPIN. The presence of the electronic spin in a doublet state splits the usual nuclear rotational levels N of a rotating molecule into doublets so that each resultant rotational level j (other than j=0.5) is split into two values with j=N±0.5. The energy of the rotational levels are given as where B is the rotational constant taken as 1.74 cm −1 [19] and the spin-rotation constant, γ was taken from experiment with a value of 4.25×10 −3 cm −1 [9]. ASPIN makes use of the CC method to solve the Schödinger equation for scattering of an atom with a diatomic molecule. The method has been described in detail before [41,47] and only a brief summary will be given here. For a given total angular momentum J=l+j the scattering wavefunction is expanded as ) (where ò i is the channel asymptotic energy), μ is the reduced mass of the system, is the interaction potential matrix between channels and l 2 is the matrix of orbital angular momentum.
The CC equations are propagated outwards from the classically forbidden region to a sufficient distance where the scattering matrix S can be obtained. The rotational statechanging cross sections are obtained as å å For doublet-state scattering, the above CC equations are modified by also coupling the projection of the spin angular momentum S with projection Σ on the internuclear axis [46]. The rotational basis functions in equation (3) are changed to explicitly include the spin term. The main result of this is to modify the analytical solutions of the potential matrix elements in equation (4) such that the Wigner 3-j symbols explicitly account for the electronic spin. The working equations for doublet-state scattering are given in the ASPIN publication [41] while a detailed derivation and discussion of the procedure implemented in ASPIN was given by Corey and McCourt [48]. The explicit treatment of collisions accounting for the doublet nature of the -C 2 molecule gives rise to spin-flip transitions in which the j quantum number changes but N stays the same.
To converge the CC equations, a rotational basis set was used which included up to j=20.5 within the CC expansion. This choice provides 21 rotational functions in total which are directly included within the scattering wavefunction expansion. The CC equations were propagated between 1.7 and 90.0 Å in 2000 steps using the log-derivative propagator [49] up to 60 Å and the variable-phase method at larger distances [50] up to 90 Å. The convergence of the scattering calculations with respect to basis set, grid points, PES expansion, propagation distance and number of steps was checked. The cross sections are converged to at least a few percent or better which will have a negligible effect on calculated rates. The potential energy was interpolated between calculated l V r R eq ( | ) values using a cubic spline and extrapolated from the end of the ab initio gird at 20 Å as V(R)=−α He /2R 4 where α He = 1.383 a 0 3 [51] to account for the correct pertubative expansion of the long range interaction [52]. This part of the scattering propagation up to the asymptotic region was carefully checked because of its crucial importance when low temperature scattering processes are considered, as in the present study. It was found that the cross sections were essentially insensitive (again to a few percent or better) to the extrapolated form of the potential since the ab initio grid already went out to 20 Å were the interaction is of the order of −0.1 cm −1 , two orders of magnitude lower than the lowest scattering energy considered here.
Scattering calculations were carried out for collision energies between 1 and 1000 cm −1 using steps of 0.1 cm −1 for energies up to 100 cm −1 , 0.2 cm −1 for 100-200 cm −1 , 1.0 cm −1 for 200-500 cm −1 and 2 cm −1 for 500-1000 cm −1 . This fine energy grid was used to ensure that important features such as resonances appearing in the cross sections were accurately accounted for and their contributions correctly included when the corresponding rates were calculated. The number of partial waves was increased with increasing energy reaching J=89.5 for the highest energies considered. Inelastic cross sections were computed for all transitions between j=0.5 to j=8.5 which should be sufficient to model buffer gas dynamics in a cold trap up to about 100 K, see below. The same levels are expected to be those most significantly populated during low-energy collisional exchanges with He atoms within ISM environments.
Results: features of cross sections and rates
Examples of the behaviour of the inelastic scattering cross sections are shown in figures 3-5 which illustrate various aspects of the system's behaviour under energy-transfer scattering events. Figure 3 shows the inelastic scattering cross sections for rotational excitations from the ground j=0.5 state to the j=2±0.5 and j=4±0.5 states. In both cases the N+0.5 states have larger cross sections. It can be seen that at lower collision energies the cross sections have a rich structure with many resonances. We observe, in fact, that between collision energies going from 10 up to around 40 cm −1 there are many resonant features in the cross sections, with further resonant structure appearing between 60 and 80 cm −1 . The most likely physical origins of such resonant features could be related either to dynamical trapping of the light He atom behind specific centrifugal barriers (broadly defined as 'shape' resonances) or to virtual excitation of the target molecule to low-lying rotational levels which become energetically closed at the collision energies in the asymptotic regions. These are usually classified as 'virtual excitations' or Feshbach resonances. In either case, we did not consider this as of interest in the present analysis, due to the current lack of experimental data on inelastic scattering processes, to further investigate the two types of resonances, while we have made sure that they all correctly contribute to the final size of the computed inelastic rates, especially in the threshold regions. Figure 4 shows examples of de-excitation cross sections and illustrates a number of aspects of doublet-state scattering. The cross sections for = = j j 2 0.5 0.5 are almost identical. This is expected since the interaction hamiltonian is spin-independent and both states end up in the same lower state, without any differences in the dynamical coupling acting during both types of collisions. This contrasts with the = = j j 3.5 2 0.5 cross sections in figure 4 where it can be seen that the spin-conserving = = j j 3. 5 1.5 transition exhibits far higher cross sections than the corresponding spin-flip = = j j 3. 5 2.5 transitions. Also shown in the same figure are the = = j j 5. 5 3.5 and = j = j 5.5 1.5 cross sections which follow the expected trend of larger Δj transitions having smaller cross sections because of the increased energy gap involved in that inelastic process. A final example for the -C 2 -He system is shown in figure 5 which shows two examples of cross sections for the spin-flip process within the same nuclear rotational level N. This process is either slightly endo or exoergic depending on the j state but can also be considered as an essentially elastic process for the purposes of buffer gas cooling.
In order to test the relative importance for the behaviour of the state-changing cross sections of treating the -C 2 molecule as a doublet system, scattering calculations were also carried out by treating the system instead as a pseudo-singlet ( 1 Σ). This constraint simplifies the dynamics as then only even j states are required in the calculations, due to the nuclear statistics of the 12 -C 2 molecule with zero spin nuclei. The scattering calculations discussed above were therefore repeated, this time treating the molecule as a singlet. The same basis set and energy grid were used and a similar increase of partial waves with energy was implemented in order to reach the same level of numerical convergence.
The excitation cross sections for the pseudo-singlet treatment of the -C 2 molecule are compared to those obtained by using the explicit doublet treatment and our present results are reported in figure 6. The relevant summed doublet cross sections are also shown for comparison. These are obtained by simply adding both cross sections for the same final N state but different j state, for example in figure 6 we show s s + 0.5 2.5 0.5 1.5 compared to s 0 2 for the singlet case. It can be see that both calculations give very similar results, this being especially true at the higher energies we have considered. The similarity of the explicit 2 Σ treatment and pseudo-1 Σ was also found in our previous work involving a much more strongly interacting system, where we analysed the inelastic scattering of the + H 2 -He system with regards to the same state-changing rotationally inelastic collisions [53]. Such results indicate that, when analysing the quantum dynamics of rotationally inelastic collisions, such processes are essentially driven by the spatial anisotropic features of the scattering potential while the effects of spin-rotation coupling terms only cause rather minor changes on the efficiency of the considered transitions.
To compare the results between the singlet and doublet treatment more quantitatively, table 3 shows the numerical values and percentage difference for the = = j j 0 0.5 2 transition cross sections at various energies. As the collision energy increases the difference between explicit doublet and psuedo-singlet treatment decreases. This occurs because as the scattering energy is increased, the differences between the pseudo-singlet and doublet terms in the V matrix become negligible with respect to the K matrix elements in the CC equations (equation (4)) which drive the magnitudes of the inelastic cross sections. The doublet terms are then essentially given as a ratio of the pseudo-singlet values, scaled by the relevant Wigner 3-j symbols.
Even at the lowest energies considered where there is considerable resonance structure in the cross sections, the difference is still only around 20%. Such findings bear well for the use of the present decoupling scheme whereby the doublet electronic state of the target molecule can realistically be treated as if it were simply another case of a closed-shell, singlet electronic state of the anion, when one wishes to produce extensive information on the size and energydependence of rotationally inelastic, state-changing cross sections with a considerable reduction of computational complexity.
From the computed inelastic cross sections which we have discussed above, we can progress to the rotationally inelastic rate constants ¢ k T j j ( ), which can be evaluated as the convolution of the computed inelastic cross sections over a Boltzmann distribution of the relative collision energies of the interacting partners as where all quantities are given in atomic units. The rate constants for all transitions considered in the previous discussion were therefore computed between 5 and 100 K, a range of temperatures for which we found the corresponding range of collision energies between 0 and 1000 cm −1 was numerically sufficient to converge the final rate values. In the supporting information we give the rates for all transitions between j=0.5 to j=8.5 and j=0 and j=8 for explicit doublet and pseudo-singlet treatment of the -C 2 anion respectively in 1 K intervals.
Examples of rate constants for both excitation (increasing j) and quenching (decreasing j) state-changing processes are shown in figure 7. As expected, at low temperatures the corresponding quenching rates are larger than the excitation rates while, as the temperature increases, both types of rates become comparable in size.
To further compare the pseudo-singlet and explicit doublet treatment of -C 2 -He collisions, figure 8 compares the rate constants for each approach. Rates for the doublet treatment were added in the same manner described above. Both approaches give very similar rate constants, only differing by less than 10%.
It is interesting to note, as a comparison with earlier calculations involving the same molecular anion, that the rates and cross sections for collisional excitation and quenching of -C 2 by He atoms are found to be around one order of magnitude smaller than those obtained earlier for collisions of the same molecular anion with Rb and Li atoms, both being open-shell, strongly polarisable atomic partners [33]. The results reported in that work behave as expected since the -C 2 -He interaction is much weaker in strength and less orientation-dependent in terms of the size of its multipolar expansion coefficients.
The rates for both the explicit doublet and pseudo-singlet treatment were least squares fit to a three parameter function of form [54,55] which gives a good analytical representation of the rate constants. The lines in figure 7 connecting the calculated rates are an example of this function. In the supporting information we give values of the three fitting parameters as well as rms error for all of the rates considered in this work for pseudosinglet and explicit doublet treatment of the -C 2 anion respectively. This analytical form gives the rates with minimal data and can be used, with caution, to extrapolate rates to higher temperatures than explicitly calculated here. This parametric representation is therefore chiefly provided for the use and inclusion of the presently calculated rotational state-changing rates within larger ISM chemical networks containing a broad range of chemical processes (e.g. the KIDA database [55]).
Relaxation dynamics in cold ion traps
The rates discussed in the previous section can also be used to analyse the population dynamics of -C 2 during He collisions. This study therefore allows for the modelling of the possible operating conditions of cold ion traps where buffer gas cooling is carried out using helium, a buffer atom which has been successfully used in many experiments to obtain specific rotational state distributions for the trapped ions [56]. The master equations one needs to solve are given by They are solved by using the collisional thermal rates obtained from the quantum dynamics of the previous sections at a specific given temperature and selected He density [53].
The P ij (T) are the rates for the destruction of the population of level i, while its formation rates are given by the C ji (T) coefficients. The coefficients are given as a function of the inelastic rate coefficients and the He density: Figure 9. Thermalisation of -C 2 ( 2 Σ) rotational state in collisions with He buffer gas at 15 K and density η He =10 11 cm −3 .
As a test of a few specific conditions in the present analysis, the initial population of the molecular anion was taken to be the Boltzmann value at 50 K with a helium gas density in the cold trap of η He =10 11 cm −3 , a typical value used in experiments within our group [35]. For the chosen buffer gas temperature of 15 K, only the j=0.5, 2.5 and 1.5 states are significantly populated. Figure 9 shows the relaxation of the rotational states of -C 2 ( S 2 ) over the examined time interval. The molecules reach their thermalised Boltzmann distributions well before one second at this selected value for this helium gas density. The behaviour is similar to that which we have already found for the case of another molecular anion, C 2 H − undergoing collisional thermalisation with He. That process turned out to occur on a similar timescale [35], as it is to be expected from the similarities in the PES anisotropic features and coupling strength.
In a recent publication [35] we have also shown that the switching on of a laser causes photo-detachment of the anion's excess electron from specific rotational states by controlling the corresponding laser wavelength and therefore selecting different rotational states of the anion in the trap. These features of the photo-detachment process for the -C 2 anion will be discussed in relation to experiments in preparation in our laboratory, in a separate, future publication.
Conclusions
We have calculated the interaction potential of -C 2 with He by employing accurate ab initio methods and further used that interaction energy surface to construct an analytical representation of the latter. Using this formulation of the PES we have carried out CC quantum scattering calculations to describe the collision of -C 2 with He at energies of 0-1000 cm −1 , treating the diatomic as a rigid-rotor and therefore focussing on state-changing inelastic processes involving solely the rotational states of the target anion. When carrying out the quantum calculations we considered the -C 2 either in its explicit doublet electronic ground state ( S + X 2 ) or, in a simpler formulation, as a pseudo-singlet ( 1 Σ) state. Both treatments where found to give similar inelastic cross sections indicating that the simpler pseudo-singlet treatment is sufficient to realistically model rotationally inelastic collisions, thereby excluding fine-structure transitions when obtaining the final cross sections and importantly, also the corresponding inelastic rates at low temperatures.
Using the computed cross sections we thus obtained the relevant thermal rate constants for rotational excitation and quenching processes at temperatures between 0 and 100 K and fit a three parameter functional form to the rates. As an example of the use of the rate constants, we modelled the buffer gas cooling of -C 2 at 15 K with typical buffer gas density for the He partner. The relaxation time required to reach thermal equilibrium was found to be similar to what we had already estimated for another molecular anion with the same buffer gas atom: the C 2 H − -He system [35]. The rotational state changing rates computed here will be used to model cooling times in an ion trap and population dynamics when a laser is used for photodetachment, in a similar manner to what we have described in detail for similar systems in a recent publication [35]. Such photodetachment experiments on -C 2 will soon be carried out in our group. The rates we have obtained here can also be directly used to model the efficiency of exciting this molecular anion when interacting with He atoms and also its collisional quenching which would be in competition with its possible radiative emission from the collisionally excited rotational levels. The entire range of the computed rates has been fitted to a parametric representation and the parameters have been reported in two tables of the present work. Thus, making use of this easier representation of our computed rates could therefore allow their employment within more extended chemical networks where one also needs to model the efficiency of the inelastic collisions between -C 2 and the abundant helium atoms present in ISM environments such as diffuse interstellar clouds where carbon-rich molecular anions are usually observed [57].
Acknowledgments
All the numerical data pertaining to our parametric fitting of the computed PES and to the actual values of the computed cross sections are available on request from the authors. We further acknowledge the financial support of the Austrian FWF agency through research grant n. P29558-N36 . One of us (LS-G) further thanks MINECO (Spain) for grants CTQ2015-65033-P and PGC2018-09644-B-100. | 8,001 | 2019-12-18T00:00:00.000 | [
"Physics",
"Chemistry"
] |
Molecular Mechanisms of Pulmonary Fibrogenesis and Its Progression to Lung Cancer: A Review
Idiopathic pulmonary fibrosis (IPF) is defined as a specific form of chronic, progressive fibrosing interstitial pneumonia of unknown cause, occurring primarily in older adults, and limited to the lungs. Despite the increasing research interest in the pathogenesis of IPF, unfavorable survival rates remain associated with this condition. Recently, novel therapeutic agents have been shown to control the progression of IPF. However, these drugs do not improve lung function and have not been tested prospectively in patients with IPF and coexisting lung cancer, which is a common comorbidity of IPF. Optimal management of patients with IPF and lung cancer requires understanding of pathogenic mechanisms and molecular pathways that are common to both diseases. This review article reflects the current state of knowledge regarding the pathogenesis of pulmonary fibrosis and summarizes the pathways that are common to IPF and lung cancer by focusing on the molecular mechanisms.
Introduction
Idiopathic pulmonary fibrosis is a progressive and usually fatal lung disease characterized by fibroblast proliferation and extracellular matrix remodeling, which results in irreversible distortion of the lung's architecture. Although its cause remains to be elucidated fully, advances in cellular and molecular biology have greatly expanded our understanding of the biological processes involved in its initiation and progression [1]. It is widely accepted that environmental and occupational factors, smoking, viral infections, and traction injury to the peripheral lung can cause chronic damage to the alveolar epithelium [2]. Based on recent in vitro and in vivo studies of IPF, the novel therapeutic reagents pirfenidone and nintedanib were developed to slow the progression of this complex disease [3][4][5]. However, these drugs do not improve lung function and patients often remain with poor pulmonary function [6,7]. Furthermore, neither drug has been tested prospectively in patients with coexisting IPF and lung cancer [8]. In previous studies, 22% of patients with IPF developed primary lung cancers, corresponding with a five-fold greater risk than that in the general population [8][9][10][11][12]. Similarly, primary lung cancer risk is more than 20 times higher in patients who undergo lung transplantation for IPF than in the general population [13,14]. These observations warrant efforts to identify pathways that are common to both disorders. Questions regarding the proper and ideal management of patients who suffer from both IPF and lung cancer are also raised. It is assumed that pathogenetic similarities between IPF and lung cancer are a starting point for investigations of disease pathogenesis and the resulting insights will improve therapeutic approaches. This review article summarizes the current knowledge of the pathogenesis of pulmonary fibrosis and outlines the common molecular pathways between IPF and lung cancer.
Dysfunctional Epithelia Trigger Aberrant Wound Healing Processes
It is assumed that fibrosis advances over long periods of time in patients with IPF. Thus, at the time of diagnosis, modifications of lung structure have already been established by the disease and pathological features, such as various stages of epithelial damage, alveolar epithelial cell (AEC) 2s hyperplasia, dense fibrosis, and abnormally proliferating mesenchymal cells, are found. At this time, it is not possible to determine the course of events that have led to lung damage; however, it is accepted that dysfunctional epithelia are key to the pathogenesis of IPF [15].
Under normal conditions of lung injury, AEC1s are replaced with proliferating and differentiating AEC2 cells and stem cells, which restore alveolar integrity by stimulating coagulation, the formation of new vessels, activation and migration of fibroblasts, and synthesis and proper alignment of collagen. Chemokines, such as transforming growth factor (TGF)-β1, platelet-derived growth factor (PDGF),
Dysfunctional Epithelia Trigger Aberrant Wound Healing Processes
It is assumed that fibrosis advances over long periods of time in patients with IPF. Thus, at the time of diagnosis, modifications of lung structure have already been established by the disease and pathological features, such as various stages of epithelial damage, alveolar epithelial cell (AEC) 2s hyperplasia, dense fibrosis, and abnormally proliferating mesenchymal cells, are found. At this time, it is not possible to determine the course of events that have led to lung damage; however, it is accepted that dysfunctional epithelia are key to the pathogenesis of IPF [15].
Under normal conditions of lung injury, AEC1s are replaced with proliferating and differentiating AEC2 cells and stem cells, which restore alveolar integrity by stimulating coagulation, the formation of new vessels, activation and migration of fibroblasts, and synthesis and proper alignment of collagen. Chemokines, such as transforming growth factor (TGF)-β1, platelet-derived growth factor (PDGF), vascular endothelial growth factor (VEGF), and fibroblast growth factor (FGF), are central to these processes. Conversely, continued lung injury or loss of normal restorative capacity invokes an inflammatory phase of the wound healing process. The associated increases in the expression levels of interleukin-1 (IL-1) and tumor necrosis factor-alpha (TNF-α) create a biochemical environment that favors chronic flaws of regeneration and tissue remodeling [16].
TGF-β
TGF-βs are multifunctional cytokines that are present as three isoforms: TGF-β1, TGF-β2, and TGF-β3. Although the biological activities of these isoforms are indiscrete, TGF-β1 plays a predominant role in pulmonary fibrosis [17]. The three TGF-β receptors, type I (TGFRI), type II (TGFRII), and type III (TGFRIII), have the potential to bind to all three TGF-βs with high affinity. However, TGF-β is the best characterized promoter of extracellular matrix (ECM) production and is considered the strongest chemotactic factor for immune cells, such as monocytes and macrophages. In these cell types, TGF-β activates the release of cytokines, such as PDGF, IL-1β, basic FGF (bFGF), and TNF-α, and autoregulates its own expression. Increases in TGF-β production are consistently observed in epithelial cells and macrophages from lung tissues of patients with IPF [18] and in rodents with bleomycin-induced pulmonary fibrosis [19]. Smad proteins are known as mediators of TGF-β signaling from the membrane to the nucleus [20]. Activated TGF-β receptors induce phosphorylation of Smad2 and Smad3, and complexes of these with other Smad proteins are translocated into the nucleus to regulate transcriptional responses. Studies show that the deficiency of Smad3 attenuates bleomycin-induced pulmonary fibrosis in mice [21] and that the inhibitory Smad7 prevents the phosphorylation of Smad2 and Smad3 via activated TGF-β receptors [22,23].
TGF-β1 is considered the most important mediator of IPF. AEC2s produce TGF-β1 following actin-myosin-mediated cytoskeletal contractions that are induced by the unfolded protein response (UPR) following ανβ6 integrin activation. The αvβ6 integrin/TGF-β1 pathway is a constitutively expressed molecular sensing mechanism that is primed to recognize injurious stimuli. TGF-β1 is a strong profibrotic mediator that promotes the epithelial-mesenchymal transition (EMT); epithelial cell apoptosis; epithelial cell migration; other profibrotic mediator production; circulating fibrocyte recruitment; fibroblast activation and proliferation and transformation into myofibroblasts; and VEGF, connective-tissue growth factor, and other pro-angiogenic mediator production [24].
PDGF
PDGF is a potent chemoattractant for mesenchymal cells and induces the proliferation of fibroblasts and the synthesis of ECM. Activated homologous A and B subunits of PDGF can form three dimeric PDGF isoforms. Alveolar macrophages with IPF produce higher volumes of PDGF-B mRNA and protein [25,26]. AEC2s and mesenchymal cells also express abnormal levels of PDGF in animal models [27]. Moreover, PDGF-B transgenic mice develop lung disease with diffusely emphysematous lung lesions and inflammation/fibrosis in focal areas [28]. In agreement, intratracheal instillation of recombinant human PDGF-B into rats produces fibrotic lesions that are concentrated around large airways and blood vessels [29]. In another study, gene transfer of an extracellular domain of the PDGF receptor ameliorated bleomycin-induced pulmonary fibrosis in a mouse model [30]. Insulin-like growth factor (IGF)-1 also promoted fibroblast proliferation synergistically with PGDF [31]. Accordingly, alveolar macrophages from patients with IPF expressed IGF-1 mRNA and protein at greater levels than those in normal alveolar macrophages [31,32].
FGF
bFGF is a stimulator of fibroblast and endothelial cell proliferation that has been correlated with the proliferative aspects of fibrosis. In particular, bFGF expression is up-regulated at various periods of wound healing, and recombinant bFGF has been shown to accelerate wound healing. Accordingly, anti-bFGF antibody inhibited the formation of granulated tissue and normal wound repair. Alveolar macrophages are a predominant source of bFGF in intra-alveolar fibrotic areas following acute lung injury [33]. In a study of IPF, mast cells were found to be the predominant bFGF-producing cells, and bFGF levels were associated with bronchoalveolar lavage cellularity and with the severity of gas exchange abnormalities [34].
TGF-α
TGF-α induces proliferation in endothelial cells, epithelial cells, and fibroblasts, and is present in fibrotic areas [35]. In proliferative fibrotic lesions in rats with asbestos-or bleomycin-induced pulmonary fibrosis, AECs and macrophages had elevated expression levels of TGF-α [36]. Similarly, in transgenic mice expressing human TGF-α, proliferative fibrotic responses in interstitial and pleural surfaces were epithelial cell specific [37]. These results indicate that TGF-α is involved in cell proliferation under fibrotic conditions following lung injury.
Keratinocyte Growth Factor (KGF)
KGF is produced by mesenchymal cells, and the KGF receptor is expressed in the epithelial tissues of developing lungs. In rats, KGF accelerated the functional differentiation of AEC2s, and the intratracheal instillation of KGF significantly improved bleomycin-induced pulmonary fibrosis [38]. These data suggest that KGF participates in the maintenance and repair of alveolar epithelium and has potential in the treatment of lung injury and pulmonary fibrosis.
Hepatocyte Growth Factor (HGF)
HGF is produced by mesenchymal cells and has been identified as a potent mitogen for mature hepatocytes. The HGF receptor is a c-Met proto-oncogene product that is predominantly expressed in various types of epithelial cells. HGF levels are higher in bronchoalveolar lavage fluid and serum from patients with IPF than in serum from healthy people [39,40]. HGF is also highly expressed by hyperplastic AECs and macrophages in lung tissues of patients with IPF. In in vitro studies of epithelial cells, HGF promoted DNA synthesis in AEC2s [41]. The administration of HGF also inhibited fibrotic changes in mice with bleomycin-induced lung injury [42]. Promisingly, the combination of HGF and interferon-γ (IFN-γ) enhanced the migratory activity of A549 cells by up-regulating the c-Met/HGF receptor [43]. Based on these observations, HGF treatments may offer a novel strategy for promoting the repair of inflammatory lung damage for patients with pulmonary fibrosis.
Changes in AEC2s that Lead to Aberrant Tissue Repair
Repetitive exposures of alveolar epithelium to microinjuries, such as infection, smoking, toxic environmental inhalants, and gastroesophageal reflux, contribute to AEC1 damage. AEC2s normally regenerate damaged cells, but when dysfunctional, their ability to reestablish homeostasis is impaired. This condition is considered indicative of the pathogenesis of IPF [44,45].
UPR
High cellular activity leads to protein over-expression, and if unchecked, it can cause endoplasmic reticulum (ER) stress. The correcting protective pathway is stimulated by the imbalance between cellular demand for protein synthesis and the capacity of the ER to dispose of unfolded or damaged proteins. This protective pathway is known as UPR, and it re-establishes ER homeostasis. To this end, this pathway inhibits protein translation, targets proteins for degradation, and induces apoptosis when overwhelmed. The activation of UPR stimulates the expression of profibrotic mediators, such as TGF-β1, PDGF, C-X-C motif chemokine 12 (CXCL12), and chemokine C-C motif ligand 2 (CCL2), and thus, can lead to apoptosis [46].
Epithelial-Mesenchymal Transition (EMT)
EMT is a molecular reprograming process, and in AEC2s, it is induced by UPR and enhanced by profibrotic mediators and signaling pathways. Under these conditions, epithelial cells express mesenchymal cell-associated genes, detach from basement membranes, and migrate and down-regulate their typical markers. The most used marker of these transitioning cells is alpha smooth-muscle actin (αSMA). However, EMT occurs during development and in cancerous and fibrotic tissues, but it is not involved in the restoration of tissues through wound healing processes [46].
Wnt-β-Catenin Signaling
Other key pathways of IPF are related to the deregulation of embryological programs, such as Wnt-β-catenin signaling, which has been associated with EMT and fibrogenesis following activation by TGF-β1, sonic hedgehog, gremlin-1, and phosphatase and tensin homolog. Deregulation of these pathways confers resistance to apoptosis and offers proliferative advantages to cells [47].
Endothelium and Coagulation
Damage to alveolar structures and the loss of AECs with basement membranes involves alveolar vessels and leads to increased vascular permeability. Wound clots form during this early phase of wound healing responses, and sequentially, new vessels are formed through the proliferation of endothelial cells and endothelial progenitor cells (EPCs). Patients with IPF with failure of re-endothelization have significantly decreased numbers of EPCs, likely resulting in dysfunctional alveolar-capillary barriers, profibrotic responses, and compensatively augmented VEGF expression. This series of endothelial changes could stimulate fibrotic processes and abnormalities of vessel functions, contributing to cardio-respiratory declines and advanced disease. Furthermore, endothelial cells may undergo a mesenchymal transition with similar consequences as those of EMT [48].
Endothelial and epithelial damage also activates coagulation cascades during the early phases of wound healing. Coagulation proteinases have several cellular effects on wound healing. In particular, the tissue factor-dependent pathway is central to the pathogenesis of IPF and promotes a pro-coagulation state with increased levels of inhibitors of plasminogen activation, active fibrinolysis, and protein C. Under these pro-coagulation conditions, degradation of ECM is decreased, resulting in profibrotic effects and the induction of fibroblast differentiation into myofibroblasts via proteinase-activated receptors [16].
Immunogenic Changes that Lead to Pulmonary Fibrosis
The pathobiology of IPF is led by aberrant epithelial-mesenchymal signaling, but inflammation may also play an important role because inflammatory cells are involved in normal wound healing from early phases. Initially, macrophages produce cytokines that induce inflammatory responses and participate in the transition to healing environments by recruiting fibroblasts, epithelial cells, and endothelial cells. If injury persists, neutrophils and monocytes are recruited, and the production of reactive oxygen species exacerbates epithelial damage. The resulting imbalances between antioxidants and pro-oxidants may also promote apoptosis of epithelial cells and activation of pathways that impair function. Finally, monocytes and macrophages produce PDGF, CCL2, macrophage colony stimulating factor, and colony stimulating factor 1. These proteins may also have direct profibrotic effects [44,49].
The roles of lymphocytes in IPF are still unclear. However, some lymphocytic cytokines are considered profibrotic due to their direct effects on the activities of fibroblast and myofibroblast. Th-1, Th-2, and Th-17 T-cells have been clearly associated with the pathogenesis of IPF. The Th1 T-cell subset produces IL-1α, TNF-α, PDGF, and TGF-β1 and has net profibrotic effects. Th2 and Th17 responses appear more important in the pathogenesis of IPF. In particular, the typical Th2 interleukin IL-4 induces IL-5, IL-13, and TGF-β1 expression, leading to the recruitment of macrophages, mast cells, eosinophils, and mesenchymal cells and the direct activation of fibroblasts. Additionally, fibroblasts from patients with IPF are hyperresponsive to IL-13, which has a positive effect on fibroblast activity and enhances the production of ECM. The Th17 T-cell subset indirectly promotes fibrosis by increasing TGF-β1 levels. Th17 cells are also positively regulated by TGF-β1, suggesting the presence of a positive feedback loop [16]. Numbers of regulatory T-cells are reportedly lower in bronchoalveolar lavage fluid and peripheral blood samples from patients with IPF than in those of healthy subjects. Regulatory T-cells (Tregs) play a crucial role in immune tolerance and the prevention of autoimmunity; deficiencies in numbers and functions of these T-cells play an important role in the initial phases of pathogenesis of IPF. The function of Treg in IPF is severely impaired due to reduced number of infiltrating Tregs in addition to dysfunction of Tregs. Interestingly, the compromised Treg function in bronchoalveolar lavage is associated with parameters of the disease severity of IPF, indicating a causal relationship between the development of IPF and impaired immune regulation mediated by Tregs [50]. Previous studies have demonstrated low IFN-γ levels in the lungs of patients with IPF. IFN-γ inhibits fibroblastic activity and abolishes Th2 responses. However, further studies are required to characterize the roles of inflammation in the pathobiology of IPF. Currently, the early stages of IPF are poorly understood, as are the mechanisms of disease progression [49,51]. Nonetheless, pirfenidone (5-methyl-1-phenyl-2-[1H]-pyridone) was designed to have anti-inflammatory and antifibrotic effects and was efficacious in the clinical setting [6].
Interactions Between ECM and Mesenchymal Cells, Fibrocytes, Fibroblasts, and Myofibroblasts
Contributions of mesenchymal cells, and particularly fibroblasts and myofibroblasts, are crucial for the pathogenesis of IPF. These cells are recruited, activated, and induced to differentiate and proliferate in the abnormal biochemical environments that are created by activated epithelial and endothelial cells. Although the initial trigger and source of mesenchymal cell recruitment remain unclear, the current published consensus defines fibroblasts and myofibroblasts as the key cell types for IPF. Circulating fibrocytes, pulmonary fibroblasts, and myofibroblasts have also been identified among mesenchymal cells that are involved in IPF [52]. The most recent studies of these processes are summarized in a well-integrated review [53].
Common Characteristics of IPF and Lung Cancer
Multiple studies compare IPF with cancer to provide insights into the pathogenesis of both diseases, for which survival rates are low. Arguments against the similarities of cancer and IPF include the presence of homogeneity, metastases, and laterality in cancers. However, cytogenetic heterogeneity has been shown in myofibroblasts, which do not metastasize to other organs. In addition, simultaneous involvement of both lungs is a definitive indication of IPF. However, this is primarily based on the generally accepted assumption that tumors are almost always monoclonal and grow in only one lung before metastasizing and invading other organs. From an anatomical viewpoint, patients with IPF mainly exhibit fibrosis in the lung periphery and in the lower lobes, which are sites of lung tumors in a high percentage of cases [54]. Additionally, patients with lung transplants due to IPF have much higher rates of lung cancer, as stated above [13,14]. These observations warrant further studies regarding the molecular connections between these two lung diseases. Furthermore, epigenetic and genetic abnormalities, changed relationships between cells, uncontrolled proliferation, and abnormal activation of specific signal transduction pathways are pathogenic features of both diseases [55,56]. Principal fibrogenic molecules, signal transduction pathways and immune cells that potentially participate both in two diseases are shown in Table 2.
Epigenetic and Genetic Abnormalities
Hypomethylation of oncogenes and methylation of tumor suppressor genes are established pathogenic mechanisms for most tumors. Epigenetic responses to environmental exposures, including smoking and dietary factors, and aging have recently been identified in patients with IPF. Recent studies also demonstrated changes to global methylation patterns in patients with IPF that are reciprocal to those in patients with lung cancers [57]. Under the conditions of IPF, hypermethylation of the CD90/Thy-1 promoter region decreases the expression of the glycoprotein Thy-1, which is normally expressed by fibroblasts [58,59]. The loss of this molecule in patients with IPF also correlates with invasive behaviors of cancers and the transition from fibroblasts into myofibroblasts. Hence, pharmaceutical inhibition of the methylation of Thy-1 gene may restore Thy-1 expression, suggesting a new therapeutic approach for this disease. Specific gene mutations have also been considered important to the origin and progression of cancer [60]. Similarly, expression of the oncogene p53, fragile histidine triads, microsatellite instability, and loss of heterozygosity were observed in approximately half of the cases of IPF, frequently in the peripheral honeycombed lung regions that are specifically characteristic of IPF [60][61][62][63]. Additionally, mutations that are generally related to cancer occurrence and development, including those affecting telomere shortening and telomerase expression, have been observed in familial IPF [64][65][66]. Recently, circulating and cell-free DNA has been considered as a diagnostic and prognostic biomarker of cancer [67]. In these studies, free circulating concentrations of DNA increased in patients with cancer and IPF compared with that in patients with other fibrotic lung diseases [68]. In addition to circulating DNA, abnormal expression levels of mRNA were correlated with the pathogenesis of both diseases. These studies suggest that short non-protein-coding RNAs regulate carcinogenesis related genes that are involved in growth, invasion, and metastasis; these features are characteristic of cancer cells [69][70][71]. Recent papers show that 10% of mRNAs are aberrantly expressed in patients with IPF [72][73][74]. Among them, let-7, miR-29, miR-30, and miR-200 were down-regulated, whereas miR-21 and miR-155 were up-regulated. These changes corresponded with groups of genes that are associated with fibrosis, regulation of ECM, induction of EMT and apoptosis. Some of these mRNAs may also affect and be affected by TGF-β expression, potentially speeding functional deterioration in patients with IPF.
Abnormal Cell-Cell Communication
Intercellular channels provide metabolic and electrical coupling of cells and are formed by proteins of the connexins (Cxs) family. Cxs are necessary for the synchronization of cell proliferation and tissue repair [75]. Among them, Cx43 is the most abundant on fibroblast membranes and is involved in tissue repair and wound healing. At wound sites, the repression of Cx43 promotes repair of injured skin tissues with increased cell proliferation and migration of keratinocytes and fibroblasts. Accordingly, down-regulation of Cx43 is related to increased expression levels of TGF-β and production of collagen and acceleration of the differentiation of myofibroblast, which likely promotes healing. These changes contribute to the loss of control over the proliferation of fibroblasts that characterizes abnormal repair and fibrosis. This contention is supported by observations of low expression of Cx43 in fibroblasts derived from keloids and hypertrophic scars than in those derived from normal skin tissues [76]. Although low expression levels of Cxs are often correlated with the progression of cancer and the loss of intercellular communication [77], human lung carcinoma cell lines with high expression of Cx43 showed reduced proliferation [78]. Reduced expression of Cx43 was reported in primary lung fibroblasts from patients with IPF, and reduced intercellular communication was also identified in these cells [79]. Limited cell-cell communications are often reported in fibroblasts from patients with IPF and in cancer cells, reflecting common defects of contact inhibition and uncontrolled proliferation.
Abnormal Activation of Signaling Pathways
The Wnt/β-catenin signaling pathway regulates molecules that are related to tissue invasion, such as matrilysin, laminin, and cyclin-D1. However, arguably, the most important function of Wnt/β-catenin pathway is to mediate crosstalk with TGF-β. This pathway is abnormally activated in some tumors, as shown in lung cancer and mesothelioma [80]. Wnt/β-catenin pathway activation was also shown recently in fibroproliferative disorders of liver and kidney tissues [81]. The Wnt/β-catenin pathway is strongly activated in the lung tissues of patients with IPF [82], potentially reflecting the activities of TGF-β [83]. Specifically, TGF-β potentially activates extracellular signal-regulated protein kinases 1 and 2 (ERK1/2), and the target genes of this pathway activate other signaling pathways, including the phosphatidylinositol 3-kinase (PI3K)/Akt pathway, which regulates proliferation and apoptosis. The roles of PI3K in proliferation and differentiation into myofibroblasts have been demonstrated following stimulation with TGF-β [84]. In cancer cells, the activation of PI3K pathway participates in the demise of regulatory controls over cell proliferation. Therapeutic inhibitors have been developed using the PI3K pathway as a target, and their effects on tumor growth and survival is being assessed in many cancers [85]. Oral administration of a PI3K pathway inhibitors significantly prevented bleomycin-induced pulmonary fibrosis in rats [86]. Hence, clinical trials of such inhibitors are eagerly awaited for patients with IPF.
Tyrosine kinases are key mediators of multiple signaling pathways in healthy cells with demonstrated roles in cell growth, differentiation, adhesion, and motility and in the regulation of cell death. Tyrosine kinase activity is controlled by specific transmembrane receptors that mediate the activity of various ligands. Conversely, abnormal activities of these kinases have been associated with development, progression, and spread of several types of cancer [87]. Recently, activities of tyrosine kinase receptors were investigated in wound healing process and fibrogenesis.
TGF-β, PDGF, VEGF, and FGF are common mediators of carcinogenesis and fibrogenesis. Among them, VEGF may directly or indirectly promote cell survival and proliferation by activating ERK1/2 and PI3K. Accordingly, elevated expression levels of VEGF mRNA were shown in EPCs from patients with IPF. Furthermore, antifibrotic strategies using multiple inhibitors of tyrosine kinase receptors have been evaluated in a rat model of bleomycin-induced fibrosis; PDGF, VEGF, and FGF inhibitors produced significant improvement in fibrosis [48,[88][89][90]. In support of these in vitro and in vivo observations, the multiple tyrosine kinase inhibitor nintedanib showed highly favorable results for the treatment of IPF [7].
Abnormal Migration and Invasion Activities
TGF-β is the most important mediator of the pathogenesis and carcinogenesis of IPF. In tumor microenvironments, TGF-β, predominantly from cancer-derived epithelial cells, induces myofibroblast recruitment at the invasive front of the cancer tissue and protects myofibroblasts from apoptosis. These cells encircle tumor tissues and produce TGF-β. With inflammatory mediators and metalloproteinases, myofibroblasts break basement membranes of surrounding tissues to facilitate tumor invasion [91,92]. Likewise, in IPF, myofibroblasts maintain proliferation through autocrine production of TGF-β, leading to their uncontrolled proliferation [93]. Moreover, related, antifibrotic prostaglandin E2 is down-regulated in myofibroblasts from IPF tissues [94]. TGF-β1 promotes the nuclear localization of myocardin-related transcription factor-A (MRTF-A), which regulates the differentiation and survival of fibroblasts, resulting in enhanced lung fibrosis [95][96][97][98]. MRTF-A has been targeted as a mediator of tumor progression and metastasis [99][100][101].
In cancer cells, the capacity to invade surrounding tissue strongly correlates with the expression of various molecules, including laminin, heat shock protein 27, and fascin [102][103][104]. In IPF, epithelial cells around fibroblast foci also express these molecules [105]. However, these molecules are exclusively expressed by bronchiolar basal cells, which are located as a layer between luminal epithelial cell and myofibroblast layers. Hence, these molecules are likely contributors to the migration of cells and the invasion of bronchiolar basal cells into myofibroblasts and luminal epithelium and are expressed at the invasive front of tumors.
Matrix metalloproteases and integrins are strongly associated with invasion and migration of cells [106]. Integrins activate cancer cells through the KRAS/RelB/NF-κB pathway and lead to the development of stem cell-like properties, such as independent growth and drug resistance. These properties provide cell-cell communications between inflammatory cells, fibroblasts, and parenchymal cells through ECM. Under conditions of IPF, integrin promotes initiation, maintenance, and resolution of tissue fibrosis. Accordingly, integrin expression was reportedly high in myofibroblasts and AECs after lung injury. Integrin is also considered a strong regulator of TGF-β during the progression of lung fibrosis. A clinical study of the humanized antibody STX-100 has been conducted for IPF [107]. Other inhibitors, such as specific antibodies against αvβ6, have also been investigated in clinical trials, and these antibodies were tested in preclinical models of fibrosis and in the murine model of bleomycin-induced pulmonary fibrosis.
Inflammatory Environment
Inflammatory reaction is described by some reports as a promoting factor in the development and progression step of tumorigenesis [108]. As described above, some kinds of macrophages produce cytokines which contribute to the inflammatory responses such as fibrosis-associated macrophages. This macrophage behaves as an M2 phenotype macrophage expressing arginase and CD206 [109]. M2 macrophages have been broadly identified as trigger cells towards tumor progression [110][111][112]. Myeloid-derived suppressor cells are associated with poor prognosis in malignancies and their accumulation in IPF is also correlated with disease progression [113]. On the other hand, infiltrating T lymphocytes play a crucial role in tumor progression and suppression, although their roles in IPF are still unclear [114]. Infiltrating Tregs are significantly correlated with the tumor progression whereas deficiency in numbers and functions of Tregs is observed in the initial step of IPF (Table 2) [50,115]. Further studies regarding the role of Treg in the IPF-related cancer are awaited.
Conclusions
In conclusion, cancer and fibrosis are both severe lung diseases, and they share biological pathways. Although the specific genetic and cellular mechanisms are not yet fully understood, several signaling pathways and microenvironments have been shown to disrupt tissue architecture and lead to dysfunction. Conversely, it is clear that lung tumorigenesis and fibrosis display highly heterogeneous behaviors, warranting personalized therapeutic approaches. Lung fibrosis may eventually be attenuated by therapies that are developed after considering mechanisms that are common to cancer and IPF. | 6,399.4 | 2019-03-01T00:00:00.000 | [
"Medicine",
"Biology"
] |
Unrecognized News from the Filter Model and Review of the Spence Model
The objective of this article is to cross a line of reflection which makes it possible to trace more solid legibility in what is similar to the explanation of the choices of educational investments and the regulation of the labor market. This analysis aims to propose a new approach which adopts as a reference the role of aptitude in determining the future of the labor market, in terms of individual decisions to invest in training and terms of expected productivity about of the signal issued by the diploma.The methodology mainly refers to the signal theory and filter theory. In our study, first, we will integrate a new concept to better analyze the different forms of filter (productive and non-productive) on which collective productivity, individual productivity, and profitability largely depend. Second, we reformulate Spence's model by integrating two levels of discrimination and three groups. This breakdown becomes more complex, but it allows a better understanding of the choices, the gains, as well as the balance on the labor market.The re-examination of the filter theory exposes the idea of regularizing the university and market system close to the abilities of individuals. The demonstrations also show that the signal effect does not own its assets, it depends on other signals.The results of this treaty are applicable in terms of rationalizing the policies of funds intended for training, guiding the functioning of the labor market as well as tackling the problem of unemployment. Codes JEL: E24, E32, G12, J23. Keywords: Filter; signal; gains; balance; labor market; diploma DOI: 10.7176/JESD/11-16-21 Publication date: August 31 st 2020
Introduction
For decades the trajectory of educational investment (private and public) has been strongly guided by theories of human capital (HC) of signal and filter. Spreading a lot of anchor of development of analysis and criticism but, their secrets remains fierce to any domestication.
The present analysis hopes to find other lines of thought and to trace a little-known field of study, thus offering a new passage in what approaches the explanation of the choices of educational investments.
The central assumption of the HC model is that education is recognized as the key determinant of the structure and evolution of individual incomes, where individuals, by forgoing an immediate gain that they would receive if they entered the labor market immediately, hope to increase their productive capacities and the associated market value.
The reporting process
The Spence model assumes that individuals are differentiated by their "p" productivities. And the population is divided into two groups, with productivity "p 1 " and "p 2 " with p 1 <p 2 . The proportion of the two groups in the population is "q 1 " for the first group and "q 2 " for the second. At first, and in a situation of imperfect information, the salary will be the same for all individuals and it will equalize the average productivity of the population: ) 1 ( 1 2 1 1 q p q p p This equation penalizes the most able in favor of the less able, and their loss will be: This loss increases if the proportion of the least able (q 1 ) increases in the population or (p 2 -p 1 ) becomes more important, that is to say that, the crack in terms of productivity increases between the two categories. . On the other hand, the less able realize a surplus of: This surplus increases with the decrease of "q 1 " or the growth of (p 2 -p 1 ). As a result, the signal process appears as a necessary phenomenon because it accords with human nature, which seeks to be distinguished. So workers will invest rationally in training so that employers can detect their skills and pay them based on those skills. It is in this sense that the diploma is considered as a signal. For employers, they will use their previous experiences and data on the labor market, to enhance these signals and will be paid according to this basis. The strategy of a worker therefore consists in choosing the optimum level of signaling which allows him to acquire the greatest income. Knowing that signal equilibrium assumes that there is a negative correlation between signal cost and skill. We consider "Y" the level of training that ensures discrimination, the cost of education will be in the form: From this structure, we see that the less able will pay more to have the same level of education, ie " Y " such that: And since skills are unobservable, employers' decisions will be made based on the "Y" signal.
The possibilities offered for an individual are either "Y = 0" or "Y= Y ", since then the decision of individuals of the type "p 1 " is then "Y = 0" and receive a salary equal to "p 1 " , since the cost here is zero, and they will not choose "Y= Y " because their income will be: p 2 -( Y / p 1 ) which is next [A] less than "p 1 ". For individuals of type "p 2 ", they will choose "Y = Y " which gives them an income equal to "p 2 -( Y /p 2 )" which is according to [A] greater than "p 2 ". If the decision is "Y = 0" the income will be "p 1 " which is not optimal.
If we combine the two optimal choices we will have: p 1 < Y <p 2 .
Figure 1: Optimal choice of reporting
However, for an edifying analysis we must distinguish at least three types of filters: the non-productive filter with these two perfect and imperfect forms and the productive filter.
The perfect non-productive filter 2.1 General framework of the model
The main idea is that education brings nothing in terms of production; its role is limited to the emission of the signal while always adopting the hypothesis that the cost of education and the ability are correlated negative, so marginal productivity manifests itself only by the innate ability "a". Where "Y" is the level of education acquired. The salary is only remunerated at the base of "Y" because "a" is unobservable, w = w (Y), as well as the cost C (a, Y) = Y/a, because the cost is negatively correlated with the skills so that the net income to be maximized is: The reporting balance presupposes two conditions: the first is, the rationality of employers demanding as well as ( ( , the second reflects the maximization of income for individuals. We will therefore have: . This amounts to solving a differential equation, at equilibrium we will have: with "k" an integration constant. However according to [B], we have: To see the impact of the skill on the demand for diplomas, we will consider double the first skill, i.e. "2a". We will have C = (Y '/ 2a) where "Y'" the new level of study knowing that the skill is equal to "2a": Similarly by replacing "2a", we will have a differential equation whose resolution is also the same: It is noted that there is a hypersensitivity to the ability: if the ability is doubled, the level of education will be multiplied by more than "4". This conception is strictly in favor of the fittest. However, this formulation was based on very strong assumptions, assuming that there is a perfect match between skills, marginal productivity and diploma, and also canceling out market imperfections.
The imperfect non-productive filter
For this model, the main difference is manifested in the insemination of the cost function, where it now depends on "a" and "θ". The latter indicates funding opportunities, therefore: The salary offered will also depend on the expected conditional productivity of the "Y" signal. And by proceeding to the same approach of income maximization, we will have: If we want to detect the effect of aptitude on investment in training, we double the aptitude. We will therefore have: Compared to the previous model, the introduction of the variable "θ" (funding opportunity) slows investment in training. The introduction of the variable "θ" also implies a process of compensation between the latter and the variable "a", where there will be a tendency to find the most suitable individuals, but who are deprived of financial opportunities at the same level education than individuals who have strong funding opportunities, but weaker skills. Regarding compensation, it is "w = (a + θ) / 2", but productivity or skill is "a". For employers to be satisfied, the salary must be at least "a": If "w> a θ> a": that is to say that the funding opportunities in the population exceed skills. In this case, we will see a second regulation of wages by employers until arriving at "w = a".
If "w <a θ <a": indicates that the skills found in the population exceed the funding opportunities. In this case, individuals will try to invest further in education so that employers can better detect their skills and reduce "w" to "a".
The productive filter 3.1 Presentation of the model
For this model, it is considered that education does not reveal innate skills only, but has its own productivity, and the cost depends only on ability (C = C (a, Y) = Y/a). Marginal productivity depends on both ability and level of education. The specification of the model is as follows: This specificity describes that, the elasticity of productivity with respect to the level of education "Y" is equal to the salary "w (Y)", thus the individual will maximize his income: 3.2. Determination of balance: When looking for "Y*", the first order maximization conditions are: It is a differential equation whose solution is: There fore: If we want to look for the impact of the skill on education, we will double the initial skill and see its effect on "Y". So we will have: This result clearly shows that those with higher abilities will seek the highest signal. For the study of the general framework we consider "λa", with λ>1: We will examine this signal demand as a function of "α" (the elasticity of productivity with respect to education level "Y").
If "α" tends to "0" (that is, we tend to cancel the effect of education): signal demand is reduced to skill supplement (demand for higher signals) If "α" tends to "1": , There is no demand limit for the highest signals.
Similarly, we can calculate the ratios of net equilibrium income: The difference in net income is reduced only to the difference in ability.
: There will be a very large depreciation of the income of the least able.
The filter hypothesis and jobs held
Another interesting advanced vision, insofar as it allows comparing the two theories, of HC and of filter for the same formulation through the introduction of another dimension which is the influence of the occupied job where variables are defined as follows: Schooling "s" to obtain a level of diploma "Y": s = s (a, Y), with sa <0: the duration of schooling is a function decreasing with ability. s Y > 0: the duration of studies varies in the same direction as the level of education for the same skills. s aY < 0: the marginal increase in education is obtained more easily for the most able.
Productivity depends on "a" and "Y". So: P = P (a, Y) With P a , P Y ≥ 0, meaning that productivity varies positively with ability and education.
The salary is a function of "Y": w = w (Y).
Income discounted over a life cycle is expressed as follows: The equilibrium is obtained by the maximization of the income and a rational anticipation of the employers, i.e. looking for "Y (a)" which maximizes R (a, Y, w (Y)) such that w (Y (a)) = P (a, Y (a)) 1 . We will now study the earnings profiles according to the nature of the job. We will start with the first pole where Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.16, 2020 197 jobs require a filter (α 0) while admitting that employers' forecasts are not biased: Hence the maximization of the logarithm of the income allows us to give us the optimal level of signal "Y" knowing the ability "a": First and second order conditions: Which shows that the optimal investment corresponds to the equalization between the rate of return of a signal . The solution is represented on the figure below, presents the gain functions for two individuals of type "a" and "a°", with a <a°: Note that the balance for the less able (a) is the same in both cases. Whereas for the most apt individuals (a°), they will adapt to a higher signal equilibrium including the filter conditions than HC, translating a straight line of the gain profiles, flatter for the filter process (W (Y)) than for the process without filter (p* (Y)).
It remains for us to study the second axis, that is to say that concerning jobs that are not subject to the filter (α 1), which requires another hypothesis, assuming that there is a logic compensation between jobs, but at the same income for the same signal level. So, for a job not subject to the filter, the income is: This income is assumed to be the same for another job.
The optimum is chosen such that: And since the return on education "W'(Y)" exceeds private income, this balance allows us to write: So, we will have: And taking into account the hypotheses already mentioned (P Y <0 et s Y >0), we will have: From these analytical developments, we draw the following conclusion: individuals in the unfiltered sector spend less time in school than those in the filtered sector. However, the income distributed in the unfiltered sector is lower than that distributed in the filtered sector. However, these income supplements are very small (flattened slope).
It should be noted here that the majority of these results are very sensitive, and that they largely depend on the basic formulation which is based on strong assumptions, so all these results are likely to be demolished if we change the benchmarks a bit. Spence's (1973) model is based on a basic assumption which assumes that individuals are unequal in the face of signaling costs, since ability reduces costs. Spence considered two productivity groups "A" and "B" "1" and "2", with (1<2). Group "A" has a cost "y" and group "B" a cost "y/2" (with better skills), to acquire the level of training "y*" paid at their marginal productivity. That is to say, "1" for group "A", and "2" for group "B". Spence has shown that group "A" has an interest in choosing a level of training "y = 0" and group "B" a level of training" y*". At signaling equilibrium, it is conceivable that the situation of group "A" will deteriorate, while the situation of group "B" will become more favorable than if the workforce of group "A" is greater than "50%". That is to say, the size of group "B" must be a minority in the population. Our goal is to extrapolate the illustration of Spence from "2" to "3" groups (A, B and C), and from a level of discrimination "y*" to two levels "x*" and "y*". This extrapolation is very delicate, very important because it can highlight two points already overlooked so far: • It illustrates the possible choices and the relative gains of an average diploma. • It allows highlighting three choices instead of two: medium signaling, strong signaling, and no signaling. Suppose that there are three groups of workers in the labor market "q 1 , q 2 , q 3 " respectively, and productivity groups "1, 2 and 4", respectively. The training is distinguished by an index "y" (the signaling means), which the agents can have by bearing a cost inversely proportional to their skills: -For group "A", the acquisition cost of a level "y" is exactly "y" units. -For group "B", the acquisition cost of a level "y" is exactly "y/2" units. -For group "C", the acquisition cost of a level "y" is exactly "y/4" units. Similarly: -For group "A", the acquisition cost of a level "x" is exactly "x" units. -For group "B", the acquisition cost of a level "x" is exactly "x/2" units. -For group "C", the acquisition cost of a level "x" is exactly "x/4" units. This is in line with the basic assumption of cost reduction with skills (we assume here that "y = 2 x"). For the employer, there are now two levels of training discrimination: the first (x*), below which it is certain to recruit a person of marginal productivity equal to "1". The second (y*), below which it is certain to recruit a person of marginal productivity equal to twice the first, that is to say "2". Beyond that, he can estimate a marginal productivity equal to twice the second, ie "4". With "y* = 2 x*" which expresses that the signaling "y*" is twice the signaling of "x*" 2 , the same for costs and marginal productivity. Next, we will explain the training strategy adopted by the candidates according to their abilities. Reading the graph shows that group "A" must support twice what group "B" must support, to have the same signal level "x*". Likewise, group "B" must pay double what group "C" pays to have the same signal level "y*". We end up with three cases: -Achieve a level of training "y = y*" (group C).
-For group C, its people have an interest in reaching "y = y*", since this level brings them more than its cost, and they have "(4-y*/4)>2". It is easy to see that the following condition must be met: 1<x*<2 and 2<y*<4. These equilibrium thus found, must be compared to the signaling equilibrium by the diploma which is obtained by the following principle: let "q 1 , q 2 , q 3 " be the probabilities of recruiting respectively an individual from group "A", from the group "B" and group "C", and these individuals are assumed to be paid at their marginal productivity. So, we will have: 1.q 1 + 2.q 2 + 4.q 3 Now we know that: q 1 + q 2 + q 3 = 1 So: q 3 = 1 -q 1 -q 2 Hence: 1.q 1 + 2.q 2 + 4.(1 -q 1 -q 2 ) = 4-(3.q 1 + 2.q 2 ) The latter equality represents signaling balance. We notice that, the less able group "A" is penalized by this signaling equilibrium, if we know that its remuneration (1) is always lower than this equilibrium whatever "q 1 and q 2 ". For group "B", and for it to benefit from this balance, its remuneration (2) must be greater than this balance: 2>4-(3.q 1 + 2.q 2 ) Hence: -(3.q 1 + 2.q 2 )<-2 and 3.q 1 + 2.q 2 >2 (I) And we know that we can write the previous balance in another way: 1-q 2 -q 3 + 2q 2 + 4q 3 = 1 + q 2 + 3.q 3 So: 2>1 + q 2 + 3.q 3 Hence: q 2 + 3.q 3 <1 At the end: -2.q 2 -6.q 3 >-2 (II) And if we sum the two results (I) and (II) we will have: 3.q 1 -6.q 3 > 0 Hence: q 1 >2.q 3 Therefore, individuals with high-level qualifications must be in the minority, and their workforce must not exceed half of the workforce of the least qualified individuals. As a result, group "B" can only benefit from this balance if the size of group "C" is reduced. It is for this reason that the assessment of the diploma of this class does not depend directly on itself (on their own signal), but on the class which is superior in terms of level of training. In other words, if the diplomas of the upper class depreciate, the group of the lower class will be automatically penalized, and with more serious consequences. For individuals in group "C", it seems that they are winners in this balance, but they can only benefit from the "4y*/4" remuneration, when their number is low on the market.
Costs and strategies
We extend this model in order to clarify the phenomenon of depreciation, by relying on signaling costs and the two frontiers of discrimination that we have already established and we combine them with university policy. Various scenarios appear.
It is now assumed that the acquisition costs of the different training levels are perfectly divisible and that the acquisition cost of a training unit for group "A" is "a 1 ", "a 2 " for the group "B" and "a 3 " for group "C", and since the productivity of the agents is in decreasing relation with the costs, we can write that "a 3 <a 2 <a 1 ". For group "B" and "C" to benefit from signaling balance, the following conditions must be fulfilled: 2 -a 21 >2 -a 11 a 21 <a 11 2 -a 31 >2 -a 11 a 31 <a 11 2 -a 31 >2 -a 21 a 31 <a 21 4 -a 22 >4 -a 12 a 22 <a 12 4 -a 32 >4 -a 22 a 32 <a 22 4 -a 32 >4 -a 12 a 32 <a 12 The first index indicates the group (A: 1, B: 2 and C: 3) and the second index shows the level of discrimination "x*" designated by "1" and "y*" designated by "2". We can show that: a 32 <a 22 <a 12 and a 31 <a 21 <a 12 (I). This means that the transition to level "y*" is less expensive for group "B" compared to group "A" and even less for group "C", and likewise for level "x*". But, the problem which arises at this level is the comparison between "a 21 and a 31 " on the one hand, and between "a 11 ", "a 22 ", on the other hand, so as to reveal their meaning in terms of decisions. Four cases to analyze: First case: a 21 >a 32 and a 11 >a 22 : a 21 >a 32 : implies that reaching level "y*" by group "C" is easier than reaching level "x*" by group "B". We will therefore have an increase in the size of group "C", since once beyond the level "x*", reaching level "y*" is easier, and part of group "B" fetch the level "y*"(if conditions are favorable), although its ability is relatively reduced to grab this level. a 11 >a 22 : reaching level "y*" is easier for group "B" relative to the effort provided by group "A", to reach level "x*". If we follow the same reasoning, we will have an increase in the size of group "C". Therefore, this description provides suitable conditions for individuals to reach the highest level "y*" (situation in favor of the most able, group "B" and "C"). Second case: a 21 <a 32 and a 11 > a 22 : a 21 <a 32 : reaching level "x*" by group "B" is easier than reaching level "y*" by group "C". So, part of the group "C" will be dissuaded (however, their skills allow them to move to a higher level), and will decide the level "x*" (if the conditions are not favorable). A concentration will therefore be located in group "B". a 11 <a 22 : massification of group "C". In total, this case favors the less able to the detriment of the more able. Third case: a 21 <a 32 and a 11 <a 22 : a 21 <a 32 : massification of group "B". a 11 <a 22 : reaching level "x*" is easier for group "A" than reaching "y*" for group "B", and there we will have an increase in staff from group "B". What makes a concentration in group "B". Fourth case: a 21 >a 32 and a 11 <a 22 : a 21 >a 32 : massification of group "C". a 11 <a 22 : massification of group "B". In this case, we will have an increase in levels, but at the expense of group "B". Thus, the first case is the most favorable to a signal balance, on the one hand, and to the increase of the levels, on the other hand. In total, if we consider that we have: .a 31 <a 32 .a 21 <a 22 .a 11 <a 12 .a 21 <a 11 and .a 32 <a 22 , the result (I) and the first case, give the following balance: a 31 <a 32 <a 2 1 <a 22 <a 11 <a 12 4.3 Subsidy policy If public policy breaks away from any principle of differentiation, and decides to allocate aid (monetary, selective, social and psychological) without any discrimination, the main obsession of which is to increase the level of basic training of the population. We consider "s" the amount of public subsidies distributed without any discrimination, we will have "a 11 -s = a 21 ", to bring the agents of group "A" (the base) to the level "x*", two cases present: First case: a 11 -s = a 21 and a 22 -s> a 32 : We will have a concentration in the level "x*", and this level will take the place of level "0". As a result, the "x*" level is depreciated, and the "y*" level remains intact. Second case: a 11 -s = a 21 and a 22 -s = a 32 : There is a depreciation of the "x* and y*" level. Public aid must therefore be directed towards the most productive individuals, who come from the least advantaged backgrounds (socially and geographically). However, the academic criterion must be protected from any intervention, and the targeted public aid must not have an impact on the relevance of this criterion. Otherwise, the diploma loses its signaling capacity, and employers will increasingly seek high-level graduates, and the accumulation principle means that all diplomas will be affected by this depreciation. In this case, we will have a dramatic situation, where the agents will increase their training level as much as possible, monopolize the highest diplomas in a first stage, and lose all motivation for these diplomas in a second stage.
Conclusion
Reflection on training based on the theory of human capital is a fertile field of study still largely unexplored, but of which we increasingly measure the importance especially in research addressing solutions to fight unemployment, the phenomena of under and over qualification, or even the wage gaps.
The relationship at the heart of human capital theory illustrates the link between wages and education. However, this link is not sufficient to strictly demonstrate this relationship. In other words, it must be ensured that people who have completed longer studies necessarily receive higher incomes. Without this, human capital theory is powerless to explain the demand for education. The vast literature that has been produced on this subject is commensurate with this issue and its objective is to assess as accurately as possible the value of private returns to education.
Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.16, 2020 202 This must guide individual educational behavior and public policies. The theory is however not systematically verified. In fact, other variables come into play that has nothing to do with productivity (economic context, specifics of the company, regions, structure of the labor market, sector of activity, gender or age of the worker....). The filter theory initially presented by Arrow explains that training, and in particular the diploma, serves to provide information on the aptitudes of individuals (intelligence, work capacity, etc.). Education, therefore, does not serve to increase the productivity of individuals but to identify them so that they can be filtered. Arrow is interested in the costs and benefits to the community of such a screening process. Signal theory is an extension of the job market of that of the filter. Spence believes that education would not increase the agent's productivity, but would select the agents who are already and will be the most productive. In this case, it is necessary to question the social profitability of education which involves significant costs without improving worker productivity. The diploma obtained is therefore simply a signal for the employer, it is proof that the agent is better than the others and that he has been selected. The reexamination of the filter theory in our study exposes the idea of strengthening the filtering function within universities, to reexamine the fall in the real costs of higher studies, and above all to regularize university studies with the model of Market. Where we have differentiated four types of filters: First, the perfect non-productive filter, in this case, we notice that there is a hypersensitivity to aptitude: if the aptitude is doubled within the population, the level of education will be multiplied by more than "4". This illustration is strictly in favor of the fittest. Then, the imperfect non-productive filter where we distinguish two cases: -Funding opportunities within the population exceed skills. In this case, we will see a new regulation of wages by employers.
-The volume of skills in the population exceeds the funding opportunities. In this case, individuals will try to invest more than necessary in education so that their skills are better distinguished. Then, the productive and balanced filter the study shows that those of which they have higher aptitudes will seek the highest signal. And if we cancel the effect of education, the demand for the signal is reduced to the additional skill (the demand for the highest signals) and similarly, the difference in net income is limited only to the difference in skill. Finally, the filter and job occupied, in this case, the analysis shows that individuals in the unfiltered sector spend less time in school than those in the filtered sector. However, the income distribution in the unfiltered sector is lower than that distributed in the filtered sector. However, these income supplements are greatly reduced. In this study, we have also presented a reformulation of the Spence model by adopting three groups of individuals, and two levels of discrimination. This, on the one hand, illustrates the possible choices and the relative gains of a holder of an average diploma. On the other hand, allow us to highlight three choices instead of two (medium signaling, strong signaling, and no signaling). The study shows that the reporting process for middle-level diplomas is only valid when the number of individuals with higher-level diplomas does not exceed half of the least educated, which means that the signal effect does not own its own strengths, it depends on other signals. In this regard, we explain the most favorable case for signal balance, on the one hand, and increasing training levels, on the other. However, the formulations presented were based on strong hypotheses, supposing that there is a perfect match between skills, marginal productivity, and diploma, and also canceling market imperfections, which can present a limit to this study. | 7,296.8 | 2020-08-01T00:00:00.000 | [
"Economics"
] |
Hybrid Verification Technique for Decision-Making of Self-Driving Vehicles
: The evolution of driving technology has recently progressed from active safety features and ADAS systems to fully sensor-guided autonomous driving. Bringing such a vehicle to market requires not only simulation and testing but formal verification to account for all possible traffic scenarios. A new verification approach, which combines the use of two well-known model checkers: model checker for multi-agent systems (MCMAS) and probabilistic model checker (PRISM), is presented for this purpose. The overall structure of our autonomous vehicle (AV) system consists of: (1) A perception system of sensors that feeds data into (2) a rational agent (RA) based on a belief–desire–intention (BDI) architecture, which uses a model of the environment and is connected to the RA for verification of decision-making, and (3) a feedback control systems for following a self-planned path. MCMAS is used to check the consistency and stability of the BDI agent logic during design-time. PRISM is used to provide the RA with the probability of success while it decides to take action during run-time operation. This allows the RA to select movements of the highest probability of success from several generated alternatives. This framework has been tested on a new AV software platform built using the robot operating system (ROS) and virtual reality (VR) Gazebo Simulator. It also includes a parking lot scenario to test the feasibility of this approach in a realistic environment. A practical implementation of the AV system was also carried out on the experimental testbed.
Introduction
The Defense Advanced Research Projects Agency (DARPA) sponsored competitions between 2004-2007 [1,2] presented new results on autonomous ground vehicles that showed large steps forward in the field. However, the results still primarily address non-complex driving environments [3]. AVs, which operate in complex environments, require methods that can handle unpredictable circumstances and reason in a timely manner in complex urban situations, where informed decisions require accurate perception.
The development and deployment of AVs on some of our roads are not only realistic but can also bring significant benefits. In particular, they promise to solve various problems related to: (i) the improvement of traffic congestion, (ii) the reduction of the number of accidents (iii) automate the parking operation including looking for a free parking space, and (iv) encourage shared use of AVs to reduce overall fuel consumption [4]. Studies show that more than 90% of all car accidents are caused by human errors and only 2% by vehicle failures [5].
Considerable research and development resources are spent in industry and academia on hardware and algorithms, which cover different challenges such as perception, planning, and controls. Decision-making while driving is a vital process that needs special attention.
The primary cause of human accidents comes from incorrect decisions, and there will be limited benefits in developing AVs that continue to make those incorrect decisions at a similar rate to humans. Hence, we need to make sure that any decision the vehicle is going to take has been thoroughly verified.
AVs depend on many sensors to find their way among static and dynamic obstacles; each of those sensors has strengths and weaknesses. Cameras and LiDARs are usually used together in perception systems to provide a high level of certainty. LiDAR often provides excellent odometry, localization, mapping, and range information but with a limit to object identification. Cameras provide better recognition but with limits to localization accuracy [6]. A multi-sensor system can provide reliable information for perception in joined-up software architecture for timely processing of the sensory data in the context of localization and mapping, planning, dynamic obstacle detection, and avoidance [7].
Intelligent software agents have been in development for the past two decades. Some well-known agent types are reactive, deliberative, multi-layered, and belief-desireintention (BDI) agents [8,9]. The limited instruction set agent (LISA) [10] is a new multilayered approach to rational agents based on the BDI agent architecture, which is particularly suitable for achieving goals by autonomous systems.
With the increasing demand for machine learning techniques and advanced planning and decision-making methods, verification and guaranteed performance of the autonomous driving process has become a challenging problem. Reconfigurable and adaptive RA-based control systems are capable of controlling a vehicle in a trajectory to avoid other vehicles and people [11]. Integration is essential to enable decision-making based on behavior rules and experience in order to make decisions with foresight and consideration to other traffic participants. RAs have demonstrated significant robustness in the implementation of various applications. However, for real-world critical applications, some safety concerns can still be raised even after extensive testing, creating the need for an appropriate verification framework. It is important to note that validation and verification usually needs to be performed together to check the system. However, this paper focuses on a new verification framework for the safety of autonomous vehicles.
The testing of systems through prototype development only answers some of the components of operational safety questions. The best that can be achieved in testing is to use a representative set of scenarios on real vehicles. Simulations can provide illustrations of the correct dynamic and social behavior of the AV. However, it is difficult to take into account rare combinations of events that may arise during the run-time of the autonomous system. It is unlikely that the designer will think of all potential scenarios to ensure complete coverage. Formal verification methods try to answer the rest of the questions by accounting for all the probabilities for a given scenario [12,13]. If accurate dynamical models are available to represent robotic skills of sensing and action, then formal verification can rely on a finite interaction model of the vehicle with a bounded model of the environment, that is based on known characteristics of traffic participants. This paper describes a novel method for the verification of the decision-making system of an AV with a proposed architecture that lends itself to verification. We take into account the computer-based system consisting of AV design and simulation for the new verification platform. Safety and ease of implementation of the system are the two central themes in this paper, with the prime focus on the safety aspect. This paper presents a prototype system of an AV parking lot scenario with the ability to deal with the most vulnerable traffic participants: vehicles and pedestrians. In general, the level of autonomy of a vehicle can vary from fully human-operated (level 0) to a fully autonomous vehicle (level 5). Our vehicle is designed to work at level 4, where it can work autonomously in a restricted environment until it is interrupted [14].
The architecture of our proposed perception system is divided into four subsystems: LiDAR-based, vision-based, tracking-classification, and coordinate transformation. The perception system is used for localization and mapping, including calculating the relative positions of objects around the AV. The cameras are responsible for object recognition and detection of free parking spaces, with the aid of the LiDAR to provide an occupancy grid. The position of the objects is converted to the camera coordinate system, defining a region of interest (ROI) in the image space, then it obtains the depth information that belongs to that object from the LiDAR point cloud.
Most autonomous robotic agents use logic-based inference to keep themselves safe and within permitted behavior by providing the basis of reasoning for a robot's behavior [15]. Given a set of rules, it is essential that the robot can establish the consistency between its rules, its perception-based beliefs, its planned actions, and their consequences. In this paper, we are concerned with the high-level software components responsible for decisions in an AV capable of navigation, obstacle detection and avoidance, and autonomous parking. These logic-based decisions can either be implemented through a rational agent [9,10,[16][17][18][19] or through fuzzy logic [20][21][22] depending on the level of performance guarantee required.
To achieve this, we have established the following stages. First, we have built an AV system and its environment in ROS [23] and the Gazebo Simulator [24]. Second, we investigated how a robotic agent can use model checking through the use of the MCMAS model checker [25] to examine the consistency and stability of its rules, beliefs, and actions through computational tree logic (CTL) for the RA that has been implemented within the LISA agent programming framework [10,26]. Third, we have formally specified some of the required RA properties through probabilistic timed programs (PTPs) and probabilistic computation tree logic (PCTL) formula, which are then formally verified with the PRISM Model checker [27] during run-time operation of the AV. Finally, within the proposed verification framework, which comprises both MCMAS and PRISM verification tools, we have obtained formal verification of our AV agent for some specific behaviors.
We used Gazebo Simulator in this work because of its full compatibility with ROS, and the huge support from the robotics community. PTP is a formalism for modeling systems whose behavior incorporates both probabilistic and real-time characteristics. In PTP, the location/space is discrete, while time is continuous. It is a good compromise between computational complexity and accurate mathematical modeling. Efficient verification algorithms have been developed to verify PTPs.
The development and deployment of these autonomous vehicles will rely on their situational awareness [28][29][30][31][32]. The vehicles will be required to co-exist alongside vehicle controlled by humans and this presents a significant problem. Whilst simulation can be used to explore edge-cases and boundaries of operation this relies on the imagination of the designer of these systems. Therefore vehicles could look to learn and adapt to situations to improve their awareness and performance. The application of this situation-based learning is out of scope for this paper but provides motivation for future work.
Contribution
This work is a continuation of our previous work [33,34] to present a new and complete verification framework for the decision-making of an AV that combines both the designtime and run-time verification. The main contribution can be summarized as follows:
1.
New verification framework for decision-making of a self-driving vehicle that merges design-time verification represented by the MCMAS model checker and the run-time verification represented by the PRISM probabilistic model checker, which provide a comprehensive approach for the verification of AV's agent decisions.
2.
Design, simulation, and implementation of an AV through ROS open-source physicsbased system for a Tata Ace vehicle. Both the AVs in simulation and experimental implementation use the same perception, rational agent, planning, and control system software designed for a parking lot environment.
Related Work
Autonomous vehicles have been a major area of research interest for the research community since the DARPA Grand Challenge, which inspired the development of many AV testbeds across the industry and academia. An example is the Stanford's Junior [35], which provides a testbed with multiple sensors for planning and recognition. It is capable of dynamic object detection and tracking and also localization. Other examples are Talos from MIT [36], and Boss from CMU [37], among many others.
In this section, we discuss some recent platforms and techniques related to our work, developed for safe self-driving vehicle operation.
In ref. [38], the authors presented a testbed called cognitive and autonomous test (CAT) vehicle, which is comprised of a simulation-based self-driving vehicle, with a straightforward transition to hardware-in-the-loop testing and execution, to support research in autonomous driving technology. The idea is to support researchers who want to demonstrate new results on self-driving vehicles but do not have an access to a physical platform to mimic the dynamics of a real vehicle in the simulation and then provide a seamless transition to the reproduction of use cases with hardware. The Gazebo Simulator utilizes ROS with a physics-based vehicle model, including simulated sensors and actuators. Gazebo comes as a default simulator with ROS and is a physics-based simulator that has also been used in our work. Gazebo is not the only option that is available to design and test self-driving vehicles. Other simulators include CARLA [39], which has been developed to support the development, training, and validation of autonomous urban driving systems. CARLA is also compatible with ROS and supports flexible specification of sensor suites and environmental conditions. Another simulator that is also useful to develop and test self-driving vehicles is LGSVL [40], which is a multi-robot AV simulator. It has been designed as an open-source simulator based on the Unity game engine to test autonomous vehicle algorithms.
LGSVL also supports ROS where it helps to connect the simulator to a physical platform for tests.
Self-driving vehicles use a perception system to perceive the environment. Sensor fusion is used to bring together inputs from multiple radars, LiDARs, and cameras to form a single model or image of the environment around a vehicle. The resulting model is more accurate because it balances the strengths of the different sensors. In ref. [41], the researchers developed a perception fusion architecture based on the evidential framework to solve the detection and tracking of moving objects problem by integrating the composite representation and uncertainty management. They tested their fusion approach with a physical testbed from the interactive IP European project, which includes three main sensors: camera, LiDAR, and radar by using real data from different driving scenarios and focusing on four objects of interest: pedestrian, bike, car, and truck. The sensor fusion provides necessary information for different parts of the autonomous driving system, such as simultaneous localization and mapping (SLAM) and planning, which include both path planning and motion planning.
Other methods in the literature include the distance sensor-based parking assistance system, which recognizes an empty space using ultrasonic and LiDAR sensors as explained in refs. [42][43][44]. The problem with this system is that it will recognize a free space as a parking slot when the space is equal to the width of the vehicle is detected, even if the space is not a parking slot. This method is usually applied to a parking assistance system where the driver can determine a parking space. However, it is not compatible with a fully autonomous parking system, where the system judges a parking space and moves the car.
The around view monitoring (AVM) [45] can compensate for the disadvantages of distance-sensor-based detection as it can detect parking spaces based on parking slot lines instead of empty spaces. However, a false-positive (FP) can be detected from shadows and 3D objects, or the parking slot lines may be occluded by a nearby vehicle. Hence, the researchers proposed a probabilistic occupancy filter to detect parking slot lines. This filter uses a series of AVM images and onboard sensors to improve the occlusion problem and reduce the false-positive from other objects. However, this method still not very accurate and could mislead the AV in some cases.
The main topic we discuss in this paper is the verification of decision-making for our self-driving vehicle. This area of research has received more attention in the last few years as the complexity of the autonomous software has increased while the safety and feasibility of these decisions have been under investigation due to series of fatal incidents that occurred with these autonomous systems as listed in ref. [46]. In ref. [19], the authors show how formal verification can contribute to the analysis of these new self-driving vehicles. An overall representation for vehicle platooning is a multi-agent system implemented within the GWENDOLEN agent programming language in which each agent captures the "autonomous decisions" carried out by each vehicle. They used formal verification to ensure that these autonomous decision-making agents in vehicle platoons never violate any safety requirements. The authors presented a method to verify both the agent behavior using Agent Java PathFinder (AJPF) and the real-time requirement of the system using the Uppaal model checker where the system is represented as timed automata.
In ref. [47], Fernandes et al. modeled an AV with a rational agent for decision-making. To achieve this, they have established the following stages. First, the agent plans and actions have been implemented within the GWENDOLEN agent programming language. Second, they have built a simulated automotive environment in the Java language. Third, they have formally specified some of the required agent properties through LTL formulae, which are then formally verified with the AJPF verification tool. Finally, within the model checking agent programming language (MCAPL) framework they have obtained formal verification of the AV agent in terms of its specific behaviors and plans.
In ref. [48], Giaquinta et al. presented probabilistic models for autonomous agent search and retrieve missions derived from Simulink models for an unmanned aerial vehicle (UAV) and they show how probabilistic model checking using PRISM model checker has been used for optimal controller generation. They introduced a sequence of scenarios relevant to UAVs and other autonomous agents such as underwater and ground vehicles. For each scenario, they demonstrated how it can be modeled using the PRISM language, give model checking statistics and present the synthesized optimal controllers.
In our work, our system is different in the following aspects: we focused on adapting and developing different techniques and methods that contribute towards the design of a safe self-driving operation. We used ROS to design the main system functions such as the perception and control subsystems. We used a similar method presented in ref. [38] where the system built-in ROS supports hardware-in-the-loop. The difference is that our ROS system was designed to satisfy the needs for our testbed-the TATA ACE electric vehicle. Further, it provides additional functions to connect to the main decision-maker onboard and the verification system. This represents a modular overall system that supports adding more subsystems when needed. For the perception system, we used a similar set of sensors usually used by others, where this is represented by a stereo camera, mono-cameras, and LiDAR. The combination of this set provides sufficient data to perceive the vehicle's surroundings. The perception system is presented in Section 4. We tested our system for autonomous parking scenarios. The AV needs to look for the attached Aruco markers on each parking slot; this method is used for its simplicity, reliability, and compatibility with the fully autonomous driving mode compared with other methods mentioned in the literature. However, this method needs to be supported in the parking lot by installing Aruco markers on some or all of the parking slots to be used by AVs.
As we mentioned, this work focused on the verification of the decision-making of AVs. The novelty of our work comes from the fact that we tried to thoroughly verify the reasoner and the decisions from multiple aspects to make sure that any decision that could be made is safe to apply. We applied the verification for the reasoner offline during the design-time and online during the run-time operation.
The reasoner software has been designed by natural language programming using software called sEnglish, as explained in Section 5. This method is used for its simplicity and compatibility with the ROS system and the verification tools. However, this method comes with some limitations and it is difficult to be used with a higher-level autonomous system presented in level five autonomy.
For the design-time verification, we used the MCMAS model checker to check the consistency and stability of the logic predicates. The PRISM model checker is used to verify the decisions made by the agent during run-time operation. Details of this method are explained in Sections 6 and 7.
System Overview
A standard AV has a control architecture that incorporates both low-level and highlevel components. The low-level components include sensors and actuators, while the high-level system components are often responsible for decision-making based on data provided by low-level components.
Our perception system provides a stream of images and 3D point cloud data obtained from sensors commonly used in AVs. It consists of eight mono-cameras (three on each side and two at the back), a stereo camera on the front, and a LiDAR on top that can be shifted left and right and tilted with a specific angle by the high-level system for better coverage. The stereo camera in front of our vehicle uses a deep-learning-based object detector that is capable of detecting different objects, including those that could exist in a parking lot environment. The perception system can also localize free parking spaces by using fiducial markers. These data are converted to high-level abstract statements that can be used by the RA onboard the vehicle. A case study of a parking lot scenario has been carried out to demonstrate the verification methods and to show the feasibility of our approach.
The AV system in Figure 1 is based on a modular design that makes practical implementations relatively simple and allows for future updates. The decision agent is central to the system design. We used the LISA agent paradigm due to its capability to execute actions based on decision-making to pursue goals while also not being too complicated to enable verification. The decision process also uses rules and abstractions from future predictions (consequences of future events) and can re-plan the path of the AV when needed. The rational agent (RA) is capable of communicating with the perception system to sense the environment and instruct the actuators to move the vehicle in a collision-free path without the need for human support. To achieve this, the perception system builds a model of the environment, localizes objects around, and keeps updating its model after each perception cycle. The software agent has rule-based reasoning, planning capability, and some feedback control skills for steering and velocity regulation. The RA has been implemented using natural language programming (NLP) in sEnglish [17], as mentioned in Section 5.
The vehicle in simulation supports a scalable, modular design to ease the implementation of different system parts and further development. The physics-engine-based simulation shown in Figure 2 consists of a model of the Tata Ace electric vehicle shown in Figure 3, with the same specifications and parameters for the vehicle and sensors.
The AV is based on packages designed with ROS, using Python and C++. ROS provides tools and libraries for writing perception and control algorithms and other applications for AVs. With various levels of hardware and software abstractions, device drivers for a seamless interface of sensors, libraries for simulating sensors, and a visualizer for diagnostics purposes, ROS provides middleware and interoperability to simulation software, and the software installation is straightforward. Being a distributed computing environment, it implicitly handles all the communication protocols. The hardware used in this work has been selected through experimental tests, a similar set has been widely adopted by other prototypes design of AVs.
Mono cameras 3D Lidar
Stereo camera However, standard ROS packages lack domain-specific requirements for experimentation with a car-like robot. A typical setup of an AV consists of a controller and a set of sensors tested and mounted to provide sensing modality that provide a complete view of the environment around the test vehicle. In order to control motion seamlessly, we created interfaces for control and consistent consumption of sensor data. We had tested the current state of the vehicle and issued control signals well before the real platform was engaged. Once algorithms were tested in simulation, they could be implemented in the real vehicle, and the physical platform was then replaced the AV in simulation. The simulated version was used as a proving ground for the algorithms, to build confidence in their operation before transferring to the, naturally more complex, physical system.
We created models of the AV, parking lot, pedestrians, and other vehicles in the parking lot mainly using the SkechUp software [49] to create 3D models recognized by Gazebo Simulator.
In this work, we are interested in both design-time and run-time verification; this process involves the analysis of the system to detect behaviors violating the required properties. Design-time architecture verification is performed using MCMAS and probabilistic run-time verification using PRISM. We have programmed a compiler from LISA to build the models for MCMAS. The latter was then used to check the consistency and stability of beliefs, rules, and actions of the AV in its environment. When the logic predicates are inconsistent or unstable, a counterexample is generated to demonstrate the violation and help developers to correct the system [50]. PRISM is used by the RA at run-time to ask questions such as 'what is the probability of success of the current action' or 'what is the probability of achieving the current goal within a time limit' [27], the parameters used to estimate the probabilities depending on the driving scenario were, for example, the speed of the AV, speed of moving objects, and the direction of movements. For example, the agent can ask what is the probability of success if the AV were to move to a specific location within a specific period, taking into account the dynamic models (generated by the agent) of other objects moving around.
Driving in urban environments is characterized by uncertainty over the intentions and behavior of other traffic participants, which is usually considered in the behavioral layer responsible for decision-making using probabilistic planning formalisms, such as Markov decision processes (MDPs) to formulate the decision-making problem in a probabilistic framework. We used a different approach in probabilistic systems represented by probabilistic timed programs (PTPs) [51] to model the behavior of the AV and the proposed behavior of the other participants. A detailed explanation is presented in the following sections.
Design and Implementation of Self-Driving Vehicle
The hierarchical system is decomposed into four components, as shown in Figure 4: The perception system is used to receive information about the environment and feeds this information to the second stage. Here the agent makes decisions on the suitable progress of the car towards the destination by rules of interaction and rules of the road. The next stages are the global path planner and the local path planner, which are responsible for generating the path of the AV from the starting point to its destination based on the directions and speed profile set by the RA, then select a continuous motion plan through the environment to achieve a local navigation task. The last component is the control system that executes the motion using actuators and corrects errors in the execution in a feedback loop. In the remainder of the section, we discuss each of these components briefly. [17,52], whereas the verification system was designed in MCMAS and PRISM verification tools.
Perception System
Modern vision-based detection techniques work by extracting image features to segment regions of interest (ROI) then detect different objects within those regions. In particular, the detection of people and vehicles has made significant progress in the autonomous and assisted driving areas [53,54]. Radar is a robust and invaluable information source for perceptual tasks; however, the spatial resolution of radar is typically poor compared to camera and LiDAR. Thus, much recent perception research is focused toward cameras and LiDAR. We have designed a parking lot scenario in ROS and Gazebo to explain the use of different sensors as shown in Figure 5.
Detection methods based on mono-cameras suffer in two ways: despite the methods proposed for moving mono-cameras, fast and accurate range measurement remains an issue, which is vital for critical object detection in autonomous driving applications. Optical sensors can suffer from a limited field of view and poor operation during low lighting conditions. On the other hand, LiDAR is usually paired with the advanced driver assistance system (ADAS) applications and has become part of the AV perception system because of the high precision range measurements and the wide field of view that it provides. The main issue for the LiDAR-based system is that the data from scans do not contain information that easily allows different objects to be distinguished between, especially in a dense environment.
Stereo cameras can provide more precise depth data and a wider angle compared with mono-cameras. However, the detection angles are smaller than LiDAR, and it is also less precise in providing depth information, especially over the long distances that are often vital for AV decision-making. The integration of cameras and LiDAR sensors can enhance fast object detection and recognition performance [41]. This type of sensor fusion system is known as the classic LiDAR-camera fusion system.
In this simulation-based system, we tried to mimic our approach for the experimental AV system, where we used a Velodyne VLP-16 LiDAR, one ZED stereo camera, and eight Raspberry Pi 3 model B mono-cameras (8 megapixels each), The properties for these sensors are mentioned in Table 1. The LiDAR is connected directly to ROS for point cloud data processing. The front-facing stereo camera is connected to the Jetson TX2 running YOLOv3 [55] deep-learning-based object detection. The mono-cameras use the processing power of their host Raspberry Pi system for aggregated channel features (ACFs) object detector of pedestrians and vehicles [56]. Those mono-cameras, along with the stereocamera, cover a 360 • FOV. The camera system has also been equipped with a method for fiducial-follow that uses Aruco markers to detect the location and orientation of free parking slots, as shown in Figure 6 (right camera one and two). Along with the occupancy grid data generated by the LiDAR, the AV is capable of detecting free parking spaces simply and efficiently. Figure 6 also shows the detection of vehicles and pedestrians, which is a vital process for normal operation of the AV.
When a known object is detected by one of the cameras, the associated LiDAR measurements are processed for the distance calculation by matching the location of the detected object with the 3D point cloud data belonging to the same object. Based on the generated depth map, the position and direction of the object are calculated from the ROI, those measurements from LiDAR are calculated according to the coordinates transformation.
We used the LiDAR odometry and mapping (LOAM) [57] ROS package for Velodyne VLP-16 3D LiDAR. This package provides a real-time method for mapping and state estimation by applying two parallel threads: The odometry thread to measure (at a higher frame rate) the motion of the LiDAR between two movements and to eliminates distortion in the point cloud. The second is a mapping thread that incrementally builds the map (at a lower frame rate) based on the undistorted point cloud, and also to compute the pose of the LiDAR on the map. Figure 7 shows the map built for the AV current path in the parking lot shown in Figure 5. The sides of the objects that are facing the LiDAR are shown on the map with white lines. We added another layer of protection using a cost map function, which helps the AV to keep an extra safe distance from any object within a specific inflation distance where this could be set according to the environment type; it is represented on the map in Figure 7 with the blue lines surrounding the white lines. Finally, the data for the detected objects and their locations are sent to the RA for further processing.
Autonomous Behavior
Recent approaches for AVs have used prediction methods in order to avoid collision by estimating the future trajectory of the surrounding traffic participants. However, real traffic scenarios include complex interactions among various road users and need to handle complex clutter and modeling interactions with other road users to ensure safety. In the DARPA urban challenge, various solutions for planning were proposed; most of those solutions were specifically tailored to the competition demands. Many approaches (e.g., refs. [36,37]) use a state machine for AV to switch between predefined behaviors. These rule-based approaches need a safety assessment in order to deal with uncertainties. AV with human-like driving behavior requires interactive and cooperative decision-making.
Other vehicle's intentions need to be modeled and integrated into a planning framework that allows for intelligent, cooperative decision-making without the need for intervehicle communication. While AVs need the ability to reason the intentions of other participants, those also need to infer the AV's intention reasonably. This results in interdependencies and interactions based on the scene and shown behavior without the need for explicit communication [58].
By simulating the proposed traffic scenario, we can search for a possible best policy measured against the AV's cost function, and then the best policy is executed from the set of available policies for the AV. Possible trajectories can also be sampled, and the reaction to the environment can be determined according to the RA model.
The AV must be able to interact with other road users in accordance with codes of conduct and road traffic rules. For a given sequence of road segments specifying the selected route, the behavior layer is responsible for selecting appropriate driving behavior based on the perceived behavior of other road users and the road conditions. For instance, when the AV searches for a vacant parking space in a parking lot, the behavioral layer instructs the vehicle to observe the behavior of other vehicles, pedestrians, and other objects during its movement and let the vehicle proceed once it is safe to go. Since the driving contexts and behaviors available in each context can be modeled as finite sets, a natural approach to automating this decision-making is to model each behavior as a state in a finite state machine with transitions controlled by the perceived driving context as the relative position to the planned route and nearby vehicles. Finite state machines, combined with different heuristics specific to the driving scenarios considered, have been adopted by most DARPA Urban Challenge teams as a behavioral control mechanism.
In the literature, similar approaches have been made by reducing decisions to a limited set of options and conducting evaluations with an individual set of policy assignments for each option. In general, the probabilistic representation of system models can be divided into four main types: discrete-time Markov chain (DTMC), continuous-time Markov chain (CTMC), Markov decision process (MDP), and probabilistic timed automata (PTA). A typical implementation of learning different driving styles in a highway simulation showed the potential of the probabilistic approach represented by MDP [59,60]. In ref. [61], the authors showed an enhanced version of the algorithm and its performance by generating human-like trajectories in parking lots, with only a few demonstrations required during learning. A partially observable MDP (POMDP), an extension of MDP, has been used in refs. [62,63] to integrate the road context and the motion intention of another vehicle in an urban road scenario.
Our RA and its physical environment have been modeled as a probabilistic timed program (PTP) model, which is an extension of PTA with the addition of discrete-valued variables that can be encoded into locations [51], while we used the probabilistic computational tree logic (PCTL) for specification logic [64]. A PTP incorporate probability, nondeterminism, dense real-time, and data. Its semantics are defined as infinite-state MDPs consists of the states of the environment and the transition between those states, which, through the conditional probabilities of the environment, correspond to triggering of predicates through the sensor system of the AV.
Pre-programmed rules are used to set the relationship between the perception predicates (beliefs) and the available actions. When this combination is verified by MCMAS during design time, then there will be no space for an unfeasible, repeated, or misleading action in the agent's actions list. The advantages of this operation are clearer when we deal with general real-life driving scenarios that could have a large number of predicates; in this case, the manual checking of those predicates would be unfeasible.
Planning System
Planning modules are concerned with vehicle motion and behavior in the perceived environment. Typically they comprise trajectory generation and reactive control for collision risk mitigation. They are organized into sub-maps to provide the flexibility of updating and to handle large environment maps. These are integrated and corrected for changes by a graph optimization approach with critical landmarks as nodes [65]. The planning system consists of two different components.
Path Planning
The RA is setting the waypoints to move the AV in the environment. These high-level commands are sent to the path planning ROS node to generate the route for the AV from the starting point to the desired destination. The entrance of the parking lot represents the starting point, and the destination is a free parking slot, which is an unknown place that needs to be discovered by the perception system while exploring the area. We used an ROS-based Dijkstra algorithm [66,67] for its simplicity and efficiency. This method represents the roads as a directed graph with weights represents the cost of passing a road segment. This process starts with a set of nodes (free space) that the AV can navigate and assigning a cost value to each one of them, this value is then increased with the next nodes, and the algorithm needs to find a path with minimum cost.
After finding the appropriate path, all the nodes in that path are translated into positions P i = (X i , Y i ) T in the reference axes. The outcome is not smooth, and some points are not compliant with the vehicle kinematics, and geometry, hence the second stage (motion planning) is necessary.
Motion Planning
In order to transform the global path into suitable waypoints, the timed-elastic band (TEB) motion planner creates a shorter set of waypoints P i = (x i , y i , θ i ) T within the original path planner waypoints. This takes into account, as much as possible, the vehicle constraints and the dynamic obstacles. Hence the map is reduced to the area around the AV and is continuously updating. When the path planning node determines the path of driving to be performed in the current context, then the ROS-based TEB local planner algorithm [68,69] will be used to translate this path into shorter continuous trajectories that are feasible for the control system and actuators to track and follow. This trajectory should also avoid collision with obstacles, detected by the sensors on-board, and should also be comfortable for the passengers. In case there is an object nearby, then the agent will check the possibility of collision using the PRISM model checker and then modify the trajectory when needed.
Control System
A control system is needed to execute the proposed trajectory of the AV. The move_base control node operates the AV by executing acceleration, braking, and steering messages. The control node takes the list of waypoints as input, and target velocities generated by the planning subsystem. Then sends these waypoints and velocities to an algorithm that calculates the amount of direction, acceleration, or deceleration to reach the target path.
Via a feedback controller, the appropriate actuator inputs are selected to perform the intended motion and correct the tracking of errors. These errors generated during the execution of a planned movement are due in part to the inaccuracies of the vehicle model. Therefore, the focus is placed on the robustness and stability of the controlled system. Different feedback controllers have been proposed in ref. [70] for executing the reference motions provided by the motion planning system.
Running the move_base node on the AV that is appropriately configured results in attempting to achieve a goal pose with its base to within a user-specified tolerance.
Background
LISA [10] is a reactive agent that uses information from the environment in order to make a decision. These decisions are based around a set of beliefs, desires, and intentions that define its behavior [8,71]. Beliefs represent the knowledge derived from sensors to provide an observation of the current state of the environment. For example, if the sensors of an AV detect a person, the agent would hold the belief that a human was nearby. Desires correspond to the long-term goals of the agent. These long-term goals can correspond to states within the environment, for example, the position of an AV in a parking space, which the agent will use to attempt to establish in its behavior. Intentions, contrasting with beliefs, represent short-term goals of the agent, for example, once a person is detected, the RA will have the intention to avoid that person while they are nearby.
sEnglish
AV's decision-making programming is complicated, time-consuming, error-prone, and requires expertise in both the proposed tasks and the platform. There are many proprietary design tools in the industry [58,72] that require specialized knowledge. In order to simplify this process and to broaden the understanding of how decisions for AV actions are taken by non-experts to understand and verify the system in case of a legal need, such a method could be crucial to law enforcement agencies, insurance companies, and lawyers in the event of an accident to review the program and the reason for AV taken a specific action.
The RA is implemented using sEnglish [17,52] natural language programming. Within sEnglish, the plans operate over a description of the world, which is captured within the system and environment ontology and maintained by data from sensors in the world model. The system ontology provides a simple, translatable description between concepts that a programmer and end-user would equally understand, such as common nouns, and those that an agent can use or manipulate, such as variables or pieces of data. In sEnglish, the agent's plans are described using English sentences in a structured text, including conditioning. The meaning of sentences is explained by an sEnglish text using sentences until further decomposition of meaning reaches the signal processing level when C++ is used to define the meaning. At this C++ level, no interpretable concepts need to be defined by the ontology.
The agent takes its decisions relying on information coming from its environmental model or knowledge base, which is a database regularly updated via sensors and perception mechanisms, and potential any learned inferences. This database is organized into a highlevel ontology and provides information about the system and especially the current state of the environment.
Plans are declared by the programmer. Although this makes the agent less creative at run-time, as the plan library is fixed and not dynamically generated by the agent, this has significant advantages in terms of fast execution and viable formal verification [73]. In many safety-critical systems, such as formal verification, the core agent is crucial. Hence, this kind of BDI agent combines the advantages of deliberative agents with the advantages of reliability and explainability.
Mathematical Representation of the Agent
The LISA rational agent definition of our AV will follow [9,16,17] and it is based on AgentSpeak-like BDI architectures of robotic agents.
A rational agent in LISA can be fully defined and implemented by listing the following characteristics: • Initial Beliefs. Initially, once the agent is initialized, it will have a set of beliefs about the environment. These beliefs are referred to as B 0 ⊂ F that are a set of literals that are automatically copied into the belief base B t (the set of current beliefs) on initialization. • Initial Actions. The initial actions A 0 ⊂ A are a set of actions that are executed when the agent is first to run. Typically these actions are general goals that activate specific initial plans set up by the programmer. • Logic rules. A set of logic-based implication rules, L = R P ∪ R B , describes theoretical reasoning about physics and behavior rules to enable the agent to adjust its current knowledge about the world and influence its decision on actions to be taken. • Executable plans. A set of executable plans or plan library Π. Each plan π j is described in the form: p j : c j ← a 1 , a 2 , . . . , a n j where p j ∈ P t is a triggering predicate, which allows the plan to be retrieved from the plan library whenever it comes true. Next the p j ∈ P t allows the plan to be retrieved from the plan library whenever the belief base dictates that its triggering conditions are true; c j ∈ B is called the context, which allows the agent to check the state of the world, described by the current belief set B t , before applying a particular plan; the a 1 , a 2 , . . . , a n j ∈ A then form a list of actions that the agent will execute.
The LISA rational agent defined in this paper will follow these rules and is defined: where: • F = {p 1 , p 2 , . . . , p n p } is the set of all predicates. In practice, this set can be infinitely large for general driving scenarios, however we are presenting this new approach to be tested on a specific limited driving scenario, which is driving in a parking lot. With some modifications and improvements this method could be generalized for other driving scenarios for future work. • B ⊂ F is the atomic belief set, the set of all possible beliefs that the agent may encounter during operation. The current belief base at time t is defined as B t ⊂ B. During operation, beliefs will always be changed. This occurs through events so that at a time t, beliefs may be added, deleted, or modified. These events are represented in the set E t ⊂ B, which is called the Event set. Events may be based on internal or external actions. Internal actions are described as "mental notes". External inputs will appear through input from a sensor and are called "percepts" as they represent a measurement of the environment. • L = R P ∪ R B = {l 1 , l 2 , . . . l n l } is a set of implication rules. These are logic-based and represent a description of how the predicates B can be linked together and interpreted. • Π = {π 1 , π 2 , . . . , π n π } is the set of executable plans or more formally plans library. At any time, t, there will be a collection of plans that could be activated. These are a subset of the complete plan library, Π t ⊂ Π, which is commonly named the Desire set. A set I ⊂ Π t ⊂ Π of intentions is also defined. This set, l, contains plans that the agent is committed to executing. Each plan is built up as a sequence π j (λ j ) of actions where π(0) is a triggering condition for the plan, and λ j > 0 ∈ A provides the subsequent series of actions that will be carried out. • A = {a 1 , a 2 , . . . , a n a } ⊂ F \ B is a set of all available actions. Actions may be either internal, when they either modify the knowledge base or generate internal events, or external, when they are linked to functions that operate in the environment.
This completes the definition of the AV agent used. The above list of steps are cyclically repeated to run the reasoning process of a robotic agent. Part of the agent program is shown in Figure 8 that has been used to generate PTP models for the AV and the other traffic participants based on perception predicates, the values shown are tailored to the physical characteristics of the vehicle.
In the example, the formation of plans is shown for an agent undertaking an autonomous parking maneuver. In this case, eight plans are presented that represent the agent's actions; each is represented by a triggering condition. The perception process represents sensing data that are collected on every evaluation. The 'ˆ[. . .]' represents the evaluation of a belief condition that can be set by an internal event. In this case, both plans start by evaluating whether a specific belief is matched. Should this belief be matched, a series of actions is then planned, again any element headed 'ˆ[. . .]' shows then update of a belief, elements shown within square brackets are executable sentences that contain code defined deeper within the structure which links to actuation.
Plan 1 can be read as follows: if I believe that no free parking space is detected, then I believe that I need to explore the parking lot. This is then extended by Plan 2, which can be read as if I believe I need to explore the parking lot, then a set of exploration waypoints should be generated, and these should be uploaded to activate the drive mode. Plan 3 is used to capture the condition when a parking space is detected and can be read: if I believe that I have detected a free space, then I can remove the belief that I need to explore the parking lot, and I believe I can commence parking operation.
Plan 4 contains the high-level code with trigger for planning this movement: if I believe that I can commence the parking operation, I should generate a set of waypoints for the parking and update the drive mode to reflect this. Plans 5, 6, and 7 can be read as two pairs; each deals with the detection of an object, either a person or a moving vehicle. In each case, if it is detected at a distance between 12 m and 6 m then new set of waypoints is generated to avoid the object, if the distance between 6 m and 3 m, then the drive mode is switched to a slower mode, and a new set of waypoints is generated; otherwise, the vehicle is stopped. Figure 8. Part of the agent code used to control the AV.
Connecting the RA to ROS
The sEnglish agent is natively compatible with ROS. The collection of sEnglish sentences that are set up by the programmer can comprise more complex sentences until atomic actions are then reached. These atomic actions can either be represented as sentences linked to libraries or native C++ code. The programmer can directly interface this C++ code to existing ROS libraries; therefore, the agent can be directly linked to the distributed ROS system.
A recent example of this operation is shown in handling nuclear material [18,74] for a robot arm. In this case, an sEnglish agent is developed and linked to an ROS network, in one case controlling a KUKA IIWA manipulator. In another, the agent is plugged into a different, but compatible drive for a KUKA KR180 manipulator. The only difference is the underlying drivers, providing an identical interface is provided, typically through topics and services available in ROS. The programmer can rapidly configure an sEnglish agent to operate within a distributed network for different applications.
Verification Methodology
In our decision framework, the agent uses model checkers MCMAS and PRISM to make appropriate and safe decisions for run-time operation. At design time, MCMAS can check if the logical reasoning system of the agent is consistent and stable [50]. The set of consistent and stable actions are fed into PRISM to find the most likely-to-succeed trajectory and action for that moment during the run-time operation.
Design-Time Verification
MCMAS is a symbolic model checker for multi-agent systems. It enables the automatic verification of specifications that use standard temporal modalities as well as the correctness, epistemic, and cooperation modalities. These additional modalities are used to capture the properties of various scenarios.
Agents can be described in MCMAS by the interpreted systems programming language (ISPL). The approach is symbolic and uses ordered binary decision diagrams (OB-DDs), thereby extending standard techniques for temporal logic to other modalities distinctive of agents. The logical reasoning system in the agent has a set of reasoning rules, which can be formulated as a Boolean evolution system (BES). B unknown is a set of unknown predicates in its initial evaluation that could be determined later as B known (B true ∨ B f alse ), or continue to be Unknown, • R is a set of reasoning rules (evolution rules) of the form X → Y, R = {r 1 , · · · , r m } defined over B.
In the logical system, a Boolean variable in B known usually represents a sensing event, e.g., a pedestrian comes close (e.g., within 5 m) to a vehicle. A pseudo-Boolean variable in B unknown can express a belief, an action, or a consequence of an action, whose value is unknown at the beginning of a reasoning cycle.
When a guard g of a rule is evaluated to true on a valuation B of B, we say that the rule is enabled. After applying all enabled evolution rules over B simultaneously, we obtain a new valuation B . If two enabled rules set a variable to different values in B , then the reasoning system is inconsistent. Starting from valuation B 0 , we can apply the evolution rules infinitely and obtain valuations B 1 , . . . , B i , . . . if the reasoning system is consistent. However, the system is unstable if for any pair of adjacent valuations B i and B i+1 , we
Run-Time Verification
PRISM is a probabilistic model checker [27], a verification tool for modeling and formal analysis of systems that present probabilistic behavior. PRISM has been used to analyze different kind of systems from different domains, such as planning and synthesis, communication, game theory, performance and reliability, security protocols, etc. PRISM can build and analyze several probabilistic models including Markov decision processes (MDPs) plus extensions of these models with costs and rewards.
PTPs is an extension of MDPs with real-valued clocks and state variables. For timed automata formalisms, discrete variables are typically considered to be a straightforward syntactic extension since their values can be encoded into locations.
Given a set S, P (S) denotes the power set of S and D(S) the set of discrete probability distributions over S. A PTP contains a set of state variables and a set of clock variables. The state variables model the discrete events in the environment and the clock variables model the time elapse, which is a continuous process. Let X be the set of clock variables. The set of clock valuations is defined as R X ≥0 = {t : X → R ≥0 }. Given a clock valuation t and δ ≥ 0, a delayed valuation t + δ is defined as (t + δ)(x) = t(x) + δ for all x ∈ X . Given a subset Y ⊆ X , a new valuation t[Y := 0] is defined by setting all clocks in Y to 0, i.e., t[Y := 0](x) is 0 if x ∈ Y, and keeping other clocks unchanged. We used probabilistic discrete time and space in this work, hence it is necessary to use clock zones to set the time for each state and the transitions between states. A clock zone can be defined as a set of clock valuations that satisfy a number of clock difference constraints of the form: ρ = {t ∈ R X 0 ≥0 | t i − t j b ij }. Let Zones(X ) be the set of all zones. Given a set V of state variables, let Asrt(V ), Val(V ), and Assn(V ) be a set of assertions, valuations, and assignments over V, respectively. Definition 2 (Probabilistic Timed Program (PTP) [75]). A PTP is a tuple of the form: P = (L, l 0 , X , V, v i , I, T ) where: • L is a finite set of locations; • l 0 ∈ L is the initial location; • V is a finite set of state variables; A state of a PTP contains the valuation of L, V, and X , and written as (l, v, t). A new state can be reached by either an elapse of some time δ ∈ R ≥0 or a transition τ = (G, E , ∆) ∈ T (l) where G ∈ Asrt(V ) is the guard, E ∈ Zones(X ) is the enabling condition, and ∆ = λ 1 ( f 1 , r 1 , l 1 ) + · · · + λ k ( f k , r k , l k )) is a probability distribution over an update f j ∈ Assn(V ), clock resets r j ⊆ X and a target location l j ∈ L.
When the agent starts a reasoning cycle, it will obtain a set of actions that can be safely applied, given the characteristics of the vehicle and measurement of the environment. This set of actions is predefined in the agent code during the design stage. If the set contains more than one action, then we use PTP to find the most suitable action for the AV to take. The most suitable action is the one that will not cause a collision, also compatible with the driving rules predefined for the agent, and will ultimately participate in reaching the destination in a shorter time and path can be considered as a safe action to apply, all of these parameters will be thought of by the agent and checked by the verification system while driving to make sure it is safe to apply. A PTP models the dynamic and uncertain physical environment containing the AV itself and other static or moving objects, such as pedestrians and other vehicles.
Verification of Decision-Making
This section presents an example of a parking lot scenario, where the AV is searching for a free parking space. During this process, the RA will continuously monitor the road users in its environment and decides its actions and trajectory based on the data from the perception system. The RA then checks all the probability of success of the intended actions before any execution using PRISM model checker.
MCMAS is used to verify (during design time) the beliefs, rules, actions, and their consequences that need to be considered within zone 1 and 2 of the AV, as shown in Figure 9. We used a limited set of rules and predicates for the parking lot scenario for proof of concept; real-life driving scenarios will need more rules and predicates to determine the proper behavior of the AV.
The AV needs to build a feasible trajectory and to maximize the distance from the objects around a suitable cost-map. The movements of the traffic participants are usually amenable to a probabilistic model based on the environment situation. A trajectory for a pedestrian walking in a parking lot is estimated by a prediction method [76,77], also ac-counting for previously collected data sets in similar scenarios, e.g., Ref. [78]. A pedestrian may keep walking at the same speed if there is a car passing nearby or could reduce the speed, stop, or change the path; the same idea can be implemented for car drivers taking into account the vehicle dynamics.
In this work, the agent generates probabilistic behavior models for the non-stationary objects based on the observed situation and from previously recorded behavior of pedestrians and drivers in real-life scenarios. The method used for trajectory prediction has been combined with prior statistics for better estimation of the object's behavior. The verification system will take into consideration probabilities for the moving objects, verifying the intended actions against them using the PRISM probabilistic model checker, to select the most likely-to-succeed action for execution. The agent keeps updating the probabilistic models of the dynamic objects and sends it to an onboard PRISM in each reasoning cycle of the agent.
This operation is repeated as long as there are no objects within zone 1 of the AV shown in Figure 9, If there is any moving object within zone 2, then the AV will halve the speed. As soon as one of the moving objects comes across zone 1, then the AV will stop based on pre-programmed rules.
Design Time Verification in MCMAS
Here we define three sets of predicates: sensing abstractions, future events consequences, and actions, as listed below. The operational logic of the RA is restricted to the parking lot scenario. The RA will choose its decisions based on the sensory abstractions and a set of rules, as shown in Figure 10, those rules determine the best action to be carried out by the AV based on the sensing abstractions and the possible future event consequences. MCMAS is used to compute with the resulting Boolean evolution system to verify the logical stability and consistency of those predicates.
The number of those rules could rapidly increase depending on the driving scenario and the environmental situation. While it is challenging for the designer to check that there is no conflict between them manually for this simple case study, it will be even harder when taking into account other general driving scenarios.
2.
The sensory abstractions of moving objects (Zone 1/outside the trajectory of the AV but predicted to come across) are:
9.
The future events (consequences) for moving objects (Zone 1) are: • FCN1: pedestrian detected and will be collide. • FCN2: car detected and will be collide. • FCN3: object detected and will collide.
12. The parking actions available to AV: • AA1: generate new motion plan for parking. • AA2: return to previous motion plan.
Predicates Definition
Here we define three sets of predicates: sensing abstractions, actions, and future events consequences, as listed in Section 7.1. The operational logic of the RA is restricted to the parking lot scenario. The RA will choose its decisions based on the sensory abstractions and a set of logic rules, as shown in Figure 10; those rules determine the best action to be carried out by the AV based on the sensing abstractions and the possible future event consequences. MCMAS is used to compute the resulting Boolean evolution system to verify the logical stability and consistency of those rules.
Worst Case Mathematical Model
Each rule can be verified by computing the minimum space-time distance of the evolution of the progress of the oncoming car/pedestrian/object (denoted by E) and that of the AV (denoted by V): Which describes the future movements of the environmental object and the AV, respectively. t c is the current time when sensing of E and AV decisions have been completed, and E c and V c are the oncoming objects and the AV position at the time of the sensor measurement are abstracted, and the decision is made by the AV what to do. We say that no collision occurs in the worst case if the geometric distance (in 3D) of these two lines is greater than 1 m for any possible heading angle α and positions E c outside Zone 1 and Zone 2 in Figure 9. s is a time separation factor defined as s = 1 m/s to make the dimensions in-space time compatible and used as a scaling factor for time equivalence of space separation (the smaller s is chosen, the bigger will be the time difference requirement for two objects occurring in the same place). The validity of all rules in Figure 10 has been checked using this type of simple worst-case analysis.
Stability and Consistency Check
Computation tree logic (CTL) [79] has been used in the verification of transition systems to specify properties that a system under investigation may possess. CTL is a branching-time logic, which considers all reasonable possibilities of future behavior for our limited parking lot driving scenario. We use CTL to formulate stability and consistency checks due to the efficient implementation of CTL model checking.
CTL is given by the following grammar: Lemma 1. Inconsistency in the belief base can be verified by the following CTL formula: Proof. If a system is inconsistent, then there must exist two successor states after a specific state such that one of them is evaluated to true and the other to false. The formula EXB i ∧ EX¬B i captures this case for variable b i . The negation ¬(. . .) captures the occurrence of inconsistency through b i . Operator AG formulates that inconsistency does not occur in any state, and we do not need to consider unknown valued variables as they cannot be assigned to unknown during evolution.
The Boolean evolution system is consistent in case the above formula evaluated to true.
Lemma 2.
The instability problem can be checked by the following CTL formula: The Boolean evolution system is stable in case the above formula evaluated to true.
Proof. For stability, we need that every path ends with a stable state, where unknown variables will not change their values anymore. Therefore, the unknown variable b i will hold one of three cases AG B i , AG ¬B i , or AG K i in the stable state. The latter means that the known variable cannot take value unknown during the evolution, and the unknown variables cannot take value known. Thus, they will not be considered in the CTL formula. AF means that eventually a stable state will be reached.
Consistent rules cannot generate contradictory conditions throughout the whole reasoning process, which means that at no time, a predicate can be assigned to true and false simultaneously. Stable rules make the reasoning process terminate in finite steps. In another word, a stable evaluation is reached eventually such that this stable evaluation is obtained by extending the reasoning process one step further. The detailed proofs of those lemmas are illustrated in our previous work [33,50]. Table 2 below is showing the properties of the verified system.
Run-Time Verification in PRISM
Probabilistic decision-making and threat-assessment methods assign probabilities to different events, e.g., how likely it is to collide with another object in the next few seconds given some assumptions on uncertainties. However, when assumptions are violated (e.g., pedestrian walks/runs faster than anticipated) then sensors onboard will detect the speed of moving objects in real-time. When necessary, the vehicle will stop depending on speed measurements for the AV and other objects, and will deal with a pedestrian running towards the AV as a possible threat. The vehicle will stop if the pedestrian is within a specific distance from the driving path of the vehicle to avoid collision. Figure 11 illustrates the proposed scenario for the AV in terms of trajectory generation based on the possible behavior of other objects around where the AV is moving forward looking for a free parking space, at the same time, a pedestrian and a vehicle (P2, V1) is moving towards the AV, another pedestrian (P1) standing in position (x = 3.5 m, y = 4 m) from the vehicle in relative coordinates. The RA will generate PTP models for the two traffic participants and also for the AV to find the best trajectory and speed under the current circumstances. The RA will keep updating the PTP models with every reasoning cycle (100 ms) and verifying those PTPs using PRISM model checker.
Because the object (P1) is not moving and it is outside (zone 2), also not in the same path of the AV, hence the agent will ignore it, and the AV will continue moving at the same speed (5 mph). However, if the pedestrian (P1) entered (zone 2), then the AV will reduce the speed according to sensory abstraction (SOF1) and action (AM2). For demonstration purposes, we discretized the trajectory by one meter apart. We also discretized the possible pedestrian's and vehicle's trajectories. While in the implementation, the RA is getting these data continuously in real-time from the perception system without the need for discretization. For the agent to build a meaningful PTP model while the AV is moving, it has been formerly equipped with a possible probabilistic behavior for both pedestrians and drivers in such an environment. Usually, when a pedestrian notices an oncoming vehicle, they may slow down with a high probability. The pedestrian may also choose to stop at some point or even change the lane to a safer one, it is also common that the pedestrian may be distracted by something, e.g., using a mobile device, and hence, does not notice the AV. If this is the case, the pedestrian continues to walk at the average speed. The last case could be included in the generated model of the traffic participants using methods explained in [80]. While there are some similar probabilities for the driver with limits to the dynamic movements of the vehicle, the driver may decide to continue driving the same speed, reduce the speed, or to stop in order to give a chance for the AV to pass easily. From the above scenario in Figure 11, we can see that the vehicle and the pedestrian are in the same horizontal line, and this gives a small gap for the AV to pass through.
To simulate a realistic scenario, and to equip the RA with the possible behavior of pedestrians and drivers, we recorded some data and objects behavior manually for parking lots, and we used JAAD dataset [81] for pedestrians and drivers reactions to vehicles around them in different scenarios. A next step implementation would be to equip the agent with probabilistic behavior prediction method, e.g., Refs. [82,83] instead of the limited approach adopted in this work.
Generating PRISM Models from the Agent Code
We designed a translator that works as an Eclipse plugin (part of the sEnglish system environment) to translate the agent reasoning code to PTP models that can be verified by PRISM; it is a direct text processing algorithm in C++ that can run in a few milliseconds (hence its time is neglected). The agent will also translate the properties of the models in PCTL and the query of questions the agent needs to ask. As soon as the equivalent PTP models verified, then the agent will know about different properties expressed in PCTL. A Boolean variable for each belief is defined, and transition probabilities are taken from the probability distributions defined in the sEnglish code.
Verification Example of a Parking Scenario
As mentioned before, all the possible states of the system can be explored during formal verification, including some extreme cases that may be difficult to discover during testing. A general parking scenario will be presented here to illustrate the use of the RA predicates (sensory abstractions, beliefs, actions, and future event consequences) designed for this case study: we have defined two regions around the AV for safety purposes depending on the direction of movement, as shown in Figure 9, assuming the AV is moving forward, as soon as the AV detect an object within (6 m) in front or (2 m) any other side represented by (zone 2), the AV will slow down from average speed of (5 mph) to (2 mph), as soon as this object become within (3 m) from the front of the AV or (1 m) from any other side represented by (zone 1), the AV will stop. Here it is essential to mention that the experimental AV has been equipped with a means of communication with other pedestrians and drivers using audio to prevent a deadlock state when the AV stop and wait for others to move and vice versa, the AV will play a voice to say to others that "you are free to move and the AV will wait for you". We have defined further details for the AV to deal with the traffic participants around by calculating the speed of those objects using the LiDAR sensor. Assuming there is an object moving fast towards the AV, as soon as this object enter (zone 2) the AV will stop instead of slowing down, this will give more time for the other object (running pedestrian or fast-moving car) to reduce their speed, change direction, or to stop, and this will reduce or eliminate any possible collision.
A simple proposed example of how the agent chooses its actions is as follows: based on the scenario in Figure 11, a car (V1) is coming in the opposite direction to the AV from a distance of (8 m) and the driver starts to slow down when they notice another vehicle coming, the AV is moving at its average speed and building its trajectory based on the map and the moving objects around. As soon as the other vehicle (V1) enters (zone 2), the sensing event (SOF2) from Section 7.1 will be activated, and this will activate the future event (FCF2) then this will trigger action (AM2), which leads to slow down. In the meanwhile, the walking pedestrian (P2) enters (zone 2), sensing event (FSFE1) is triggered and this may lead to collision according to a future event (FCF1), the AV here will not take any further action because it is already working in reduced speed. However, as soon as the car or the pedestrian or both enter (zone 1) (SON2 or FCNE1 or both), future events (FCN1 or FCN2, or both), this will trigger the action (AM1) to execute stop action. All the stationary parked cars in the parking lot will not be considered as a threat because they are not in the proposed path of the AV, and they are not moving.
The regulation for the speed of vehicles in a parking lot is limited to (10 mph), based on this and for safety reasons and prototype development we set the speed of our AV to be (5 mph) in case of no moving objects within (zone 1 and 2). As mentioned, both the RA and the planning system will send control commands to the move base system to set the movements of the AV. However, actions such as (AA1 and AA2) have a pre-programmed sequence for performing a parking maneuver, as shown in the video link we referred to in the abstract. In case there are two or more rules in conflict with each other, MCMAS will present this case by a counterexample showing how the inconsistency is reached. Further, it cannot be the case that two different actions are activated at the same time.
For the run-time verification, the initial PTP model generated by the RA for the AV's trajectory is shown in Figure 12. We use a relative coordinate system considering that the LiDAR position on the top of the AV is the center of the coordinates at any time, knowing that the RA is taking the dimensions of the AV into calculations while processing. In this example we will refer to the coordinates of the participants according to a fixed moment at a particular time interval (x 1 , y 1 ) to represent the coordinates of the AV, (x 2 , y 2 ) for object (P2), the (x 3 , y 3 ) for object (V1). The (C) letter in the PTP models represents the clock, which will be counting and resetting with every transition. The complexity of solving PTPs with two or more clocks is EXPTIME-complete. Our previous work [64] shows experiments on several complex models and properties and the results are promising. Figure 13 shows the PTP model for the pedestrian's possible behavior. For this example, we assume that the average speed of the pedestrian is near the speed of the AV inside the parking lot. The pedestrian may prefer to stop after noticing the AV with the probability of (0.1) or to stop later when the distance became critical. We assume that the pedestrian will keep walking in the same lane with a probability of (0.6), they could also decide to change the lane and walk behind the moving car (V1) for more safety with a probability of (0.3). In both cases, the pedestrian may prefer to walk at the same speed or to reduce it with some probabilities, as shown in Figure 13. Figure 14 shows the possible PTP model for (V1). We assumed that the driver might notice the AV and decide to stop with probability (0.1). With a probability of (0.6), the driver may decide to slow down, or may prefer to continue the same speed with a probability of (0.3). The RA will then modify the AV's PTP model according to the newly generated behavior model of the other objects around.
Note that the parameters used to generate the PTP models, such as the speed and probability, may not reflect the exact behavior of the AV, P2, or V1. The RA is building those PTPs based on the location, speed, and direction of the moving objects. In general, this framework will help to predict a possible behavior for the different objects around, then to verify the current trajectory/action for the AV against the possible trajectory/action of the nearby objects, and this will help in reducing the possibility of collision. More accurate PTP models could be generated after collecting more behaving data through real tests.
To avoid any possible collision, we require that the pedestrian and/or the vehicle is at least (1 m) away from the AV. This can be represented by the following expression: where (x 2 , y 2 ), represent the coordinate of the pedestrian, (x 3 , y 3 ) is the coordinate for the car. As PRISM cannot deal with real numbers, we multiply the distance by 2 (we partition the distance by 0.5 m. Therefore, the location would have values such 0.5 and 1.5 m, by multiplying it by 2, we obtain an integer). We compute the maximum probability of the violation of Equations (7) and (8), by the following PCTL property: Due to the discretization of the trajectory, the negation of Equation (7) is translated into the following expression: ((y 2 > y 1 ∧ y 2 − y 1 ≤ 1) ∨ (y 1 > y 2 ∧ y 1 − y 2 ≤ 1))) While the negation of Equation (8) is translated into: The verification results for the proposed scenario are shown in Table 3 returned from PRISM for Formula (9), which indicates information about the model generated for both the pedestrian and the car and the chance of collision with every one of them under the current motion plan. All the computations in this work were carried out using two computers running on Ubuntu OS version 16.04, first is equipped with (Intel core i7 CPU, 16 GB of RAM, and GTX 1070 GPU) for simulation, perception, planning, and control systems and the second with (Intel core i7, 16 GB of RAM, and GTX 860 GPU) to run the agent code and the verification platform.
Conclusions and Future Work
A new approach is presented for the verification of an agent-based decision-making system for a self-driving vehicle. The approach considers both the design-time and runtime verification. To contribute towards the open-source development of the self-driving vehicles, a self-driving vehicle is presented in the simulation that is available in ROS and the Gazebo Simulator.
A rational agent in a real traffic scenario usually faces a vast amount of situations with related behavior rules. Many of these can be identified during the design stage. Remaining scenarios, with possible probabilistic events in the environment, can then be handled by run-time evaluations. Our approach is presented through a case study. The power of the combination of the two verification tools can help the designer to eliminate any conflict and redundancy in the agent predicates. Further, the verification tools can help to check the agent rules for any possible instability or inconsistency with the benefit of obtaining a counterexample when a faulty state has been reached.
The second stage of verification deals with the possible behavior of the traffic participants to determine the probability of success for the best AV action. A limited set of beliefs, rules, and actions are presented to provide a proof of concept and to illustrate the proposed platform. For higher levels of rationality, the agent could yet be equipped, during design time, with a methodology for rules and predicates generation. Such a system would be able to learn new driving scenarios for run-time verification by implementing a machine learning approach. Data Availability Statement: Data available on request due to restrictions. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. | 18,613 | 2021-06-29T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Quasisymmetric Functions from Combinatorial Hopf Monoids and Ehrhart Theory
We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class of complexes, called forbidden composition complexes, also forms a Hopf monoid, thus demonstrating a link between Hopf algebras, Ehrhart theory, and commutative algebra. We also study various specializations of quasisymmetric functions.
Introduction
Chromatic polynomials of graphs, introduced by Birkhoff and Lewis (1946) are wonderful polynomials. Their properties can be understood as coming from three different theories: 1. Chromatic polynomials were shown by Beck and Zaslavsky (2006) to be Ehrhart functions for inside-out polytopes.
J. White Stanley (1973). Chromatic polynomials form a situation where 'Ehrhart polynomial = Hilbert polynomial = polynomial coming from a Hopf algebra'. The idea of 'Ehrhart = Hilbert' has been studied before by Breuer and Dall (2010). We call such polynomials triune, because they can be studied from three different perspectives at one time.
The primary goal of this paper is to study triune quasisymmetric functions which are Ehrhart functions, specialize to Hilbert functions, and come from combinatorial Hopf algebras. The motivation is that such invariants have three different aspects, which give them a rich structure. Given any combinatorial Hopf monoid H with a Hopf submonoid K, there is a natural quasisymmetric function Ψ K (h) associated to every element h ∈ H. This invariant is a special case of the work of Aguiar et al. (2006). In our case, the invariant can be studied from the perspective of geometric combinatorics: there is a canonical relative simplicial complex (Γ K,h , ∆ h ) associated to h, with a natural geometric realization in R I , such that Ψ K (h) enumerates lattice points with positive coordinates inside of the complex. The resulting Ehrhart function is an Ehrhart quasisymmetric function as defined by Breuer and Klivans (2015). We show how principal specialization is a morphism of Hopf algebras to the ring of 'Gaussian polynomial functions', and that the corresponding Ehrhart 'Gaussian polynomial' is a Hilbert function of (Γ K,h , ∆ h ) with respect to a certain bigrading. Setting q = 1 recovers known results.
The paper is organized as follows: we review definitions regarding the Coxeter complex of type A, and from Ehrhart theory. We discuss the relationship between Ehrhart theory and Hilbert functions for relative simplicial complexes (Γ, ∆), where ∆ is a subcomplex of the Coxeter complex, and define forbidden composition complexes. In Section 3, we review material on Hopf monoids, and define triune quasisymmetric functions, which are special cases of invariants defined by Aguiar et al. (2006). In Section 4, we show that forbidden composition complexes form the terminal Hopf monoid in the category of pairs of Hopf monoids, which implies that every triune quasisymmetric function is the Ehrhart quasisymmetric function for some canonical forbidden composition complex. Thus we have a link between geometric combinatorics and combinatorial Hopf algebras that was known only in special cases. In Section 5, we discuss various specializations of quasisymmetric functions from the Hopf algebra point of view. This is motivated by the lecture notes of Grinberg and Reiner (2015), which emphasize principal specialization at q = 1. This gives new combinatorial identities, including for Ehrhart polynomials. In the process, we discuss the notion of Gaussian polynomial function, which are linear combinations of polynomials in q with q-binomial coefficients.
Relative Composition complexes and Ehrhart Theory
The motivation for this work comes from the study of chromatic polynomials: 1. In Steingrímsson (2001), chromatic polynomials of graphs are shown to be Hilbert functions for coloring ideals, which is the Stanley-Reisner module for the relative coloring complex. Beck and Zaslavsky (2006), chromatic polynomials of graphs are shown to be Ehrhart polynomials of an inside-out polytope, which is the geometric realization of the relative coloring complex.
In
Thus, the Ehrhart polynomial of the inside-out polytope of a graph is the Hilbert polynomial of coloring ideal. We give a q-analogue of this result for arbitrary relative composition complexes. A set composition is a sequence C 1 , . . . , C k of disjoint subsets of I such that ∪ k i=1 C k = I. The length of the composition is ℓ(C) = k. We denote set compositions with vertical bars, so 12|3 corresponds to the set composition {1, 2}, {3}, and 21|3 = 12|3. The sets C i are blocks. Similarly, an integer composition α is a sequence α 1 , . . . , α k of positive integers whose sum is n.
Given a set composition C, there is a natural flag of sets F (C) : Similarly, given such a flag F , there is a set composition C(F ) := C 1 , C 2 , . . . , C k , where C i = S i \ S i−1 . This is analogous to the classic situation for integer compositions, where there is a correspondence between integer compositions of length ∆ and subsets of [n] of size k − 1. We use both notations: S i for the sets in the flag, and C i for the blocks. The Coxeter complex of type A is the order complex on the boolean lattice 2 I \ I. We let Σ I denote the Coxeter complex of type A on the set I.
Ehrhart Quasisymmetric Function
Let x 1 , . . . , x i , . . . be a sequence of commuting indeterminates indexed by positive integers. A quasisymmetric function is a power series in x 1 , . . ., whose terms have bounded degree, such that for any a 1 , . . . , a k , and Given a quasisymmetric function Q, and q ∈ K\{0}, and n ∈ N, the principal specialization ps(Q)(n) is given by ps(Q)(n) = Q(1, q, q 2 , . . . , q n−1 , 0, 0, 0, . . .). For a fixed q, we view ps(Q) as a function from N to K. When q = 1, we denote the specialization by ps 1 (Q)(n). It is known that this is a polynomial function. The stable principal specialization is given by sps(Q) = Q(1, q, q 2 , . . .). This gives a formal power series. However, it turns out that the coefficients Q(n) of the resulting power series is a quasi-polynomial in n.
Given a face F = ∅ ⊂ S 1 ⊂ S 2 ⊂ · · · ⊂ S m ⊂ I of Σ I , there is a corresponding polyhedral cone in the positive orthant R I ≥0 . The cone is given by the equations x i < x j whenever i ∈ S k , j ∈ S k for some ∆, and x i = x j whenever i ∈ S k if and only if j ∈ S k . For example, for the flag {2, 4} ⊂ {1, 2, 4, 7} ⊂ {1, 2, 3, 4, 7, 9}, we obtain the polyhedral cone given by x 2 = x 4 < x 1 = x 7 < x 3 = x 9 < x 5 = x 8 . Thus, for any collection F of faces of Σ I , there is a collection C(F ) of open polyhedral cones in R I ≥0 . Given a lattice point a ∈ R I >0 , we let x a = i∈I x ai be its monomial, where the coordinates of a are encoded in the indices, not the exponents. The Ehrhart quasisymmetric function for C(F ) is given by where the sum is over all lattice points which lie in some cone of C(F ). Since E C(F ) = F ∈F M type(C(F )) , this is a quasisymmetric function, first appearing in the work of Breuer (2015).
We mention specializations of E C(F ) , and their combinatorial interpretations. First, ps 1
Relative Composition complexes
We define Stanley-Reisner modules for relative simplicial complexes, and introduce relative composition complexes, which have a natural geometric realization as open polyhedral cones. We show that specializations of the Ehrhart quasisymmetric function for relative composition complexes give the Hilbert function of the Stanley-Reisner module.
J. White
A relative simplicial complex is a pair (Γ, ∆) where Γ ⊆ ∆, and ∆ is a simplicial complex. Given ∆ with vertices S, we let C[S] be the polynomial ring with indeterminates s 1 , . . . , s k , the vertices of S. The Stanley-Reisner ideal for ∆ is generated by σ ⊆ S : σ ∈ ∆ , and the Stanley-Reisner module for (Γ, ∆) is I Γ /I ∆ . The module is graded by total degree, and its Hilbert function H(Γ, ∆)(n) is the number of monomials of degree n in the module. It is known that the Hilbert function is in fact a polynomial: details can be found in Stanley (1984).
Now we define the simplicial complexes that are of interest to us. A relative composition complex is a relative complex (Γ, ∆) where ∆ ⊆ Σ I . Given a relative composition complex (Γ, ∆), a composition C of Γ, and a block B of C, B is forbidden if every composition of ∆ that refines C does not contain B as block. (Γ, ∆) is a forbidden complex if every composition of Γ either has a forbidden block, or is a facet of ∆. While the definition seems unusual, we will see that forbidden composition complexes arise naturally in the study of Hopf monoids in species. Forbidden composition complexes generalize coloring complexes. Given a graph g, let Γ g denote the collection of set compositions C for which some block contains an edge of g. This is the coloring complex introduced by Steingrímsson (2001). We let (Γ g , Σ I ) be the relative coloring complex. The Stanley-Reisner module for the double cone over (Γ g , Σ I ) is the coloring ideal. Our relative coloring complex is thus an example of a forbidden composition complex.
Our first result follows from work of Breuer and Klivans (2015). However, in their setting there is no natural Stanley-Reisner module. The second result is similar to work of Breuer and Dall (2010).
Hopf monoids and Characters
In this section, we dicuss combinatorial Hopf monoids, their characters, and their quasisymmetric functions. Hopf monoids are a generalization of graphs, posets and matroids. The idea is that we have some notion of combinatorial structure, called a species, as introduced by Joyal (1981). Moreover, we have rules for combining and decomposing these structures in a coherent way. Hopf monoids in species were originally introduced in Aguiar and Mahajan (2010), although the variation we discuss here can be found in Aguiar and Mahajan (2013). Hopf monoids allow us to define a whole class of quasisymmetric functions, and prove identities relating quasisymmetric functions in the same class, such as the class of chromatic symmetric functions of graphs.
Hopf monoids in species
Definition 3 A species is an endofunctor F : Set → Set on the category of finite sets with bijections. For each finite set I, F I is a finite set, and for every bijection σ : I → J between finite sets, there is a bijection All species in this paper are connected, and 1 F denotes the only element of F ∅ .
Example 4 We list various examples of species.
1. The graph species G: the set G I consists of all graphs with vertex set I. Given σ : I → J, and The poset species P: the set P I consists of all partial orders on I. Given σ : I → J, and p ∈ P I , G σ (p) = q is the partial order on J where i ≤ q j if and only if σ −1 (i) ≤ p σ −1 (j). P(x) = 1 + x + 3 x 2 2 + 19 x 3 6 + · · · .
Definition 5 A monoid is a species F, equipped with associative multiplication maps µ S,T : F S × F T → F S⊔T for every pair S, T of finite sets, where S ⊔ T denotes disjoint union. We denote the product of f ∈ F S , g ∈ F T by f · g. Associativity means that (f · g) · h = f · (g · h) whenever the multiplication is defined. Moreover,
Example 6 We list various monoid operations.
1. The graph species G is a monoid. Given two graphs g and h with disjoint vertex sets, g · h is their disjoint union: the graph with edges i ∼ j if and only if i, j ∈ V (g) and i ∼ j in g, or i, j ∈ V (h), and i ∼ j in h.
The poset species P is a monoid. The product is also given by disjoint union of partial orders.
3. The matroid species M is a monoid. The product is the direct sum.
For any
We are working with partial functions, so if one side of the equation is undefined, then so is the other side.
Characters and Inversion
Now we discuss characters of Hopf monoids.
Definition 9 Given a Hopf monoid H, and a field K, a character is a multiplicative function ϕ : H → K.
For every finite set I, there is a map ϕ I : The set χ(H) of connected characters on H is a group, with multiplication given by: for ϕ, ψ ∈ χ(H), where the right hand side is 0 for any S where h| S or h/S is undefined. The inverse of a character ϕ is defined recursively: We discuss characters coming from Hopf submonoids K ⊆ H. A Hopf submonoid K is a subspecies, meaning that K I ⊆ H I for all I. Moreover, the product, restriction, and contraction of elements of K remain in K. Given a submonoid K ⊂ H, there is a character ϕ K : H → K given by: In the case of graphs, one Hopf submonoid is the species of edgeless graphs. In the case of posets, there is the Hopf submonoid of antichains. There is a Hopf monoid of generalized Permutohedra, and the character Aguiar and Ardila (2010) study also comes from a Hopf submonoid. Finally, the Hopf monoid of composition complexes is a Hopf submonoid of Φ. In each of these cases, we obtain a character.
The quasisymmetric function associated to a character
We recall the quasisymmetric function associated to a character on a Hopf monoid H. Given a set composition C of I, and h ∈ H I , define Given a combinatorial Hopf monoid, the vector space generated by the equivalence classes of H-structures forms a combinatorial Hopf algebra, which appears in Aguiar and Mahajan (2010). Moreover, by work of Aguiar et al. (2006), there is a unique morphism from this Hopf algebra to QSym. Our definition Ψ ϕ (H) is the resulting map.
There is a description for Ψ in terms of colorings. Given a coloring f : I → N, and i ∈ N, we let
Theorem 12
Let H be a combinatorial Hopf monoid, with a character ϕ : H → E. Fix a finite set I, and h ∈ H I . Then For a coloring of a graph g, , the ith minor is the induced subgraph on the ith color class, so ϕ(g| i ) = 1 if and only if the ith color class is an independent set. Thus our quasisymmetric function enumerates proper colorings, giving the chromatic symmetric function introduced by Stanley (1995). For example, for the graph in figure 3.2 the resulting chromatic symmetric function is 24M 1111 + 4M 211 + 4M 121 + 4M 112 + 2M 22 . For posets, ϕ f (p) = 1 if and only if f : I → N is a strictly order preserving map, which is the quasisymmetric function for strict P -partitions considered by Stanley (1972). For example, for the poset p in figure 3.2, the quasisymmetric function is given by 5M 1111 + 2M 211 + M 121 + 2M 112 + M 22 .
Forbidden composition complexes
We show that, for any pair K ⊆ H of Hopf monoids, and any element h ∈ H I , there is a forbidden composition complex (Γ K,h , ∆ h ) whose Ehrhart quasisymmetric function is Ψ ϕK (h). Let H be a combinatorial Hopf monoid, h ∈ H I , and define ∆ h ⊆ Σ to be those faces F such that h i is defined for all S i ∈ F . This defines a morphism of Hopf monoids ∆ : H → C, the species of composition complexes.
Let K ⊆ H be a Hopf submonoid, and define ∆ K,h to consist faces F ∈ ∆ h such that some minor h| i ∈ K Si−Si−1 . Since K is a Hopf submonoid, Γ K,h is a simplicial complex. Moreover, (Γ K,h , ∆ h ) is a forbidden composition complex, and the map Γ K : H → Φ defined by Γ(h) = (Γ K,h , ∆ H ) is a morphism of Hopf monoids. However, even more is true: the quasisymmetric function Ψ ϕK (h) is the Ehrhart quasisymmetric function for Γ(h): Theorem 14 Given a set I, let Φ I denote the set of all forbidden composition complexes on I, and C I denote the set of all composition complexes on I.
For a graph g, ∆ g is the relative coloring complex. Given a poset p, let C(p) be the polyhedral cone in R I bounded by equations x i ≤ x j , for all i ≤ j in p. Then ∆ p consists of all cones in the Coxeter arrangement which lie in C(p). Similarly, Γ K,p consists of the cones which lie on the boundary of C(p).
Specializations
We discuss specializations of quasisymmetric functions, and interpretations of Ψ under specialization. We show combinatorial identities relating quasisymmetric functions for various elements of the same combinatorial Hopf monoid. It is known that ps 1 is a Hopf algebra homomorphism from QSym to K[x]. We show that ps is a morphism of Hopf algebras in general. The image of ps is the ring of Gaussian polynomial functions, which are q-analogues of polynomials. We also study the stable principal specialization psp. While this section primarily emphasizes the Hopf algebra perspective, many of the results are of combinatorial interest.
Gaussian polynomials and principal specialization
Clearly, ps(Q) : N → C is a polynomial function when q = 1. This leads to the question of what type of function we get for general q. For now, assume that we are working over C(q). For any integer m, define D m (f ) : N → C(q) by D m (f )(n) = f (n + 1) − q m f (n), and D m (f ) = D m • D m−1 (f ). A function f is a Gaussian polynomial function of degree at most d if D d+1 (f ) = 0. We recovering the classical definitions when q = 1. The terminology comes from the fact that q-binomial coefficients are sometimes called Gaussian polynomials, and all Gaussian polynomial functions can be expressed as linear combinations of q-binomial coefficients. Consider a Gaussian polynomial function of degree m. Then we can define f (−n) = q −m (f (−n + 1) − D m (f )(−n)), for n > 0. Thus Gaussian polynomials are functions from Z → C.
Theorem 15
The algebra of Gaussian polynomials, G, is a Hopf algebra, with basis given by [x] n , n ∈ N. The unit is 1, and multiplication is given by [x] Moreover, ps : QSym → G is a morphism of Hopf algebras, and G is graded as an algebra, but not as a coalgebra.
For a poset p, [q n ]P ϕ (p, q, m) is the number of p * -partitions of n with part size at most m.
Proposition 17
Let H be a combinatorial Hopf monoid with character ϕ, and let h ∈ H I , k ∈ H J , where I and J are disjoint sets. Then the following identities hold:
Conclusion
We conclude with questions: 1. Which properties of complexes are stable under the Hopf monoid operations in Φ? Do shellable complexes form a Hopf submonoid? What about Cohen-Macaulay complexes, or partitionable complexes?
2. What properties of a forbidden composition complex allow us to conclude that the triune quasisymmetric function is positive in the basis of fundamental quasisymmetric functions? This question is interesting: The complex (Γ, ∆) in Example 1 part 2 has the feature that the Ehrhart quasisymmetric functions of Γ and ∆ are not F -positive, but the triune quasisymmetric function for (Γ, ∆) is F -positive.
If we linearize Φ, what other natural bases does it possess?
Forbidden composition complexes, and triune quasisymmetric functions merit further study, as these geometric objects and their symmetric function invariants can be approached from three distinct perspectives. | 4,974.2 | 2016-03-31T00:00:00.000 | [
"Mathematics"
] |
Findings on celestial pole offsets predictions in the second earth orientation parameters prediction comparison campaign (2nd EOP PCC)
In 2021, the International Earth Rotation and Reference Systems Service (IERS) established a working group tasked with conducting the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) to assess the current accuracy of EOP forecasts. From September 2021 to December 2022, EOP predictions submitted by par‑ ticipants from various institutes worldwide were systematically collected and evaluated. This article summarizes the campaign’s outcomes, concentrating on the forecasts of the dX, dY, and dψ, dε components of celestial pole offsets (CPO). After detailing the campaign participants and the methodologies employed, we conduct an in‑depth analysis of the collected forecasts. We examine the discrepancies between observed and predicted CPO values and analyze their statistical characteristics such as mean, standard deviation, and range. To evaluate CPO forecasts, we computed the mean absolute error (MAE) using the IERS EOP 14 C04 solution as the reference dataset. We then compared the results obtained with forecasts provided by the IERS. The main goal of this study was to show the influ‑ ence of different methods used on predictions accuracy. Depending on the evaluated prediction approach, the MAE values computed for day 10 of forecast were between 0.03 and 0.16 mas for dX, between 0.03 and 0.12 mas for dY, between 0.07 and 0.91 mas for dψ, and between 0.04 and 0.41 mas for dε. For day 30 of prediction, the correspond‑ ing MAE values ranged between 0.03 and 0.12 for dX, and between 0.03 and 0.14 mas for dY. This research shows that machine learning algorithms are the most promising approach in CPO forecasting and provide the highest prediction accuracy (0.06 mas for dX and 0.08 mas for dY for day 10 of prediction).
Graphical abstract 1 Introduction
The irregularities in the Earth's rotation are observed as variations in the rotation rate, polar motion, and alterations in the direction of the rotation axis in space, known as precession and nutation.The Earth's precession and nutation are largely generated by the lunisolar tidal torque.Diurnal retrograde variations in the atmospheric and oceanic angular momenta in an Earth-fixed reference system, combined with the free core nutation effect, induce additional nutation motions (Dehant et al. 2015).The precession-nutation effect pertains to the movement of the celestial intermediate pole (CIP) within the celestial reference frame (McCarthy and Petit 2004).This motion occurs with a frequency range from − 0.5 cycles per sidereal day (cpsd) to + 0.5 cpsd, as detailed by Capitaine et al. (2005).
In contrast, polar motion encompasses the CIP's motion within the celestial frame across all other frequency ranges or its motion within the terrestrial frame for all frequencies, excluding those falling between − 1.5 cpsd and − 0.5 cpsd.This distinction incorporates retrograde, nearly diurnal ocean tidal terms into nutation, as observed from the terrestrial reference frame.In addition, polar motion encompasses nutation terms with frequencies below − 0.5 cpsd or above + 0.5 cpsd, as perceived within the celestial reference frame (Gross 2015).
Earth orientation parameters (EOP) include corrections to the conventional precession-nutation model, i.e., celestial pole offsets (CPO), polar motion, differences between universal time and coordinated universal time (UT1-UTC), and Length-of-Day (derivative of UT1-UTC).They are necessary for transformation between International Celestial and Terrestrial Reference Frames (ICRF and ITRF, respectively).However, the complexity and time-consuming nature of the required data processing invariably results in report delays.Currently, the official and most accurate EOP solution obtained from the combination of observations from different space geodesy techniques is provided by the International Earth Rotation and Reference Systems Service (IERS) with the delay of up to 6 weeks.Less accurate and more quickly processed data are available with a delay of one to several days.Consequently, accurately predicting EOP based on past observed data in conjunction with geophysical phenomena is of great scientific and practical significance.Short-term predictions of EOP are routinely used for many real-time advanced geodetic and astronomical tasks, such as navigation and positioning on Earth and in space.
The CPO signifies the disparity between the observed position of the celestial pole and its position predicted by a precession-nutation model.The IERS consistently monitors and reports the ongoing differences between the observed and modeled celestial pole positions.The newest CPO definition, introduced in 2000 by the International Astronomical Union (IAU), assumes CPO as the corrections dX and dY applied to the coordinates of the CIP within the ICRF (Resolution B1.6, McCarthy and Capitaine 2003).The IAU 2000 recommendations introduced a new parametrization of the CPO based on the non-rotating origin of the Earth's orientation matrix (McCarthy and Capitaine 2003).The IERS regularly publishes the CPO based on the IAU 2000A precession-nutation model.The conventional offsets expressed in terms of longitude (dψ) and obliquity (dε), associated with the former IAU 1980 theory of nutation and the IAU 1976 precession model (Kaplan 2005), can still be accessed from the IERS website.
Accurate determination of CPO through very-longbaseline interferometry (VLBI) measurements has been possible since 1984.Today, VLBI is widely recognized as the most accurate technique for observing CPO (Kiani Shahvandi et al. 2024).In addition, combined solutions are calculated by integrating VLBI with other space-geodetic techniques.While some models solely include CPO determined from geodetic measurements, others also offer predictions.Among the many utilized CPO models accessible to the public are the United States Naval Observatory (USNO) combined CPO series produced by the IERS Rapid Service/Prediction Center (Dick and Thaller 2015;Wooden et al. 2010), the International VLBI Service for Geodesy and Astrometry (IVS) combined CPO series produced by the IVS Combination Center (Böckmann et al. 2010), and the IERS EOP 14 C04 combined CPO series developed by the IERS Earth Orientation Product Center at the Paris Observatory (Bizouard and Gambis 2009).Comparative analyses of these different CPO series have been conducted by Malkin (2010aMalkin ( , b, 2013Malkin ( , 2014Malkin ( , 2017)), demonstrating substantial differences among them, reaching several tens of μas.
At present, EOP predictions are regularly provided by the IERS Rapid Service/Prediction Centre (Luzum et al. 2001) and many other research groups working on EOP predictions (Kiani Shahvandi et al. 2023;Belda et al. 2018;Modiri et al. 2024).However, the predictions provided by these institutes differ in terms of input data, forecasting method, and prediction horizon, leading to different levels of accuracy for each prediction.
Since the beginning of this century, major progress has been made in processing geodetic observations for estimating EOP (Bizouard et al. 2019;Karbon et al. 2017;Nilsson et al. 2014).The First Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC), which was conducted in 2006-2008, aimed to assess and compare the accuracy of different prediction methods (Kalarus et al. 2010).These methods included the leastsquares (LS) extrapolation and autoregression (AR) (Wu et al. 2019;Xu et al. 2015), spectral analysis combined with LS (Zotov et al. 2018;Guo et al. 2013), artificial neural networks (ANN) (Schuh et al. 2002), wavelet decomposition and auto-covariance method (Kosek et al. 2006), and Kalman filtering (Xu et al. 2012;Gross et al. 1998).The main conclusion from this campaign was that no single prediction technique could be considered optimal for all EOP components and all prediction intervals.It was also proved that the prediction accuracy benefits from the use of atmospheric and oceanic angular momentum (AAM and OAM, respectively) data and forecasts.
At present, there is increased understanding of the influence of the Earth's surficial fluid layers (i.e., atmosphere, oceans, and hydrosphere) on the rotational changes of the solid Earth (Schindelegger et al. 2016;Nastula et al. 2019).As additional data in the EOP forecasting process, teams often use not only AAM and OAM data and predictions but also hydrological angular momentum (HAM) and sea-level angular momentum (SLAM).Moreover, the number of research groups actively developing advanced methods for EOP This paper summarizes the results of evaluation of predictions of CPO components (dX, dY and dψ, dε) collected during the 2nd EOP PCC.The analyses are based on comparison between observed CPO taken from the IERS 14 C04 solution and predicted values.We study in detail statistics of prediction residuals as well as the mean absolute error (MAE) of predictions.
The remainder of the paper is structured as follows.Section 2 presents an overview of CPO predictions and their preliminary assessment, specifically, statistics of prediction methods, input data and submitted files (Sect.2.1) and the analysis of the prediction residuals (Sect.2.2).Detailed evaluation of the accuracy of CPO forecasts and the benefits of transformation of dψ, dε to dX, dY parameters is presented in Sect.3. Finally, Sect. 4 presents the ranking of all CPO predictions, summarizing the campaign results and identifying the most reliable forecasting techniques for dX, dY predictions.
Prediction methods, input data and statistics of submitted files
An overview of the prediction techniques, input data, and prediction horizons exploited by campaign participants is presented in Table 1.A full description of each approach is provided in Table 6.Each campaign participant could apply more than one prediction technique, and no recommendations for predictions were given, allowing participants freedom in the choice of the prediction method, forecast horizon, and input data.The prediction methods used by the campaign participants were LS extrapolation, AR (both methods are used alone or in combination), Kalman filter, empirical free core nutation (FCN), and machine learning (ML).Participants sent their predictions for time periods of 11, 31, 90, 179 and 364, and 365 days.Each registered prediction approach was assigned an individual ID by the EOP PCC Office.All IDs predicted dX, dY parameters and only IDs 100 and 101 additionally provided forecasts of dψ, dε (Table 1).It should be noted that the dψ, dε predictions provided by ID 101, according to the participant's declaration, were not directly forecasted but transformed from their dX and dY predictions.During the campaign period, all participants sent 559 predictions of dX and dY and 185 predictions of dψ and dε using nine different forecasting approaches.In addition, we used CPO predictions provided by the Rapid Service/Prediction Centre of IERS as a comparative dataset.These predictions received the ID 200.The IERS forecasts are sourced from regularly updated files finals.daily,based on the previous IAU1980 convention for precession-nutation, and finals.2000A.daily,based on the current IAU2000A convention for precession-nutation (https:// www.iers.org/ IERS/ EN/ DataP roduc ts/ Earth Orien tatio nData/ eop.html -accessed on May 1, 2023).These forecasts are collected by the EOP PCC Office every Wednesday, following the same procedure used for submissions from other participants.
The entire set of submitted forecasts was tested to find erroneous predictions, which cannot be used in further processing.A two-step approach was applied to eliminate outlier predictions separately for 10-and 30-day prediction horizon.In the initial stage of data selection, known as the "σ criterion", we independently calculated the standard deviation S j of the differences between refer- ence (IERS 14 C04) and prediction ( x obs − x pred ) for each submitted prediction independently.Subsequently, we computed the overall standard deviation of differences for all submissions ( S total ).Individual predictions with S j > S total were excluded from further analysis.This process targets highly inaccurate predictions that deviate significantly from observational data and other submissions, possibly due to many factors, such as producing highly inaccurate predictions related to incorrect units, errors in algorithms, or incorrect use of input data.
In the second step of data selection, to exclude individual predictions from a specific participant that significantly deviate from the rest of the predictions provided by the same participant, we applied a criterion based on the β parameter, computed separately for every single prediction as described in Kalarus et al. (2010): (1) where I denotes the length of prediction (I = 10, or 30), MDAE is a median absolute prediction error defined for the i th day in the future, and the prediction residu- als ε i,j = x obs i − x pred i,j are used to calculate the differences between observed EOP data and their i th point for the j th prediction.If β j < 0 , the predictions were rejected and not included in further processing.The α parameter was determined empirically, and in this study, its value was chosen as α = 3.
Table 2 shows number of rejected and total submitted predictions of dX, dY and dψ, dε for 10-and 30-day prediction horizon together with percentage of rejection.For 10-day horizon, the set of submitted files was reduced by 4.9% because of highly inaccurate forecasts, while for 30-day predictions, the percentage of rejection was 3.5%.In general, the highest percentage of outlier forecasts was detected for ID 127, while the lowest-for ID 101.More Figure 1 shows the number of accepted predictions for each submission day after applying sigma and beta criteria.It can be seen from the plot that in the case of dψ, dε, the number of accepted files is rather stable during the whole campaign duration (2-4 submissions), while for dX, dY the number of uploaded files has increased after April 2022.This is probably due to the addition of new methods by one of the participants (IDs 154 and 155).
Analysis of prediction residuals for dX and dY
This part of our study presents basic statistics of prediction residuals (ε i,j ) between observed and predicted values of the parameters dX and dY.
Figures 2 and 3 show time variability of prediction residuals for day 1 (ε 1,j ) and day 8 (ε 8,j ) computed for each ID over the entire campaign duration.The differences between the reference and predicted dX, dY series for day 1 of prediction range from 0.13 to 0.61 mas (Fig. 2), while these differences for day 8 of prediction are between 0.24 and 0.58 mas (Fig. 3).
Figure 4 shows the minimum, mean, maximum and range of prediction residuals for dX and dY, computed for day 1, day 8, day 15, and day 22 of prediction for each ID.Since the predictions from IDs 127 and 134 are 11 days long, their statistics were computed only for day 1 and day 8.The maximum range of prediction residuals for all considered days is obtained for ID 100 for both dX and dY (Fig. 4).For dX, the ε i,j values of ID 100 are 0.44, 0.49, 0.52, and 0.52 mas for day 1, day 8, day 15, and day 22, respectively.The corresponding ε i,j values for dY are equal to 0.61, 0.58, 0.57, and 0.54 mas, respectively.ID 200 has the smallest range of differences for day 1 of prediction, both for dX and dY (equal to 0.13 mas for dX and 0.16 mas for dY), but this value visibly increases for day 8, day 15, and day 22 and is comparable to those received for other IDs.
As a next step, the distribution of the prediction residuals ( ε i,j ) of dX, dY parameters was studied by analysing their histograms (Fig. 5).The histograms display a symmetric, bell-shaped curve with a single peak around the mean showing that the data follows a normal distribution but with an additional tail.In the case of day 8, the distribution of individual values is more dispersed than for day 1, for which we observe more consistent values of prediction residuals.Figure 5 shows that for day 1, the most common values of differences between the reference and predicted series (indicated by peaks in the histograms) are (-0.07)-0.03mas for dX and (-0.05)-0.10mas for dY.For day 8, the most frequent values of differences are (-0.06)-0.00for dX and (-0.03)-0.05mas for dY.It is Fig. 3 Prediction residuals for a dX and b dY for day 8 of prediction also visible that the prediction residuals are mostly negative for dX, while for dY there is a greater balance between positive and negative values.Moreover, a larger deviation of residual values is observed for dY than for dX.
We now analyse relations between prediction residuals obtained for day 1 and corresponding residuals received for day 8, day 15 and day 22.To do so, for each ID separately, we computed correlation coefficients: between prediction residuals ε 1,j and ε 8,j , between ε 1,j and ε 15,j , and between ε 1,j and ε 22,j , which are presented in Table 3.
For ID 100 there is a strong positive correlation between prediction residuals for day 1 and corresponding residuals for other days (between 0.77 and 0.84 for both dX and dY).A weak relationship between residuals for day 1 of prediction and residuals for other days was found for ID 200 (correlation coefficients ranging between 0.15 and 0.26 for both dX and dY).This may be due to a different behavior of the prediction accuracy for ID 200 in the first days of the forecast than in the following days (see also Fig. 4 with statistics of prediction residuals for day 1, day 8, day 15, and day 22).Notably, for dX of ID 155, the correlations between residuals for day 1 and other prediction days are above 0.50, while for the dY component the corresponding correlations are lower and decrease with subsequent days of prediction (i.e., the correlation between residuals for day 1 and day 8 is higher than the correlation between those of day 1 and day 15).This may suggest that the residuals of predicted dY values do not change substantially with prediction day.Overall, we do not observe a change in correlation larger than 40%, except for ID 104, where there is an increase of 60% from day 15 to day 22 (dY), for ID 155, where is decrease of 50% (dY) and −42% from day 8 to day 15 (dY), and for ID 155, where is decrease of 42% (dX) from day 8 to day 15.This may indicate that the accuracy of prediction does not change as the prediction day increases.
In the following, we analyse correlations between participants' prediction residuals separately for day 1, day 8, day 15, and day 22 (Fig. 6).For day 1 of prediction for both dX and dY, a strong positive correlation (between 0.80 and 1.00) was found for the following pairs: IDs 155 and 102, IDs 134 and 102, IDs 127 and 6a, b).The highest correlation coefficients are detected for ML-based methods, either between prediction residuals from two between IDs 155 and 134) or between prediction residuals from ML and from other techniques (between IDs 155 and 102, between IDs 134 and 102, between IDs 127 and 104, between IDs 154 and 104).For day 1, predictions from ID 200 disseminated by IERS, are characterized by lower correlations (between − 0.20 and 0.40) than those of other IDs (except for correlation between IDs 101 and 134 and between IDs 101 and 102).For those pairs of IDs that had the highest correlations for day 1, the correlations are also high for day 8 (see Fig. 6c, d), day 15 (see Fig. 6e, f ) and day 22 (Fig. 6g, h).Table 3 Correlation coefficients: between prediction residuals ε 1,j and ε 8,j , between ε 1,j and ε 15,j , and between ε 1,j and ε 22,j , computed for each ID separately In brackets, the percentage change in correlation coefficients relative to the previous one is shown There is no noticeable decrease in the correlation between different IDs for day 15 and day 22 of prediction compared with the values received for day 1 and day 8, and no negative correlations are noted.Despite the use of different prediction methods and different forecast horizons, there is a positive correlation between prediction residuals obtained for different IDs.
The correlation between residuals for ID 200 and residuals from the other participants increased in day 8, day 15 and day 22 compared to the correlations received for day 1, especially for the dY component.Taking into account all considered prediction days, residuals of ID 200 have the highest agreement with the residuals for IDs 101 and 154 and the lowest correspondence with the residuals for ID 102.
MAE and its time evolution
In this section, we assess the quality of CPO predictions from all IDs based on MAE computed according to the following equation (Kalarus et al. 2010): (2) where n p is the number of predictions related to the same ID and the same dX, dY or dψ, dε data.We consider MAE for the 10-day and 30-day prediction horizon (Figs. 7 and 8, respectively).Figures 7 and 8 additionally include MAE values for day 0, which represents the day of submission (the last observational data record).Day 0 is used to assess whether participants encountered any errors during the preparation of observational data, which could affect their forecast accuracy.Since final IERS 14 C04 solution is usually published with around 6-week delay, to perform prediction, participants usually use IERS 14 C04 supplemented with different rapid solutions that are not as accurate as the final IERS 14 C04 series due to limited access to all data and shorter processing time.Therefore, differences at day 0 between various participants may result from diverse rapid data used or different methods of processing of that data.Large errors at day 0 may indicate problems with correct data preparation or limitations in access to the latest observational data.Except for IDs 100 (Fig. 7a) and 101 (Fig. 7b), there were no issues at the data preparation stage, as MAE for day 0 is relatively low for most IDs.For day 0, the MAE for ID 200 is lower than for other participants; however, for this ID MAE increases rapidly after day 1 of prediction for both dX and dY, suggesting some modelling errors.For the dX component, most IDs show a similar course of the MAE change, with little increase in error between day 1 and day 10 (Fig. 7a).However, MAE for ID 100 is visibly higher than that of the other IDs (between 0.14 and 0.16 mas) for the whole prediction horizon.Notably, for ID 200, MAE increases almost linearly (MAE equal to 0.04 mas for day 1, and 0.13 mas for day 10).The MAE of dX forecast from ID 200 is higher than that of any other ID after day 2 of prediction.Of all IDs, ID 154 provides the lowest MAE value on day 10 (about 0.05 mas).
For the dY component, the MAE for the consecutive forecast days remains relatively stable for all IDs except 200 (Fig. 7b).For IDs 100 and 101, the MAE is greater than that for other IDs and reaches 0.09-0.12mas for the whole prediction horizon.The forecasts provided by IDs 134 and 127 are the most accurate for day 10 of the prediction (MAE values about 0.06 mas).Similar to the results for dX, MAE for the dY parameter provided by ID 200 is lower than corresponding values for other IDs only for day 1 and day 2 of the prediction.The almost linear increase in error causes the MAE of ID 200 to reach 0.09 mas on day 10 of prediction.
Figure 8 shows that, for a 30-day prediction horizon, the MAE values for dX and dY do not increase linearly; however, about every seventh day of prediction there are peaks of increased prediction errors.The nature of these peaks is not entirely known, but they appear practically for every ID, so it might be a matter of the C04 data.For ID 104, these peaks might indeed be somewhat different, but generally in dX, they are not as pronounced as in dY, and more varied depending on the ID.In dY, however, distinct peaks appear practically for all IDs.Similar to the 10-day prediction horizon, MAE for forecasts from ID 200 rises most rapidly for the first 10 days of prediction; however, for the subsequent days, the change in MAE as the prediction day increases is of a similar course as in the case of MAE for other participants.For the dX component, the lowest MAE on day 30 of the prediction is found for IDs 104 and 154 (0.05 mas).For the dY component, the lowest MAE is provided by IDs 117 (0.08 mas) and 102 (0.06 mas).
We also investigated whether participants improved their methods throughout the campaign by plotting the MAE for a 10-day prediction horizon for dX and dY (Figs.To quantify the change in MAE in each period relative to the previous one, the percentage change (PCh) of MAE for each of the above periods was calculated as follows: where MAE i is the value for the i th point of prediction computed for the n th period.If PCh > 0, the preceding period has a lower MAE (predictions are improved).If PCh < 0, the preceding period has a higher MAE (predictions are worsened).The PCh n values are shown in Fig. 11.
Figure 9 shows that for dX, the mean value of MAE computed for the whole campaign duration and mean value of MAE obtained for each period is comparable in the P1 (Fig. 9a) and P7 periods (Fig. 9g).Conversely, in the P8 period (Fig. 9h), the mean MAE for this 2-month (3) period is substantially higher than for the previous periods and the whole campaign duration.This is due to the high value of MAE detected for IDs 100 and 200.The accuracy of predictions from IDs 200 and 117 is higher than the mean MAE in the P1 (Fig. 9a) and P2 periods (Fig. 9b).Over the following months, the accuracy of both forecasts increased considerably.However, the MAE value for ID 200 increased substantially again for the last 4 months (P7-P8) of the campaign, while ID 117 maintained a high forecast accuracy.During the period of increased forecast errors for ID 200 (P1, P2, P8), there was also a clear linear increase in MAE for this prediction, especially between day 2 and day 6 of forecast.In other periods, the behavior of MAE for ID 200 is similar to that observed for the other IDs.From January 1, 2022 to June 30, 2022 (P3-P5), the MAE values for each ID are below 0.15 mas and remain stable for the whole prediction horizon.Starting from around the middle of the campaign duration, the average MAE for the period is changed only by single outlier IDs, for which the errors are visibly higher than for the others [IDs 100 and 117 for P5 (Fig. 9e), IDs 101 and 102 for P6 (Fig. 9f ), IDs 100 and 102 for P7 (Fig. 9g), IDs 100 and 200 for P8 (Fig. 9h)].
For the dY predictions (Fig. 10), the mean MAE computed for the whole campaign duration and for each Fig. 10 MAE for dY prediction for individual 2-month periods (a-h).The thick black line represents the mean value of MAE over the 2-month period ("Mean for period"), the thick magenta line ("Mean for all") represents mean MAE for the whole campaign duration period separately is comparable for the P4-P6 periods (Fig. 10d-f ).The mean MAE for the P3 (Fig. 10c) and P8 periods (Fig. 10h) is higher than the MAE for the whole campaign period, which relates to the high MAE of ID 101.For P3 (Fig. 10c), which covers the period between January 1, 2022 and February 28, 2022, all MAE values are very high (above 0.05 mas starting from day 1).In the P7 period (Fig. 10g), the highest MAE values are for IDs 100 and 101.In the P6 period (Fig. 10f ), ID 101 has the highest MAE values, whereas IDs 101 and 104 have the highest MAE values in the P5 period (Fig. 10e).The highest MAE value was observed for ID 101 in the P3 and P8 periods (Fig. 10c, h, respectively).
The values of percentage change of MAE in analysed periods are shown in Fig. 11.It can be seen that the accuracy of predictions of dX component varies between the 2-month periods for all IDs, but we do not observe a constant decrease or increase in MAE, but rather alternating periods of improvement and deterioration in accuracy (Fig. 11a).The period P8 exhibits a clear increase in accuracy for almost all IDs as most values of PCh are positive.For ID 134, after some decrease of accuracy in P2 (November-December 2021), and P3 (January-February 2022) there is a prominent MAE improvement in the P5 (May-June 2022) and P8 (November-December 2022) periods.In the case of P7 (September-October 2022) period, we note a decrease of prediction accuracy for all IDs except for ID 101.
Figure 11b shows that the accuracy of dY predictions increased for most IDs in most periods.A decrease of MAE from one period to the next was observed in the following cases: in period P4 (November-December 2021) for all IDs; in period P5 (May-June 2022) for ID 100 (73%), and ID 200 (40%); for period P7 (September-October 2022) for all IDs excluding IDs 100 and 200; for period P8 (November-December 2022) for all IDs excluding IDs 101 and 127.In period P5, for most IDs the deterioration in accuracy is noticeable.In general, for dY predictions of most IDs, after declines in prediction accuracy in the first half of the campaign, the accuracy improves in the majority of cases in the last months of the 2nd EOP PCC duration.In contrast, for dX forecasts, periods of increased and decreased prediction accuracy alternated with each other.
Transformation between dX, dY and dψ, dε
Many of the existing algorithms that are applied to positional astronomy are reliant on conventional transformations (Hohenkerk 2017).These transformations involve expressing the sequence of rotations between the terrestrial and celestial systems using familiar angular quantities based on the equinox and sidereal time.Even though the IAU 2000A precession-nutation model and the new definition of UT1 can be implemented without adopting the (X, Y) coordinate scheme for pole coordinates used by the IERS, the new models still describe the pole's position using conventional angles (Kaplan 2005).The X and Y components must be derived from these angular quantities.Consequently, even users implementing the new IAU models may need to convert dX and dY values to their equivalent dψ and dε values.
This section discusses the influence of conventional transformation between dψ, dε and dX, dY components of CPO on the MAE values for the 10-day forecast horizon.To do this, we compare MAE for original dX, dY predictions with MAE of dX, dY predictions obtained by transformation from dψ, dε forecasts.This analysis is conducted only for IDs that provided forecasts for both dX, dY and dψ, dε components of CPO (IDs 100,101,and 200).
To perform a transformation of CPO from IAU 1980 (dψ, dε) to IAU 2000 (dX, dY) model, we used the package of subroutines, uai2000.package,available at the Earth Orientation Center of Paris Observatory (https:// hpiers.obspm.fr).The programs, originally written by Christian Bizouard from Systèmes de Référence Temps Espace (SYRTE), are based upon the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) matrix transformations.SOFA service (http:// www.iauso fa.org/) provides astronomical software packages that contain sets of algorithms and procedures for implementing standard models used in fundamental astronomy (Wallace 1998).
First, we analyse the accuracy of original predictions of dψ, dε by showing their MAE over the 10-day prediction horizon (Fig. 12).One can see in the figure that in the case of dψ, MAE values for day 0 for IDs 100 and 101 are much higher than in the case of ID 200 and reach 0.46 and 0.66 mas, respectively (Fig. 12a).In contrast, the MAE for day 0 of ID 200 equals 0.07 mas and increases almost linearly for the next 10 days.The MAE for day 0 for the dε parameter is equal to 0.04 mas for ID 200 and 0.10 mas for ID 101 and does not change noticeably for the next 10 days of prediction.Conversely, the MAE for day 0 for ID 100 reaches 0.23 mas, it increases until day 7, reaching a maximum value of 0.41 mas, and then begins to decrease again until 0.32 mas at day 10.We now come to the comparison of the accuracy of original dX, dY forecasts (shown in Fig. 7) with the accuracy of forecasts received by transformation from dψ, dε.MAE for the transformed dX, dY are plotted in Fig. 13a, b, while the MAE differences between original dX, dY predictions and transformed dX, dY predictions are shown in Fig. 13c, d.Note that, as declared by the participant submitting predictions under ID 101, their predictions of dψ, dε are not direct forecasts of these components, but they are transformed values of the dX, dY predictions developed by that participant.Therefore, in this case we deal with a double transformation.
The transformation results show higher MAE values in all cases for transformed than for directly predicted dX and dY values.The smallest difference in MAE between original and transformed predictions of dX, dY is obtained for the case of ID 200.This might suggest that for ID 200 both dX, dY and dψ, dε are predicted with similar level of accuracy.The differences between MAE computed for original and transformed dX, dY predictions are highest for ID 101 (in the case of dX transformed from dψ) and ID 100 (in the case of dY transformed from dε).This means that after parameter prediction transformations, the MAE increases compared with the untransformed data.This also suggests issues with the prediction of dψ, dε by IDs 100 and 101, which contribute to the increased MAE of dX, dY predictions after transformation.As a result, replacing predicted dψ, dε with their transformation to dX, dY is not recommended.This analysis illustrates the influence of differences in accuracy between dX, dY and dψ, dε predictions on the results of the parameter transformation, rather than the impact of the transformation itself on the accuracy of the transformed predictions.
Summary and conclusions
In this study, we analyzed the accuracy of CPO predictions collected during the 2nd EOP PCC, using the IERS 14 C04 solution as a reference.The campaign's primary objective was to evaluate the current potential of EOP prediction.This involved exploring emerging methodologies such as ML, which have seen rapid advances in recent years.The 2nd EOP PCC was an excellent and innovative opportunity for scientists from a range of countries and institutes to collaborate and compete in enhancing EOP predictions.With the participation of 23 institutions worldwide, the operational phase of the campaign spanned 70 weeks and yielded an unprecedented collection of EOP forecasts.The 2nd EOP PCC served as a valuable endeavor to assess different prediction techniques within a standardized framework and under consistent rules and conditions.During the campaign, CPO were predicted by 6 groups with 9 different approaches, and more than 500 predictions were submitted to the EOP PCC Office.It was found that the ML and Kalman filter approaches achieved the highest accuracy for CPO prediction.Depending on the evaluated prediction approach, the MAE values computed for day 10 of forecast are between 0.03 and 0.16 mas for dX, between 0.03 and 0.12 for dY, between 0.07 and 0.91 mas for dψ, and between 0.04 and 0.41 mas for dε.For day 30 of prediction, the corresponding MAE values range between 0.03 and 0.12 mas for dX, between 0.03 and 0.14 mas for dY.
To summarize the achievements of the 2nd EOP PCC in CPO prediction, we devised a ranking of IDs based on the following criteria: 1) Percentage of rejected submissions: this criterion evaluates the credibility of predictions by measuring the proportion of unreliable or inconsistent submissions; 2) Range of differences between the reference values and the prediction: this criterion examines the repeatability of predictions by assessing the range of prediction residuals.Forecasts with high stability over time should exhibit a small range of prediction residuals; 3) MAE values for day 1, day 6, day 7 and day 10: this criterion evaluates the quality of predictions at the beginning, middle, and end of a 10-day prediction horizon.Predictions for 30 days into the future were not considered to include all IDs in the ranking; 4) Median PCh: this criterion assesses the stability of the method's accuracy.
Under the classification, each ID has been assigned points (from 0 to 10) corresponding to its position, with the understanding that a lower number of points indicates a higher position in the ranking.The rankings for dX and dY are shown in Tables 4 and 5, respectively.Overall, predictions made by ML algorithms (IDs 127,134,154,and 155) are at the top of the ranking, indicating the credibility of this approach in CPO forecasting.For prediction of the dX and dY parameters, the lowest rankings are represented by prediction techniques based on the LS + AR (except for ID 101, which took fourth place for dX).
One of the main conclusions of this study is that the CPO predictions provided by the IERS are not sufficiently reliable, especially for the first days of prediction, due to an almost linear increase of the MAE for up to 10 days into the future.Overall, the results of the 2nd EOP PCC are promising as most of CPO predictions processed by campaign participants achieve accuracy similar or better than the accuracy received for forecasts provided by the IERS, especially after around third day of prediction.Moreover, in contrast to the forecasts disseminated by the IERS, predictions developed by 2nd EOP PCC participants do not show a significant increase in prediction errors with increasing prediction day.Therefore, MLbased forecasts can be successfully used in operational applications where accurate predictions for the first days of the forecast horizon are most important.
Appendix
See Table 6.
Table 6 (continued)
Names and affiliations of participants: Mostafa Kiani Shahvandi, Matthias Schartner, Junyang Gou, Benedikt Soja ETH Zurich, Institute of Geodesy and Photogrammetry, Zurich, Switzerland Predicted parameters: dX, dY Description of method: The architecture used is based on the first-order neural ordinary differential equations (Neural ODEs).In this architecture the hidden state in the hidden layer should follow a differential equation.To apply this concept to the EOP, it is assumed that EOP follow first-order differential equations the exact form of which should be determined by fitting neural networks to the observations.The general approach of Neural ODE differential learning (Kiani Shahvandi et al. 2022a) is modified (i.e., in a way that does not require using the EOP rates) and used as the primary architecture.A variation of this architecture is the so-called simple recursive method (Kiani Shahvandi et al. 2022b), in which an attempt is made to incorporate the uncertainties in the observational data in the training for a more reliable estimation of parameters of the neural networks (Kiani Shahvandi and Soja 2022).As a result, the loss function here is the mean squared error.The architecture does not require any preprocessing of the input features.The forecasting horizon includes both 10 and 30 days.The input sequence length is 10 days.Each architecture is trained for each prediction epoch to take advantage of the most recent available EOP and EAM data
Fig. 1
Fig. 1 Number of accepted predictions for each submission day after applying σ and β criteria
Fig. 4
Fig. 4 Minimum, mean, maximum, and range of prediction residuals for a dX and b dY, computed for day 1, day 8, day 15, and day 22 of prediction for each ID.Note that the predictions of IDs 127 and 134 are 12 days long so data for day 15 and day 22 are omitted
Fig. 5
Fig. 5 Distributions of the prediction residuals for a dX and b dY for day 1 and day 8 of predictions for all IDs with their respective best-fitted normal distributions
Fig. 7
Fig. 7 MAE for a dX and b dY predictions for up to 10 days into the future for each ID
Fig. 9
Fig.9MAE for dX predictions for individual 2-month periods (a-h).The thick black line represents the mean value of MAE over the 2-month period ("Mean for period"), the thick magenta line ("Mean for all") represents mean MAE for the whole campaign duration
Fig. 11
Fig. 11 Percentage change (PCh) of MAE for a dX and b dY predictions in individual analysis periods (P2-P8) in relation to the previous periods (P1-P7).The periods where data are not available are marked as grey, red colors indicate a MAE reduction, green colors indicate a MAE increase
Fig. 13
Fig. 13 Impact of transformation from dψ, dε to dX, dY on MAE: a MAE for dX obtained by transformation of d ψ,), b MAE for dY obtained by transformation of d ε , c differences of MAE between original submitted dX predictions and the transformed dX from d ψ predictions, and d differences of MAE between original submitted dY predictions and the transformed dY from d ε predictions
Table 1
List of predicted parameters, length of prediction, prediction techniques, and input data for each IDA more detailed description of prediction techniques is given in Table6*Dobslaw and Hill, 2018
Table 2
Number of N/M of rejected (N) and total submitted (M) predictions of dX, dY and dψ, dε for 10-and 30-day forecast horizon
Table 4
Ranking of IDs according to the adopted criteria and the number of points awarded to each ID in individual categories for dX
Table 5
Ranking of IDs according to the adopted criteria and the number of points awarded to each ID in individual categories for dY | 9,436 | 2024-07-30T00:00:00.000 | [
"Physics"
] |
Analysis and Identification of Dermatological Diseases Using Gaussian Mixture Modeling
Skin diseases are common and are mainly caused by virus, bacteria, fungus, or chemical disturbances. Timely analysis and identification are of utmost importance in order to control the further spread of these diseases. Control of these diseases is even more difficult in rural and resource-poor environments due to a lack of expertise in primary health centers. Hence, there is a need for providing self-assisting and innovative measures for the appropriate diagnosis of skin diseases. Use of mobile applications may provide inexpensive, simple, and efficient solutions for early diagnosis and treatment. This paper investigates the application of the Gaussian mixture model (GMM) based on the analysis and classification of skin diseases from their visual images using a Mahalanobis distance measure. The GMM has been preferred over the convolution neural network (CNN) because of limited resources available within the mobile device. Gray-level co-occurrence matrix (GLCM) parameters contrast, correlation, energy, and homogeneity derived from skin images have been used as the input data for the GMM. The analysis of the results showed that the proposed method is able to predict the classification of skin diseases with satisfactory efficiency. It was also observed that different diseases occupy distinct spatial positions in multidimensional space clustered using the Mahalanobis distance measure.
I. INTRODUCTION
Human skin performs various functions like Vitamin-D synthesis, internal organs protection, control of water loss, and shielding the body from environmental hazardous. Human skin consists of three layers: epidermis, dermis, and hypodermis as shown in Fig. 1. The external layer is called epidermis. It is the thinnest layer with thickness varying from 0.05 to 0.15 mm. It provides mechanical resistance and acts as barrier against bacteria, harmful chemicals, and ultraviolet (UV) radiations [1]. Dermis is the middle layer whose thickness varies from 1.5 mm to 4 mm. Its primary function is to protect the body from mechanical stress and strain. It is divided in two strata, papillary dermis and reticular dermis. Papillary dermis consists of loose fiber bundles connecting it to the epidermis. Whereas, the reticular dermis is much thicker than the papillary dermis and contains dense networks of elastin, collagen, reticular fibers, capillary vessels, sensory receptors, and hair follicles [2]. Beneath the dermis, is a layer of fat and loose fibers known as hypodermis. It stocks fat and provide thermal insulation. Skin diseases are generally caused by virus, bacteria, fungus, and chemical disorders. Uncontrolled spread of the skin diseases may be dangerous and hence, timely treatment is important and also contagious skin diseases may prove to be even more dangerous [3] for which various methods are in use for automatic identification, classification, and prediction of the necessary precautions to be taken [4]. The problem is more severe in visually similar skin diseases.
In resource-poor environment, where health workers have even lesser expertise specially in dermatology, need more convenient and innovative measures for the proper diagnosis of the skin diseases. In these areas, dermatological services are commonly provided by medical staff and expertise in the dermatology cannot be expected. Therefore, queries are generally sent to specialists and the response takes several days to arrive. Studies conducted in rural areas of countries like Colombia showed that average waiting time for a dermatologist was more than three weeks [5]- [6]. Thus, the use of mobile applications to enable real-time dermatological diagnosis in these areas has great applicability. Innovative technical solutions can help in bridging the gap in resource-poor environment [7]- [8]. Several dermatology related mobile phone applications are available and leading to the share of teledermatology from 11.0% in 2014 to 20.1% in 2017 [9]. Most of these applications provide only consultation for self-diagnosis using visual, audio, and data services of mobile communication [10]- [15]. Teledermoscopy reduces costs, avoids unnecessary biopsies, and decreases the time to initial therapy [16]- [17].
In dermatology, identification of the problem of skin, nails, and hair is carried out. Sometimes, allergies, irritants, genetic structure, and immune system disorder is also responsible for dermatitis, hives, and other skin problems such as acne, cold sore, blisters, hives, actinic keratosis, carbuncle, eczema, psoriasis, measles, etc. Human skin has many types of cancers like melanoma, basal cell carcinoma, and squamous cell carcinoma. Dermoscopy is a non-invasive and visual symptoms based method for the identification of skin abnormalities. Identification carried out by naked eye is generally limited in accuracy, therefore, computer assisted techniques are more effective [18].
Recently, artificial intelligence has also been used in dermoscopy [19]. CNN has shown encouraging results in accurate diagnosing of the skin diseases. These applications under-perform with the images taken in poor lighting conditions and generally lead to wrong diagnoses [20]. The problem is more severe in the diseases with similar symptoms. The main limitations of CNN is the code complexity and the requirement of large amounts of input data for training [20]- [ 21].
Some of the important algorithms used in the area of image processing for estimation and approximation of images include adaptive image equalization algorithm [22] which automatically enhances the contrast of an image using GMM. Contrast equalized image is generated by the preeminent gaussian component and cumulative distribution functions of the input intervals. Nicholas et al. [23] introduced sub-regions histogram equalization that partitions the image based on its smoothed intensity values that are obtained by convolving the input image with a gaussian filter. Multilayer feed forward neural network [24] for precise and computationally effective division of components from the dermoscopic image utilizing genetically optimized fuzzy grouping approach is used. The literature reviewed on melanoma skin cancer [25] highlights that various approaches like artificial neural network (ANN) and data mining can be used for classifying skin cancer images. Accuracy obtained by these respective algorithms are 95-98% and 85%. In continuation to the above literature, various skin diseases can be detected and classified with various approaches, some of the important ones include: wavelet transformation and fuzzy inference system [26], support vector machine (SVM) [27] with 65.56% accuracy, kmeans clustering and fuzzy-c means clustering [28], rule based and forward chaining inference engine [29], case based reasoning [30] achieving accuracies of 70%, 66.6% and 90%, respectively. For human skin color detection various methods have been used which include statistical modeling (GMM) [31][32][33] and genetic algorithm [34].
GMM has been used in various applications. In this context, GMM for classification of Alzheimer's disease is introduced in [35]- [36] leading to the fact that the approach used in [36] is better than statistical hypothesis testing. A combination of GMM and various generative models [37] like k-nearest neighbors, naive bayes, multilayer perceptron and discriminative models (SVM, decision trees) have been reported for emotion recognition.
Also, GMM classifier is used for identification of normal and abnormal retinal images of patients suffering from diabetes which attained an accuracy of 97.78%. GMM is used for multiple limb motion classification [38]- [39], using continuous myoelectric signals. In continuation, GMM along with genetic algorithm is also used in [40] for auto segmentation of magnetic resonance images (MRI) lesions. Gaussian mixture model and logarithmic linearization algorithms [41] are used for pattern classification of ECG signals achieving an accuracy of 99.21%. In [42], Equal-Variance GMM has been used to model the characteristics of images, where, equal variance is shared by all the GMM variables. It has also been used in identification of cancer chemosensitivity of heterogeneous cellular response to perturbations in fluorescent sphingolipid metabolism [43] for extracting texture and intensity from the cellular images of the flow cytometry assay. GMM-based approach has also been used in [44] to multiparametrically characterize prostate tissue on transrectal dynamic contrast-enhanced ultrasonography giving an accuracy of 81%.
GMM has also found its application [45] for detection of falling positions in human beings. In this context, authors contribution has been to extract six postures of physically movements of human beings including lying, sitting, standing, getting up, walking, and falling from height captured in video camera. Mixture of gaussian model combined with average filter models have been used in this approach. Although, GMM has widely been used for several classification based applications, its use for analysis and classification of skin diseases has not yet gained much momentum.
Mostly, Euclidean distance is used for multidimesnional classification and hence leads to limited accuracy for search spaces with different weighted coordinate axis. Zhang et.al [46] developed a method called low-rank and sparse matrix decomposition-based mahalanobis distance (MD) method for anomaly detection. Their method used MD for detection of probable anomalies lying in the images analysed from sparse matrix decomposition. MD has also been used in Ribonucleic acid (RNA) sequencing to analyse molecules for prediction of breast cancer survival rate [47]. In [48], it was reported that MD solved the clustering problems associated with traditional Euclidean Distance (ED) in clustering ECG features by reducing iterations to 50%.
Melanoma detection method based on Mahalanobis distance learning and constrained graph regularized nonnegative matrix factorization has been successfully applied in [49] by incorporating global along with the local geometry in supervised learning based training for dimensionality reduction.
In [50] extreme learning machine method for multiclassification with Mahalanobis distance approach has also been investigated. MD was used for inter-class and ED for intra-class distance measurement resulting in about 1% improvement. The same approach has been adopted in the present investigations for distance measurement in four dimensions of the feature vectors (C, Cr, E, and H ) using 72 weights, 8 priors, 8×4 centers and 8×4 co-variances for GMM based classification of skin diseases.
The objective of the paper is to investigate the discriminative capabilities of gaussian mixture model based algorithm for the diagnosis of skin diseases from their visual images using Mahalanobis distance measure for mobile platforms where implementation using CNN is difficult because of the limited resources available within the device. GMM is computationally affordable, tractable, and efficient for small datasets in comparison to CNN [51]- [53]. Eleven different types of skin diseases (Molluscum Contagiosum, Milia, Discoid Lupus Erythematosus, Tinea Corporis, Warts, Acne Blackhead, Psoriasis, Discoid Eczema, Chromoblastomycosis, Athletes foot, Melanoma) along with their variants were taken for the investigations. The methodology for the estimation of GMM parameters has been discussed in the following section. The results and discussions are presented in Section III. Conclusions and future work have been discussed in Section IV.
II. METHODOLOGY
This section describes the material and the algorithm used for investigating the discriminative capabilities of GMM based algorithm for skin diseases from their visual images. Multivariate Gaussian density over two variables 1 Y and 2 Y is shown in Fig. 2. The proposed method is shown in Fig. 3. Images of skin patches having different diseases were taken from DermNet Nz database [54]. For investigation, image of the normal human skin is taken as the reference. Images are resized to 256 pixels x256 pixels and RGB components are separated for each image. Each RGB component is segmented into 8x8 blocks. For each block, GLCM parameters (contrast, energy, correlation and homogeneity) are calculated. The distribution of GLCM parameters is approximated using GMM, which is a parametric density estimation approach assuming that input data is to be generated by more than one Gaussian process [55]. GMM may be written as a weighted sum of m components of Gaussian densities: where, x is a D-dimensional feature vector, Clustering can be improved by using GMM algorithm which can be used to estimate GMM parameters, i.e. mean ( k μ ), weight ( i w ), and covariance ( i ) [56].
The advantages of using GMM based algorithm is that it has low complexity and scalability. It computes the probabilities of cluster memberships by maximizing the log-likelihood of the data generated. GMM is an iterative method in each step of which posterior probability t ik P at t iteration is given by [57]- [58]. Parameters are updated on the basis of the probabilities from the previous step using: Mostly, the clustering algorithms use Euclidean distance for classification assuming the data to be isotropically gaussian [59]. In multivariate modeling, the feature vectors don't satisfy this condition and, hence, the clustering leads to wrong classification. The solution to this problem may be the use of Mahalanobis distance and covariance matrix Σ . It is scale-invariant [61]. It is based on correlations between variables leading to efficient identification and analysis of different patterns available in the input feature vectors. MD measures the relative distance between two variables with respect to the centroid [62]. It is a data driven measure that can ease the distance distortion caused by a linear combination of the attributes [63].
III. RESULTS AND DISCUSSIONS
The distributions of contrast, correlation, energy and homogeneity of red, green, and blue components of the chosen dermatological diseases were modeled using GMM. About 100 iterations were needed for convergence of the GMM and its approximation of the feature vectors for each type of skin diseases provided 8 priors, 8×4 centers, and 8×4 co-variances for each RGB component, giving a total of 72 valued feature vectors. For classification of the diseases, Euclidean and Mahalanobis distances amongst the diseases were also estimated with respect to the normal skin. Fig. 4 shows the output of GMM modeling of these feature vectors for normal human skin, whereas, Fig. 5 to Fig. 15 In all the diseases and its variants, maximum wide peak is observed for correlation and minimum wide peak for energy in RGB components. Similar results were observed for normal skin also.
Mathematical and visual analysis of the GMM modeled feature vector of different diseases show that peak structure is disease depended and may be very useful for predicting the dermatological diseases from their visual images. For example, the Mahalanobis based scatter plots (Fig. 17) show better results as dissimilar diseases get relatively more scattered as compared to that of Euclidean based scatter plots (Fig. 16). Further, instances of same disease (e.g. Melanoma in Fig. 19) give close grouping as compared to Euclidean based scatter plots in Fig. 18.
IV. CONCLUSION AND FURURE WORK
Investigations using GMM based modeling of GLCM parameters (contrast, correlation, energy and homogeneity) showed that different types of dermatological diseases have unique peak structure and, hence, they can be easily predicted only using their colored images. It was also observed that different diseases occupy distinct positions in Mahalanobis based classification. The extension of the work to other skin diseases on larger data sets is in our future plan.
NO CONFLICT STATEMENT
On behalf of all authors, the corresponding author states that there is no conflict of interest. | 3,365.6 | 2019-01-01T00:00:00.000 | [
"Computer Science"
] |
A proof of the Shepp-Olkin entropy monotonicity conjecture
Consider tossing a collection of coins, each fair or biased towards heads, and take the distribution of the total number of heads that result. It is natural to conjecture that this distribution should be 'more random' when each coin is fairer. Indeed, Shepp and Olkin conjectured that the Shannon entropy of this distribution is monotonically increasing in this case. We resolve this conjecture, by proving that this intuition is correct. Our proof uses a construction which was previously developed by the authors to prove a related conjecture of Shepp and Olkin concerning concavity of entropy. We discuss whether this result can be generalized to $q$-R\'{e}nyi and $q$-Tsallis entropies, for a range of values of $q$.
Introduction and notation
In this paper, we consider the entropy of Poisson-binomial random variables (sums of independent Bernoulli random variables). Given parameters p = (p 1 , . . . , p n ) (where 0 ≤ p i ≤ 1) we will write f p for the probability mass function of the random variable B 1 + . . . + B n , where B i are independent with B i ∼ Bernoulli(p i ). We can write the Shannon entropy as a function of the parameters: (1) Shepp and Olkin [16] made the following conjecture "on the basis of numerical calculations and verification in the special cases n = 2, 3": where p n (t) = p n + t, omit the subscript on f p(t) for brevity and write ∂f ∂t (k) = g(k − 1) − g(k), for k = 0, 1, . . . , n, where g is the probability mass function of B 1 + . . . + B n−1 , which is supported on the set {0, . . . , n − 1} and does not depend on t. Here and throughout we take g(−1) = g(n) = 0 if necessary. As in [16,Theorem 2] we can use (2) to evaluate the first two derivatives of H(p(t)) as a function of t. Direct substitution gives The negativity of each term in (4) tells us directly that (as proved in [16,Theorem 2]) the entropy H(p(t)) is concave in t (of course, we also know this from the full Shepp-Olkin theorem proved in [7,8]) so it is sufficient to prove that the derivative ∂H ∂t is non-negative in the case p n = 1/2, since the derivative is therefore larger for any smaller values of p n .
However, at this stage, further progress is elusive. Considering convolution with B n means that we can express f (k) = (g(k) + g(k − 1))/2. However, substituting this in (3) does not suggest an obvious way forward in general, though it is possible to use the resulting formula to resolve certain special cases. For example, careful cancellation in the case where p 1 = p 2 = . . . = p n−1 = 1/2 and hence g is binomial allows us to deduce that, in this case, the entropy derivative (3) equals zero (see Example 2.7 below for an alternative view of this). However, this calculation does not give any particular insight into why the binomial case might be extreme in the sense of the conjecture.
Instead of expressing f as a linear combination of g, our key observation is that we can express g as a weighted linear combination of f , as described in the following section.
Entropy derivative and mixing coefficients
The following construction and notation were introduced in [7], based on the 'hypergeometric thinning' construction of Yu [18,Definition 2.2]. The key is to observe that in general we can write for certain 'mixing coefficients' (α) k=0,1,...,n . The general construction for (α) k=0,1,...,n in the case of Shepp-Olkin paths is given in [7, Proposition 5.1], but in the specific case where only p n varies, in the case p n = 1/2, we can simply define the following values: Definition 2.1. For k = 0, . . . , n, define .
In [7,Proposition 5.2] this result was stated in the form α k−1 ≤ α k , but the strict inequalities will help us to resolve the case of equality in Conjecture 1.1. It will often be useful for us to observe that Definition 2.1 implies that for k = 0, 1, . . . , n and that for k = 0, 1, . . . , n − 1 Remark 2.2. Summing (8), we can directly calculate that which will play an important role in our proof of Conjecture 1.1. Further, it is interesting to note by rearranging (6) that α k ≤ 1/2 if and only if g(k − 1) ≤ g(k), which by the unimodality of g (see for example [12]) means that k ≤ mode(g). This may suggest that the Shepp-Olkin conjecture can be understood as relating to the skewness of the random variables g. Direct calcuation shows that the centred third moment of B 1 + . . . + B n−1 is but it is not immediately clear how this positive skew will affect the entropy of f . Remark 2.3. In [7] we used these mixing coefficients (α) k=0,1,...,n to formulate a discrete analogue of the Benamou-Brenier formula [2] from optimal transport theory, which gave an understanding of certain interpolation paths of discrete probability measures (including Shepp-Olkin paths) as geodesics in a metric space. We do not require this interpretation here, but simply study the properties of α k in their own right.
We now define a function which will form the basis of our proof of Conjecture 1.1: where we take 0 log 0 = 0 to ensure that ψ is continuous at 0 and at 1.
We can express the derivative of entropy in terms of these functions and the mixing coefficients, as follows: Hence by (11), the entropy derivative (3) is positive if each of the odd centred moments n k=0 f (k)(α k − 1/2) 2r+1 ≤ 0, for r = 1, 2, . . .. Proof. Using the fact that g(−1) = g(n) = 0 and adding cancelling terms into the sum (3), we can use g(k)/(2f (k)) = 1 − α k and g(k − 1)/(2f (k)) = α k (see (8)) to obtain that since α 0 = 0 and α n = 1 so that α 0 log Since (by (10) above) the n k=0 f (k)α k = 1/2, subtracting off the linear term makes no difference to the sum and we can rewrite (13) as 2 n k=0 f (k)ψ(α k ), as required. We can exchange the order of summation in because of Fubini's theorem, since as mentioned above the power series for ψ converges absolutely. Hence if each odd centered moment is negative then the entropy derivative (3) is positive.
We shall argue that the binomial example, Example 2.7, represents the extreme case using the following property, which will be key for us: Proof. See Appendix A.
Note that comparing averages, and taking the values of α 0 = 0 and α n = 1 from (7), Proposition 2.8 implies that or that if all the p i ≤ 1/2 then α k ≥ k/n for 0 ≤ k ≤ n, showing that the binomial distribution of Example 2.7 is the extreme case in this sense.
Proof of Shepp-Olkin monotonicity conjecture
We are now in a position to complete our proof of Conjecture 1.1.
Definition 3.1. First we introduce some further notation: As proven in (7) and Proposition 2.8 respectively, the sequence (β k ) k is non-decreasing and (β k+1 − β k ) k is non-increasing.
3. We define the family (B p (k)) k by B 0 (k) = 1 and, for 1 For other values of k, B p (k) is not defined. 4. The notation ∇ stands for the left-derivative operator: ∇v(k) = v(k) −v(k −1). This operator satisfies a product rule of the form: 5. For n ≥ 1 and p ≥ 1 we define the polynomial (symmetric in its inputs) where the sum is taken over all the p-tuples 0 ≤ i 1 , . . . , i p ≤ n such that i 1 + . . . + i p = n. We also set Q 0,p = 1 and Q −1,p = 0 for all p ≥ 1. Clearly, Q n,p (X 1 , . . . , X p ) is non-negative if X 1 , . . . , X p are non-negative.
We now state three technical lemmas that we will require in the proof; each of these are proved in Appendix B. First, the fact that B p (k) is decreasing in k: We next give an integration by parts formula. Note that although we restrict the range of summation for technical reasons, the values A p (k) and A p+1 (k) are zero outside the respective ranges: Lemma 3.3. For any function v(k) that is well-defined on p ≤ k ≤ n − 1 and any p ≥ 0 we have Finally, a result concerning differences of the Q polynomials: Lemma 3.4. For n ≥ 0 and p ≥ 1, we have We now state and prove the key Proposition: is increasing in p. Here note that S r,r+1 = 0 since Q −1,p+1 = 0.
(Note that by restricting to this range of summation the B p (k) is well-defined).
Proof. We first take v(k) = B p (k)Q r−p,p+1 (β 2 k+1 , . . . , β 2 k−p+1 ) in the integration by parts formula (17) from Lemma 3.3 to write where here and throughout the proof, the ∇ refers to a difference in the k parameter. Now, using the product rule (15) with v(k) = B p (k) and w(k) = Q r−p,p+1 (β 2 k+1 , . . . , β 2 k−p+1 ) yields: In order to transform the first sum, we use equation (18) from Lemma 3.4: . Further Lemma 3.2 gives that ∇B p (k) ≤ 0 for k ≥ p and Q r−p,p+1 (β 2 k , . . . , β 2 k−p ) ≥ 0, so the second sum is ≤ 0. We finally conclude that We are now able to prove the following theorem, which confirms Conjecture 1.1: Theorem 3.6. If all p i ≤ 1/2 then H(p) is a non-decreasing function of p. Equality holds if and only if each p i equals 0 or 1 2 . Proof. As described in Proposition 2.6, it is sufficient for us to prove that for every r ≥ 1 we have Using (8) we know that α k = g(k − 1)/(2f (k)) and 1 − α k = g(k)/(2f (k)), so that (subtracting these two expressions) This means that, using a standard factorization of β 2r k+1 − β 2r k , since g(−1) = g(n) = 0 we can write = S r,1 .
However, Proposition 3.5 gives S r,1 ≤ S r,r+1 = 0, and we are done. Note that an examination of (20) allows us to deduce conditions under which equality holds for the cubic case (r = 1). In this case we can rewrite (20) using the integration by parts formula (17) as Here g(k) and α k are positive for k ≥ 1, and Proposition 2.8 tells us that the second bracket is negative, and so the centered third moment equals zero if and only β k+1 − β k is constant in k, which means that α k = k/n. However, (10) tells us that this implies that so that equality can hold if and only if p i ≡ 1/2.
Monotonicity of Rényi and Tsallis entropies
As in [8,Section 4] where a similar discussion considered the question of concavity of entropies, we briefly discuss whether Theorem 3.6 may extend to prove that q-Rényi and q-Tsallis entropies are always increasing functions of p for p i ≤ 1/2. We make the following definitions, each of which reduce to the Shannon entropy (1) as q → 1.
Definition 4.1. For f p as defined above, for 0 ≤ q ≤ ∞ define 1. q-Rényi entropy [14]: 2. q-Tsallis entropy [17]: Note that, unlike the concavity case of [8,Section 4], since they are both monotone functions of n x=0 f p (x) q , both H R,q (p) and H T,q (p) will be increasing in p in the same cases. We can provide analogues of (3) and (4) by (for q = 1) Again, the second term is negative, and therefore H T,q (p) will be increasing for all p n ≤ 1/2 if it is increasing in the case p n = 1/2. Clearly for q = 0 (24) shows that the entropy is constant (indeed we know that in this case H R,q = log(n + 1) and H T,q = n). Curiously, we can simplify (24) in the case of collision entropy (q = 2) by substituting for f as a linear combination of g (which is the argument that did not work for q = 1).
Proof. In (24) we obtain which is equal to the term stated in (26) by relabelling. Note that (curiously) this property will hold for any g, including the mass function of any B 1 + . . . + B n−1 (not necessarily with p i < 1/2).
It may be natural to conjecture that Tsallis (and hence Rényi) entropy is increasing for all q. However, the following example shows that this property in fact can fail for q > 2 (note that Rényi entropy is not concave in the same range -see [8,Lemma 4.3]). gives that the entropy derivative is exactly and we note that 2 q − 2q ≥ 0 for q > 2, so the leading coefficient is negative and so the derivative will be negative for ǫ sufficiently small.
However, we conjecture that these entropies are increasing for 0 ≤ q ≤ 2, since we know that the result holds for q = 0, 1, 2: Conjecture 4.4. If all p i ≤ 1/2 then Tsallis entropy H T,q (p) and Rényi entropy H R,q (p) are non-decreasing functions of p for 0 ≤ q ≤ 2.
We use an argument similar to that which gave Proposition 2.6 to give a moment-based condition related to this conjecture. Proposition 4.5. Let us fix 0 < q < 2. If, for all r ≥ 1, then ∂H T,q ∂t ≥ 0 holds.
Proof. We first add a telescoping sum in equation (24): where, using the binomial theorem, the function ψ q can be expressed as From the assumption 0 < q < 2, it follows that q 2r i=2 (q − i) < 0. The proof is completed as in Proposition 2.6.
B Proof of technical lemmas
Proof of Lemma 3.2. Given j ≥ 0, each sequence (β k+1 − β k−j ) k is non-negative and nonincreasing, so any product of such sequences is also non-increasing. In more detail, the , and each term in the product is positive by (7). Further, each of these terms is well-defined since k − j − 1 ≥ k − p ≥ 0.
To prove Lemma 3.4, we observe that equivalently, the family of polynomials (Q n,p (X 1 , . . . , X p )) n≥0 can be defined using the generating function: Proof of Lemma 3.4. We first notice by direct calculation that .
C Heuristics in continuous case
We now explain some calculations in the continuous case that helped us to find a rigorous proof of Theorem 3.6, and that help suggest our conjecture about Renyi and Tsallis entropies. We remark that Ordentlich [13] used the original paper of Shepp and Olkin [16] to motivate conjectures concerning continuous random variables. Let us consider a density function f (x), defined for x ∈ R, which is assumed to be everywhere positive, smooth and with all derivatives well-behaved at ±∞. This density will serve as a continuous analogue of both the mass functions (f (k)) k and (g(k)) k . As a consequence, one could also see the function 1 2 − log(f ) ′ (x) 4 (resp. − log(f ) ′ (x) 4 ) as continuous analogues of the family (α) k (resp. (β) k ). We will make the assumptions that (log f ) ′′ ≤ 0 and (log f ) ′′′ ≥ 0, which correspond to the property α k ≤ α k+1 and α k − 2α k+1 + α k+2 ≤ 0. We now prove the continuous version of equation (19) (in the case where q = 1) and (28) (for q = 1): Proposition C.1. Suppose that (log f ) ′′ ≤ 0 and (log f ) ′′′ ≥ 0 then for every real parameter q > 0 and every integer r ≥ 1 we have: Proof. For any 0 ≤ p ≤ r we set with A 0 = 1 and A p = p−1 k=0 (2r − 2k) for p ≥ 1. In particular A r = 0 so I r,r = 0. We now prove that the sequence (I r,p ) is non-increasing in p: for every 0 ≤ p ≤ r − 1, using the fact that f q (log f ) ′ = f q f ′ /f = f q−1 f ′ = (f q ) ′ /q we have: Here, again we apply integration by parts, followed by the product rule. The first integral is exactly I r,p+1 , and the second one is non-negative because of the assumptions on log f ′′ and log f ′′′ . We thus have I r,p ≥ I r,p+1 . We thus have R f (x) q (log f (x) ′ ) 2r+1 dx = I r,0 ≥ I r,r = 0, which proves the result. | 4,198.6 | 2018-10-23T00:00:00.000 | [
"Mathematics"
] |
Entanglement monogamy in three qutrit systems
By introducing an arbitrary-dimensional multipartite entanglement measure, which is defined in terms of the reduced density matrices corresponding to all possible two partitions of the entire system, we prove that multipartite entanglement cannot be freely shared among the parties in both n-qubit systems and three-qutrit systems. Furthermore, our result implies that the satisfaction of the entanglement monogamy is related to the number of particles in the quantum system. As an application of three-qutrit monogamy inequality, we give a condition for the separability of a class of two-qutrit mixed states in a 3 ⊗ 3 system.
By introducing an arbitrary-dimensional multipartite entanglement measure, which is defined in terms of the reduced density matrices corresponding to all possible two partitions of the entire system, we prove that multipartite entanglement cannot be freely shared among the parties in both n-qubit systems and three-qutrit systems. Furthermore, our result implies that the satisfaction of the entanglement monogamy is related to the number of particles in the quantum system. As an application of three-qutrit monogamy inequality, we give a condition for the separability of a class of two-qutrit mixed states in a 3 ⊗ 3 system.
Quantum entanglement is an essential feature of quantum mechanics, which distinguishes the quantum from the classical world. Because of entanglement, different quantum systems can affect each other, even if there is no classical connection between the multiple quantum systems. So quantum entanglement can be used to perform a number of tasks which can not be completed in the classical mechanical system. Quantification of quantum entanglement plays an important role in quantum information processing and quantum computation [1][2][3][4][5] . The mathematical study of entanglement has become a very active field and has led to many operational and information theoretic insights.
Entanglement is monogamous, which was first discovered by tangle for three qubit systems in the seminal paper of Coffiman, Kundu and Wootters 6 . It describes the constraint on distributed entanglement among many parties. It is also a key ingredient in quantum cryptography security 7, 8 , statistical mechanics 9 , the foundations of quantum mechanics 10 and black-hole physics 11 . In addition to having a wide range of practical applications, monogamy has also profound theoretical significance, allowing simplified proofs of no-broadcasting bounds and constraints for qubit multitap channel capacities 12 .
The author stated in ref. 12 that the monogamy inequality in the condensed matter physics gives rise to the frustration effects observed in, e.g., Heisenberg antiferromagnets. The perfect ground state for an antiferromagnet would in fact consist of singlets between all interacting spins. However, as a particle can only share one unit of entanglement with all its neighbors, it will try to spread its entanglement in an optimal way with all its neighbors leading to a strongly correlated ground state. Such qualitative statements have been turned into quantitative ones in n-qubit systems through the square of the concurrence 12 , the square of the entanglement of formation 13 and the square of convex-roof extended negativity 14 , respectively.
Suppose that E is an entanglement measure for the multipartite system . Monogamous relation expressed in terms of inequalities can be represented as The proof of this theorem can be found in the Supplemental Material. For n-qudit pure state |ψ〉 in the system Consider the state = + + GHZ ( 100 010 001 ) 1 3 , we find that , which violates the monogamy inequality. Now we add a coefficient which is related to the particle number of systems in Eq. (3), and let . Thus, the following result follows immediately from Theorem 1.
Corollary 1.
For an 3-qubit system, N satisfies the monogamy inequality. The above discussion implies that the concurrence itself does not satisfy monogamous relation. This, together with Corollary 1, shows that the satisfaction of entanglement monogamy characterized by an entanglement measure is generally related to the number of particles of the system.
Next we discuss the entanglement monogamy in three qutrit systems. Until now, no true entanglement measure has been proven to be monogamous for three-dimensional tripartite systems. Taking the square of concurrence as an example, an explicit counterexample showing the violation of the monogamy inequality in three-dimensional quantum systems is as follows 16 , . For an arbitrary pure state |Φ〉 AB , a discussion just as in ref. 16 , which means that the square of concurrence does not work for monogamy inequality on a three-qutrit system. Using the entanglement measure M , it can be calculated that M . More generally, we will prove that the measure M satisfies the monogamy inequality in a three-qutrit system. As a first step toward proving this inequality, we will now derive a computable formula for M .
Discussions
The monogamy of entanglement characterized by the entanglement measure describes quantitatively the entanglement between quantum systems. Choosing the proper entanglement measure helps to reveal the nature of entanglement. The more system information reflected by an entanglement measure, the better it can describe the entanglement of the system. Through giving an entanglement measure which is related to the number of particles of the system, we prove that multipartite entanglements cannot be freely shared among the parties in both n-qubit systems and three-qutrit systems. Corollary 1 and the discussion perior to Corollary 1 imply that the satisfaction of entanglement monogamy characterized by an entanglement measure is generally connected with the number of particles of the system. For the state |Ψ〉 given before Lemma 1 in a three qutrit system ⊗ ⊗ , that is, the monogamy inequality holds, where N is defined in Eq. (4). More generally, we conjecture that the entanglement measure N satisfies the monogamy inequality in three qutrit systems. As a subsequent work, we will continue to discuss it.
In addition, the entanglement monogamy inequality gives an upper bound for the entanglement degree of two-qutrit mixed states, for which the general separability criteria and computable entanglement measures remain still open. In the Supplemental Material, by such an upper bound, a condition is given for the separability of a class of two-qutrit mixed states in a 3 ⊗ 3 system.
Methods
Proof of Theorem 2. Let |φ〉 ABC be a pure state in the three-qutrit system Using Lemma 1, we calculate the entanglement between the particle A and the particles BC, Next we estimate the entanglement between particles A and C. Let → : (i = 0, 1, 2) be three projections defined, respectively, by Thus, by Lemma 1, we obtain the entanglement degree of |τ j 〉 (j = 0, 1, 2), 2 3 cos 2 3 and 1 , , Similarly to the above discussion for AC M , consider a decomposition ρ ψ ς ς Let λ j1 , λ j2 and λ j3 be the three non-negative eigenvalues of s j ρ A (|τ j 〉) (j = 0, 1, 2), then | 1,618.4 | 2017-05-16T00:00:00.000 | [
"Physics"
] |
Well-Dispersed Nanoscale Zero-Valent Iron Supported in Macroporous Silica Foams : Synthesis , Characterization , and Performance in Cr ( VI ) Removal
Well-dispersed nanoscale zero-valent iron (NZVI) supported inside the pores of macroporous silica foams (MOSF) composites (Mx-NZVI) has been prepared as the Cr(VI) adsorbent by simply impregnating the MOSFmatrix with ferric chloride, followed by the chemical reduction with NaHB4 in aqueous solution at ambient atmosphere. Through the support of MOSF, the reactivity and stability of NZVI are greatly improved. Transmission electron microscopy (TEM) results show that NZVI particles are spatially well-dispersed with a typical core-shell structure and supported inside MOSF matrix. The N2 adsorption-desorption isotherms demonstrate that the Mx-NZVI composites can maintain the macroporous structure of MOSF and exhibit a considerable high surface area (503m2⋅g−1). X-ray photoelectron spectroscopy (XPS) and powder X-ray diffraction (XRD) measurements confirm the core-shell structure of iron nanoparticles composed of a metallic Fe core and an Fe(II)/Fe(III) species shell. Batch experiments reveal that the removal efficiency of Cr(VI) can reach 100% when the solution contains 15.0mg⋅L−1 of Cr(VI) at room temperature. In addition, the solution pH and the composites dosage can affect the removal efficiency of Cr(VI). The Langmuir isotherm is applicable to describe the removal process. The kinetic studies demonstrate that the removal of Cr(VI) is consistent with pseudosecond-order kinetic model.
Introduction
Water pollution caused by heavy metal ions, such as Ni(II), Cr(VI), Mo(VI), and Pb(II) in groundwater, is one of the most serious environmental problems.Among the toxic metal oxyanions, chromium is widely distributed and exists in the waste coming from paint industry, metal finishing, textile dyeing, electroplating, and leather tanning [1].Chromium mainly exists as trivalent [Cr(III)] and hexavalent [Cr(VI)] form in the natural environment.Because of the low solubility, mobility, and the weak ability to oxidize other species, the toxicity of Cr(III) is much lower than Cr(VI) [2].In contrast, Cr(VI) demonstrates the higher toxicity, which can produce mutagenic, teratogenic, and carcinogenic effects in biological systems by reacting with nucleic acids and other cellular components [3].Due to high toxicity of Cr(VI), applying efficient methods to remove Cr(VI) from waste water is of great importance.
So far, various kinds of methods have been developed to reduce the harmful effects of Cr(VI), such as chemical extraction [4], reduction-precipitation [5], ion exchange [6], bioleaching process [7,8], and biosorption [9,10].Among these methods, adsorption holds the significant position due to its high removal efficiency, low energy demand, and less chemical investment [11][12][13].In the past years, researchers have applied various adsorbents to remove Cr(VI) from waste water, such as activated carbons [14], zeolites [15,16], clays [17], and nanomagnetic particles [18].However, these adsorbents have many defects including low porosity, low surface area, and lack of functional groups [19], which is of great importance for an efficient adsorbent.Hence adsorbents with high porosity, large surface area, and high functionality need to be developed for efficient removal of Cr(VI).
Nanoscale zero-valent iron (NZVI) has been extensively applied to treat various contaminants in aqueous solution because of its low cost and strong reducing activity [20][21][22][23][24]. Also, NZVI has demonstrated the excellent ability to remove Cr(VI) from waste water through the mechanism of reduction, adsorption, or coprecipitation.However, some serious drawbacks associated with the practical application of NZVI need considering.The severe aggregation of iron nanoparticles during preparation and storage as well as the agglomeration into micrometer particles after the reaction with Cr(VI) may cause the dramatic deterioration in the reactivity [20,25].To conquer these issues, dispersing NZVI in supporting materials, such as activated carbon, polymers, clay minerals, and molecular sieves based on silica, is a promise solution.Because silica-based molecular sieves have a porous structure giving a large surface area and uniform pore sizes, which are of great importance for a good adsorbent, it has been greatly used as the potential support for the fabrication of efficient adsorbent.To date, for the fabrication of NZVI based adsorbents for Cr(VI) removal, porous silica such as SBA-15 [26][27][28][29] and MCM-41 [30][31][32] and silica fumes [33,34] has been used as the matrix to support NZVI particles in order to minimize the aggregation and increase the reactivity of NZVI.However, this porous silica has relative small pores below 10 nm.Whether larger pore size can promote the reactivity of NZVI is still unknown.What is more, NZVI in these composites is supported on the external surfaces of the supports rather than going into pores [26,27,30,33], which causes the underutilization of pores of the porous materials.Zero-valent iron nanoparticles inside the pores of ordered mesoporous silica have been successfully reported by other researchers [28,29,31,34,35], but a hydrogen reduction process under a harsh and dangerous condition including explosive hydrogen and higher temperatures or a complicated "two solvents" reduction technique using toxic cyclohexane as solvent is in demand.Therefore, it is necessary to develop a facile method to disperse nanoscale zero-valent iron nanoparticles homogeneously inside the pores of the porous matrix under mild, safe, and green condition.
In this work, macroporous siliceous foams (MOSF) [36] with large pores of around 100 nm and high pore volumes were chosen as the support material to load ZVI nanoparticles for the preparation of efficient adsorbent for Cr(VI) removal.Nonionic block copolymers are used as the supramolecular template to synthesize MOSF materials via a facile supra-assembly approach.Appropriately modified MOSF can be applied in bioapplications, phosphate and arsenic adsorption [37][38][39][40].In this paper, we have synthesized MOSF-supported nanoscale zero-valent iron composites (Mx-NZVI) simply by the direct reduction of Fe 3+ ions in MOSF with NaBH 4 at normal pressures and temperatures, where water was used as a green solvent.The final materials were tested for their applicability in the remediation of Cr(VI).The main objectives of this work are (1) to synthesize nanoscale zero-valent iron supported inside MOSF composites (Mx-NZVI) with different NZVI contents; (2) to characterize Mx-NZVI composites with TEM, SEM, XRD, XPS, nitrogen isotherms analysis, magnetization measurements, and so on; (3) to evaluate Cr(VI) adsorption performance of Mx-NZVI composites; (4) to study the possible mechanism for the removal of Cr(VI) using Mx-NZVI composites.
Materials.
The following reagents were used as purchased without further purification: EO 20 PO 70 EO 20 (denoted as P123, where EO is poly(ethylene oxide) and PO is poly(propylene oxide)) was purchased from Sigma-Aldrich.Tetramethyl orthosilicate (TMOS) was purchased from Energy Chemical (Shanghai, China).Other chemicals were purchased from Kelong Chemical Reagents Factory (Chengdu, China).
Synthesis of MOSF.
MOSF was synthesized at 35 ∘ C in a pH = 5.0 buffer solution with P123 as the template according to the method reported previously [36].Briefly, at 35 ∘ C, P123 (1 g) and Na 2 SO 4 (1.7 g, 0.40 M) were dissolved in pH = 5.0 NaAc-HAc (Ac = acetate) buffer solution (30 g) ( = 0.04 M, where = NaAc + HAc ) to form a homogeneous solution under stirring.To this solution mixture, TMOS (1.52 g) was added under stirring.After 5 minutes, the stirring was stopped.The resultant mixture was kept in a static condition for 24 h and then hydrothermally treated at 100 ∘ C for another 24 h.The white precipitates were filtered, repeatedly washed with water to remove the inorganic salts, and then dried at room temperature.The final MOSF products were obtained by calcination at 550 ∘ C for 5 h at heating steps of 2 ∘ C⋅min −1 .
Preparation of MOSF-Supported Nanoscale Zero-Valent
Iron Composites (Mx-NZVI).MOSF-supported nanoscale zero-valent iron was synthesized according to a protocol reported by Petala [30].Briefly, MOSF (0.2 g) was dispersed in absolute ethanol (5 g), followed by the addition of a 10 wt% ethanolic solution (0.5, 1.0, and 1.5 g) containing FeCl 3 ⋅6H 2 O.The mixture was heated at 45 ∘ C to evaporate the solvent, and then the obtained powder was dispersed in 5 mL of absolute ethanol again.The reducing agent was prepared by dissolving NaBH 4 (0.56, 0.112, and 0.168 g) in 50 mL of deionized water and was added drop-wise to the MOSF-Fe 3+ solution while swirling by hand.The mixture was filtered and washed with water once and absolute ethanol three times and then dried in vacuum oven overnight.The weight percentage of iron in the final product was calculated to be 4.31, 8.30, and 12.8 wt% according to the results of AAS (see Characterization), denoted Ma-NZVI, Mb-NZVI, and Mc-NZVI, respectively.
Characterization.
The 2 X-ray powder diffraction data (XRD) were collected with a DX-1000 CSC diffraction instrument at 40 kV and 25 mA.The scanning scope and scanning speed were in the 2 range from 5 to 80 ∘ , in steps of 3 ∘ per min.Scanning electron microscopy (SEM) images of Mx-NZVI were taken using a Navo NanoSEM 450 field-emission scanning electron microscope operated at 5 KV.X-ray photoelectron spectroscopy (XPS) measurements were performed with an AXIS UltraDLD (KRATOS).The linear background was subtracted from all spectra.N 2 adsorption-desorption isotherms were measured on a Quantachrome NOVA 1000e surface area analyzer after degassing the samples at 180 ∘ C for 6 hours.The pore volume was calculated from the adsorption isotherms using BJH (Barrett-Joyner-Halenda) method.To determine the actual iron content loaded on the samples, the composites were extracted by diluted hydrofluoric acid and nitric acid.Obtained solution was analyzed by Atomic Absorption Spectroscopy (AAS) using SpectrAA 220FS.Magnetization () measurements were performed on a superconducting quantum interference device (SQUID) magnetometer (MPMS VSM).Magnetic hysteresis loops were characterized at temperature of 300 K in external applied magnetic fields () ranging from −7 to +7 T.
Batch Experiments for the Reduction of Cr(VI)
. Cr(VI) adsorption isotherms were acquired through batch experiments.K 2 Cr 2 O 7 was selected as the source of Cr(VI).0.03 g of Mx-NZVI was added to 30 mL of K 2 Cr 2 O 7 water solution (concentration of Cr(VI): 3, 6, 9, 12, 15 mg⋅L −1 ) followed by shaking (200 rpm) at 25 ∘ C for 24 h.The initial pH of the suspension was adjusted to 2 by 0.1 M HCl or NaOH solution.
To explore the effect of coexisting cations on Cr(VI) removal, 100 mg⋅L −1 of each cations was added to 15 mg⋅L −1 of Cr(VI) solution without adjusting pH, respectively.After shaking, the suspension was filtered through a 0.45 m membrane filter.The Cr(VI) concentration of the solution was then determined by using the 1,5-diphenylcarbazide method [41].
All adsorption isotherm data were fitted with Langmuir isotherm model and Freundlich isotherm mode.The mathematical description of Langmuir isotherm model is given below [42]: where eq is the adsorption capacity at equilibrium (mg⋅g −1 ), eq is residual metal ion concentration at equilibrium (mg⋅L −1 ), max (mg⋅g −1 ) is the maximum adsorption amount of metal ion per gram of adsorbent, and is a constant related to the energy or net enthalpy of adsorption (L⋅mg −1 ).The Freundlich isotherm explains the adsorption on a heterogeneous surface with uniform energy.This equation has the following form as where and are the Freundlich constants, which are related to adsorption capacity and strength, respectively.The adsorption kinetic experiments were performed by adding a given mass of Mx-NZVI to 50 mL of K 2 Cr 2 O 7 solution with the concentration of 15 mg⋅L −1 followed by shaking (200 rpm) at 25 ∘ C for 24 h.The initial pH of the suspension was adjusted to 2, 5, and 8.During the reaction, at different periods, aliquots of the under study suspension were taken at certain time intervals.After filtration, the Cr(VI) concentration was analyzed.The contact time () was calculated after the addition of adsorbent into the solution.
In order to investigate the mechanism of absorption and potential rate controlling step, the pseudo-first-order and the pseudo-second-order kinetic model were used to fit experimental data.The Lagergren first-order equation is generally expressed as after integration of (3) with the boundary conditions as follows, = 0, = 0 , and, at = , = , the integrated form is given as where 0 and express Cr(VI) concentration in the solution at time 0 and and obs is the rate constant of the pseudo-firstorder reaction (min −1 ).The values of were linearly correlated with .The straight-line plots of against should give a linear relationship, from which rate constants ( obs ) can be determined from the slope and intercept of the plot.The pseudo-second-order kinetic rate equation is expressed as where eq is the sorption capacity at equilibrium (mg⋅g −1 ), is the amount adsorbed at a contact time (mg⋅g −1 ), and is the rate constant (g⋅mg −1 ⋅min −1 ). and eq were calculated from the slope and intercept of the plots of / versus according to equation: dots with a high contrast in Figures 3(b) and 3(c)) without aggregation can be clearly seen through the whole sample.NZVI particles supported in MOSF have the elliptical shape with the size distribution of 20-120 nm according to the size distribution histogram of NZVI particles counted in Figure 3(b) (Supporting Information, Figure S2).Inset of Figure 3(c) shows TEM image of NZVI nanoparticles inside MOSF with higher resolution.NZVI nanoparticles possess a typical core-shell structure, in which the shell thickness is less than 10 nm, similar to the previous observations.The core is mainly made up of Fe 0 and the shell could result from the inevitable oxidation of zero-valent iron [22,44,45].Figure 3(d) is a typical high resolution TEM image of NZVI particles supported by MOSF, where the (200) lattice fringes of Fe 0 can be clearly observed in the NZVI.TEM observation confirms that, with the supporting of MOSF matrix, the aggregation degree of NZVI particles can be minimized.Mx-NZVI composites with lower NZVI loading amount, namely, Ma-NZVI and Mb-NZVI, were also characterized by TEM (Supporting Information, Figure S3).Due to the lower content of iron, the number of ZVI nanoparticles supported in MOSF is less compared with Mc-NZVI.Elemental maps of Mc-NZVI elucidate the homogeneous distribution of zerovalent iron nanoparticles in MOSF (Figure 4).Fe, Si, and O elements are found uniformly distributed and well correlated with the shape of the sample area.
Results and Discussion
To further confirm the successful loading of homogeneously dispersed NZVI particles in MOSF, XPS analysis was carried out.The survey spectrum of Mc-NZVI (Figure 5(a)) reveals the existence of Fe, O, Si, and C, in good agreement with the results of elemental maps.In Fe 2p (Figure 5(b)), a photoelectron peak appears at 707 eV, indicating the presence of Fe 0 inside MOSF.It is noteworthy that two photoelectron peaks are located at 711.7 eV and 725.4 eV, which can be assigned to the Fe 2p 3/2 and Fe 2p 1/2 for Fe(II) and Fe(III) species [22].Such results are conflicting with the XRD results.From XRD analysis, the presence of Fe(II)/Fe(III) species inside MOSF cannot be detected, while, according to XPS results, Fe(II)/Fe(III) species and Fe 0 are both found in MOSF.Such conflict may be due to the amorphous nature of Fe(II)/Fe(III) species acting as shells around the NZVI, or because of the small amount that cannot be detected by XRD.Because the XPS analysis could only detect the photoelectrons from the outer surface with the thickness of 10 nm, it is supposed that the thickness of the shell of Fe(II)/Fe(III) species around the ZVI nanoparticles could be less than 10 nm considering the appearance of Fe 0 signal in the Fe 2p spectrum [46].According to the results of TEM, XRD, and XPS, it can be concluded that NZVI nanoparticles inside the pores of MOSF have a core-shell structure, where the core is composed of NZVI and the shell is Fe(II)/Fe(III) species with the shell thickness of less than 10 nm.The similar results are found in the XPS analysis for Ma-NZVI and Mb-NZVI (Supporting Information, Figure S4(a-b)).Magnetization measurements were taken to reveal the physical properties of Mx-NZVI samples.Figure 6 shows the hysteresis loops of Mx-NZVI composites recorded at 300 K.All samples show ferromagnetic or ferrimagnetic characteristics, corresponding to the metallic Fe 0 or iron oxide phases.Saturation magnetization (Ms) at 20 KOe is ∼3.77 and 11.81 to 17.70 emu/g for Ma-NZVI, Mb-NZVI, and Mc-NZVI, which comes as a consequence of the hybrid-microstructured nature with the introduction of iron species.The hysteresis loops of Mb-NZVI and Mc-NZVI display coercivity (Hc) of about 0.275 and 0.278 kOe, which are higher than that of the Ma-NZVI (about 0.062 kOe), indicating the difference in the shell thickness of iron oxide and crystal size of iron core [46].The magnetization with applied field shows smooth change in the hysteresis loops, suggesting that iron core and iron oxide shell were in intimate contact and exchange coupled [47].
The maximum adsorption capacities of the Mx-NZVI composites on hexavalent chromium removal were estimated by conducting a series of batch experiments.The Cr(VI) adsorption isotherms and the fitting results are demonstrated in Table S2.The adsorption data are slightly better fitted to Langmuir isotherm model (Figure 7(a)) than Freundlich isotherm model (Supporting Information, Figure S5a) because the coefficient ( 2 ) for Langmuir isotherm model is higher.Such correlation results indicate the adsorption process of Cr(VI) occurs on the homogeneous surface of Mx-NZVI materials [40].It is observed that the adsorption capacities of Mx-NZVI composites can be improved with increased iron loading amount.The maximum Cr(VI) adsorption capacities of Ma-NZVI, Mb-NZVI, and Mc-NZVI are calculated to be 5.415, 7.658, and 12.665 mg⋅g −1 , respectively.
Figures 7(b) and 7(c) display the Cr(VI) adsorption kinetics of Mx-NZVI composites, and the kinetic parameters are summarized in Table S3.All the experimental data can be fitted to the pseudo-second-order kinetic model with a high correlation coefficient over 0.98 (Supporting Information, Figure S5(b-d)), suggesting that the sorption of Cr(VI) by Mx-NZVI is mainly through chemisorption [48].In addition, the pseudo-first-order model was also used to interpret the experimental data, but the fitting result was not very good as pseudo-second-order model (Supporting Information, Figure S6).It is noted that, in all kinetic experiments, a rapid removal rate of Cr(VI) is displayed during initial 3 h, which hints that most of the adsorption sites exist on the surface of the adsorbent and are easily accessible by the Cr(VI) species [49].Then, the removal rate slightly declines in the later adsorption stage.The rate declination can be explained as below.During the adsorption process, first Cr(VI) species in aqueous solution move to Mx-NZVI.Then, physical/chemical adsorption of Cr(VI) occurs on the surface of Mx-NZVI material.Finally, Fe 0 is oxidized to Fe(III) and Cr(VI) is reduced by Fe 0 to Cr(III), and precipitation of Cr(III) forms on the surface of Mx-NZVI [50].The rate declination is caused by the formation of chromium oxide precipitates or Fe(III)-Cr(III) hydroxides, which may exist as a thin layer on the surface of Mx-NZVI.The presence of thin layer prevents the electron transferring from NZVI to Cr(VI) and thus accordingly eliminates the following reduction of Cr(VI) to Cr(III) [44].
When the dosage of Mx-NZVI is 3 g⋅L −1 and the initial concentration of Cr(VI) is 15 mg⋅L −1 , the equilibrium can be reached after 500-700 min (Figure 7(b)).After 24 h adsorption, 48.28% of Cr(VI) can be removed by Ma-NZVI, while nearly 100% of Cr(VI) can be eliminated using Mc-NZVI.According to the rate constant which is related to removal rate of Cr(VI), Mc-NZVI with the highest rate constant of 0.0115 g⋅mg⋅min −1 exhibits the fastest Cr(VI) removal rate from water among three samples.
The effect of Mc-NZVI dosage (1.0 to 3.0 g L −1 ) on the adsorption kinetics of Cr(VI) with the initial concentration of 15.0 mg⋅L −1 was investigated.As exhibited in Figure 7(c), the Cr(VI) removal efficiency increases significantly from 45.04% to nearly 100% as the dosage of Mc-NZVI grows from 1 g⋅L −1 to 3 g⋅L −1 in 24 h.This phenomenon is attributed to the increase of the active sites on the surface of Mc-NZVI [51].In addition, the adsorption rate of Cr(VI) is also enhanced with the increase of Mc-NZVI dosage.With the dosage changing from 1 to 3 g⋅L −1 , the rate constants are 0.00304, 0.00381, and 0.01115 (g⋅mg⋅min −1 ), respectively.Apparently, the high dosage of Mc-NZVI is beneficial for the fast adsorption rate due to increment of active sites.The dependence of the Cr(VI) removal efficiency on pH was investigated by adjusting the solution pH to 2, 5, and 8.The initial Cr(VI) concentration is 15 mg⋅L −1 and the Mc-NZVI dosage is 3.0 g⋅L −1 .As shown in Figure 7(d), the Cr(VI) removal efficiency decreases significantly with the increase of initial pH.Only 21.16% of Cr(VI) is adsorbed at pH 8.0 after 24 h, while 100% of Cr(VI) can be removed within 24 h at pH 2.0.What is more, adsorption capacity of Mc-NZVI at other higher pH has also been studied (Figure 7(e)).Removal efficiency was 100% at pH 2 and 3. When the pH was higher than 3, a sharp decrease can be clearly seen in the removal efficiency.Clearly, the acidity of the Cr(VI) solution has a major influence on the removal efficiency of Cr(VI), which can be explained by following points.On one hand, the reduction of Cr(VI) by Fe 0 would produce hydroxyl ions.Under low pH condition, hydroxyl ions can be consumed by H + , leading to the much easier reaction between Cr(VI) and Fe 0 .This process can be clearly expressed by the following equations ( 7)-( 9): HCrO 4 − + 3Fe 2+ + 7H + → 3Fe 3+ + Cr 3+ + 4H 2 O (8) On the other hand, pH has an impact on the surface charge of Mc-NZVI and Cr(VI) species.In the pH range of 2-8, the predominant species of Cr(VI) is negatively charged HCrO 4 − /CrO 4 2− [52].The lower initial pH of the solution can result in the surface of Mc-NZVI with more positive charge.Hence, in pH of 2, the electrostatic interaction between Cr(VI) species and Mc-NZVI is much stronger compared with that in pH of 11.Accordingly, the Cr(VI) adsorption capacity of Mc-NZVI decreases with the increase of pH [53].What is more, the solubility of Fe(III)-Cr(III) coprecipitation existing as a thin layer around NZVI is very low when the pH of solution is comparatively high [54], providing resistance for the subsequent redox adsorption of Cr(VI) [30].These explain why a lower pH environment benefits the Cr(VI) removal in aqueous solution.
The effect of common cations (Na + , K + , Mg 2+ , and Ca 2+ ) in ground water was also investigated without adjusting pH.As shown in Figure 7(f), with the absence of coexisting cations, the removal efficiency was only 30.56%.With the addition of K + , the removal efficiency can be enhanced to 53.84%.The removal efficiency can be as high as 100% in the presence of Na + , Mg 2+ , and Ca 2+ .Obviously, the presence of cations can greatly improve the removal of Cr(VI) by Mc-NZVI composites, indicating the applicability of Mx-NZVI composites in the removal of Cr(VI) in ground water.
To provide direct evidence to our explanation for possible adsorption and reduction mechanism of Cr(VI) with Mx-NZVI, the XPS analysis was carried out for Mc-NZVI after absorbing Cr(VI) (15 mg⋅L −1 ) at initial pH 2 and 25 ∘ C in a powder mode.The survey spectrum (Figure 8(a)) confirms coexistence of Fe, O, Si, Cr, and adventitious C. Figure 8(b) shows the high resolution XPS spectra of Fe 2p of Mc-NZVI after Cr(VI) removal.The Fe species in the form of Fe 0 cannot be detected because the NZVI particles are covered with the oxide layer and/or Fe(III)-Cr(III) coprecipitation, which hinder the reaction process.The XPS scan of the Cr 2p region is shown in Figure 8(c) with Cr 2p 1/2 and Cr 2p 3/2 lining at 586.0 and 576.7 eV for Cr(III), respectively.It can be confirmed that Cr(VI) is reduced to Cr(III) by NZVI particles on the surface of the sample.The peak positions of Cr 2p 1/2 and Cr 2p 3/2 for Cr(VI) are comparatively higher located at 587.9 and 579.0 eV [22,28,55].According to the quantitative curve fitting to the individual peak areas of Cr 2p peaks, about 70% of the chromium species has been reductive transformation into Cr(III) on the surface of Mx-NZVI.After the reduction of Fe 0 , Cr(III) and Fe(III) form a thin layer of Fe(III)-Cr(III) hydroxides on the outer surface of ZVI nanoparticles.Aforementioned date imply that the adsorption of Cr(VI) is based on both chemisorption and chemical reduction processes, and chemical reduction played a main role.
In light of the aforementioned results, we hypothesize that the removal of Cr(VI) by Mx-NZVI composites may go through the reduction or/and precipitation processes.When Cr(VI) species in the solution diffuse into the pores of Mx-NZVI and are absorbed on the surfaces of the NZVIs, Cr(VI) is reduced to Cr(III) by NZVI inside the macropores [28,52].Such reduction process could proceed via direct or indirect pathway as shown in Figure 9.The direct pathway can be described by the reduction of Cr(VI) to Cr(III) due to the electron transfer from Fe 0 core, coupled with direct oxidation of Fe 0 to Fe(III).Meanwhile, another indirect pathway presents the reduction reaction between Cr(VI) and Fe(II) [22,50].These active Fe(II) species derive from the electron transfer of Fe 0 species, expressed by the following equations: Fe − 2e → Fe 2+ (10) Fe + 2Fe 3+ → 3Fe 2+ In the precipitation process, (Cr Fe 1- )(OH) 3 or Cr Fe 1- OOH precipitates could form through the reaction of Cr (III) and Fe (III).Such precipitates are coated on the surface of NZVI as a passive layer [50], causing the gradual increase in the resistance of electron transform from Fe 0 to Cr(VI).As a result, Cr(VI) species retain on Fe(III)/Cr(III) hydroxide layer on the surface of Mx-NZVI rather than being reduced to Cr(III) [55].
Conclusion
In this study, well-dispersed nanoscale zero-valent iron supported in macroporous silica foams composites as the efficient Cr(VI) adsorbents has been fabricated and characterized.Through the support of MOSF matrix with large surface area and high pore volume, the reactivity and stability of Mx-NZVI composites were improved due to the prevention of aggregation of NZVI.NZVI nanoparticles inside MOSF showed a typical core-shell architecture, in which the core mainly consisted of Fe 0 and the thin shell (less than 10 nm) is largely made of Fe(II)/Fe(III) species.Mx-NZVI composites with macroporous structure and homogeneously dispersed NZVI particles in nanoscale range (20-120 nm) exhibited the good Cr(VI) adsorption performance.Batch experiments showed the composites were efficient adsorbents for the fast removal of Cr(VI) from aqueous solution.The kinetic data were well fitted to pseudo-second-order kinetic model, implying a chemisorption process.The adsorption capacities increased as the Mc-NZVI dosage and NZVI loading amount increased and fell as pH increased.It was also observed that the adsorption of Cr(VI) was fitted well on the Langmuir isotherm equilibrium.However, further experiments are still needed to investigate the remove process in real waste water and for other contaminants.
Figure 1 Figure 2 :Figure 3 :
Figure1shows the wide-angle X-ray diffraction (XRD) patterns of Mx-NZVI ( = , , and , where the weight percentage of iron is 4.31, 8.30, and 12.8%, resp.; see Materials and Methods).Mx-NZVI composites with different iron loading amount have the similar diffraction patterns.The characteristic peak at 2 ≈ 22 ∘ in the XRD patterns of samples indicates the presence of amorphous silica[39].The peak | 6,228.6 | 2017-09-10T00:00:00.000 | [
"Engineering"
] |
Morphological and Behavioral Effects in Zebrafish Embryos after Exposure to Smoke Dyes
Solvent Violet 47 (SV47) and Disperse Blue 14 (DB14) are two anthraquinone dyes that were previously used in different formulations for the production of violet-colored smoke. Both dyes have shown potential for toxicity; however, there is no comprehensive understanding of their effects. Zebrafish embryos were exposed to SV47 or DB14 from 6 to 120 h post fertilization (hpf) to assess the dyes’ potential adverse effects on developing embryos. The potential ability of both dyes to cross the blood–brain barrier was also assessed. At concentrations between 0.55 and 5.23 mg/L, SV47 showed a dose-dependent increase in mortality, jaw malformation, axis curvature, and edemas. At concentrations between 0.15 and 7.54 mg/L, DB14 did not have this same dose-dependence but had similar morphological outcomes at the highest doses. Nevertheless, while SV47 showed significant mortality from 4.20 mg/L, there was no significant mortality on embryos exposed to DB14. Regardless, decreased locomotor movement was observed at all concentrations of DB14, suggesting an adverse neurodevelopmental effect. Overall, our results showed that at similar concentrations, SV47 and DB14 caused different types of phenotypic effects in zebrafish embryos.
Introduction
Smoke dyes are synthetic dyes used to color smoke in pyrotechnic devices for a broad range of applications, including entertainment (i.e., special effects, fireworks), safety (i.e., distress signals and location markers), or military (i.e., signals and training). Many of those synthetic dyes are also used in other applications such as paper, plastics, leather, cosmetics, food, and textiles [1]. The industrial use of synthetic dyes has led to high levels of wastewater contamination that threaten aquatic environments [2,3]. Dyes have been detected in industrial effluents at varying concentrations, with general reports of 10-50 mg/L of dyes detected in effluents and reports of up to 300 mg/L from textile effluents [4,5]. It is difficult to quantify the amount of global dye consumption, but it is estimated that 700,000 tons of synthetic dyes are produced per year [6]. Regardless, the presence of dyes in wastewater is a pervasive issue that has led to safety concerns surrounding their discharge into the environment [6].
Among the most commonly used classes of dyes are azo and anthraquinone dyes, which make up approximately 70% and 15% of industrial dye consumption, respectively [7,8]. Compared to azo dyes, anthraquinone dyes are more difficult to degrade during wastewater treatment due to the stability of their chemical structure. Yet, toxicity information for azo dyes is more abundant than for anthraquinone dyes [9].
Anthraquinone dyes have been observed to induce toxicity at various trophic levels. For example, Reactive Blue 4 was shown to inhibit root growth and germination in common wheat (Triticum aestivum) and induce cytotoxicity and genotoxicity in human keratinocyte and fish epithelial cell lines at concentrations between 10 and 200 mg/L [10]. Disperse Blue 3 inhibited bacterial luminescence in Vibrio fischeri (EC50 = 488 mg/L), inhibited algal growth in Selenastrum capricornutum (EC50 = 0.5 mg/L), and significantly decreased the ingestion rate of Tetrahymena pyriformis at 500 mg/L [11]. Vat Green 3 induced yolk sac edema and swim bladder deflation in zebrafish at 100 mg/L [12]. Since anthraquinones are such a broad class of dyes, toxicity associated with these dyes has not been studied in detail [13] warranting the need for further testing.
Solvent Violet 47 (SV47) and Disperse Blue 14 (DB14) are two anthraquinone dyes that have been historically used in different dye mix formulations to produce violet-colored smoke. SV47 is now primarily used as an intermediate dye for the production of disperse and vat dyes [14]. DB14 is now used to color textiles and lubricants and has been identified in sewage treatment plant wastewater [2,15,16].
There has been increasing concern about the potential neurotoxic effects of synthetic dyes. For instance, some food coloring dyes have been linked to neurobehavioral alterations such as sleep disorders, hyperactivity, and even autism [17,18]. The developing nervous system and the blood-brain barrier (BBB) are particularly vulnerable to chemicals, with the early onset of exposure linked to many neurological disorders, including autism spectrum disorder, Alzheimer's disease, and Parkinson's disease [19].
The BBB is a physical barrier formed by astrocytes along with the cerebral microvascular endothelium, pericytes, neurons, and the extracellular matrix. It prevents many substances from entering the brain, through both physical (tight junctions) and metabolic (enzymes, diverse transport systems) barriers [20], thus protecting the brain against chemical substances [21]. Chemicals that can cross the BBB could potentially compromise the central nervous system and lead to neurotoxicity. For instance, lead, a well-known neurotoxicant, crosses the BBB and concentrates in the brain due to its ability to substitute for calcium ions [20]. Here, we tested the ability of SV47 and DB14 to cross the BBB in order to better understand their potential to induce neurotoxicity and neurodevelopment.
The structure of the early-developing zebrafish is similar to other vertebrates, with the advantage of being transparent, allowing for automated visual assessment of developmental outcomes [22,23]. Additionally, the development of the central nervous system and the BBB are also well conserved between zebrafish and other vertebrates [24][25][26]. Specifically, the formation of a functional BBB in zebrafish embryos has been observed at about 72 h post fertilization (hpf) [27,28], with maturation occurring until at least 10 days post fertilization (dpf) [29]. Due to these similarities, the rapid development of the brain, and its small size, the zebrafish is being increasingly used as a complementary model for in vivo neurotoxicity screening [19] and developmental toxicity testing. Here, we utilize the zebrafish embryo developmental toxicity assay to screen SV7 and DB14 for toxicity and report a comprehensive set of phenotypic outcomes.
Materials and Methods
Fertilized embryos (Tropical 5D) were selected and staged, according to Kimmel et al. [30]. The chorions of 4 hpf embryos were removed using 83 µL of 25.3 U/µL pronase (Roche, Indianapolis, In) using a custom automated dechorionator, as described by Mandrell et al. [31]. At 6 hpf, the embryos were transferred into individual wells of a roundbottom 96-well plate filled with 100 µL of embryo medium. The smoke dyes DB14 (Def Std 68-58/2) and SV47 (mil-D-3688) were provided by Walrus Enterprises LLC (Northampton, MA, USA) and dispensed into each well using an HP D300 Digital dispenser. Each dye was suspended in 100% DMSO and added to the single-use cassette wells of the D300 at 20 mM. After the dyes were dispensed, the wells were normalized with 0.64% DMSO. SV47 was tested at 0, 0.55, 1.20, 3.16, 4.20, and 5.23 mg/L, while DB14 was tested at 0, 0.15, 0.75, 1.69, 5.37, and 7.54 mg/L. For each of the dyes, embryos were exposed to 6 concentrations with 32 animals per concentration on two replicate plates. Afterwards, parafilm was placed between the lid and the wells to reduce evaporation. The plates were placed on an orbital shaker at 235 rpm at 28 • C for 16 h to create a homogenous test solution before being placed in a static incubator until 120 hpf.
After the chemical exposures were initiated, the embryos were kept in the dark until 24 hpf to test for embryonic photomotor response (EPR) [32]. The EPR assay is a behavioral assay that detects embryonic zebrafish spontaneous movement in response to visible light. Briefly, the assay consists of 3 phases: 30 s of darkness (Background), a pulse of intense visible light (13,000 lux), 9 s darkness (Excitation), a second pulse of visible light, and 10 s darkness (Refractory). Following the EPR assay, the embryos were evaluated for mortality and delays in progression. The plates were placed back into the incubator until 120 hpf. At 120 hpf, the embryos were subjected to a larval photomotor response assay (LPR) using the Viewpoint Zebrabox system (Viewpoint Life Sciences, Lyon, France). The assay was a total of 24 min, with a datapoint recorded every 6 s. The total distance was tracked for each of the 4 light-dark cycles, with the first cycle treated as an acclimation period and discarded from the analysis. Each cycle consisted of 3 min of alternating visible light (1000 lux) and dark (IR). Animals exhibiting morbidity or mortality were excluded from the analysis. After LPR, the embryos were assessed for a suite of malformations [18], which included yolk sac or pericardial edema, body axis, trunk length, caudal and pectoral fin, pigmentation, somite deformities, eye, snout, jaw, otolith malformations, gross brain development, notochord and circulating deformities, swim bladder presence and inflation, and the presence of a touch response. These effects were collected in a binary manner and stored in a laboratory information management system [22].
Analytical Chemistry
Samples arrived in the laboratory dissolved in DMSO and at varying volumes. Samples were further diluted in methylene chloride to reduce the effect of the DMSO solvent and analyzed using an Agilent 6890 Gas Chromatograph and 5973 Mass Spectrometer (GC-MS) equipped with a polymer (5% diphenyl/95%dimethylsiloxane) column measuring 30 m × 0.25 mm × 0.25 µm. The oven parameters were as follows: initial temperature of 40 • C held for 0.5 min, 10 • C/min to 100 • C, 25 • C/min to 280 • C held for 3 min, 5 • C/min to 300 • C held for 3 min, 25 • C/min to 325 • C. Instrumental control parameters, including mass spectrometer tuning, were performed following USEPA SW 846-Method 8270 guidelines. Calibration was achieved using a 5-point response curve and internal standards to adjust for instrument variability. Calibration standards were prepared using solid dyes provided by the supplier noted previously. Data reductions were performed using the Chemstation software (Agilent Technologies, Santa Clara, CA, USA).
Blood-Brain Barrier Permeability
The BBB-PAMPA Permeability Assay was performed by Creative Bioarray (Shirley, NY, USA) using a protocol based on Rabal et al. [33], with propranolol as the positive control. Both compounds were tested at a concentration of 10 µM. Briefly, the donor solutions of SV47 or DB14 (10 µM, 150 µL in PBS/DMSO 19:1) were added to each well of the donor plate, whose PVDF membrane was precoated with 5 µL of 1% brain polar extract (porcine)/dodecane mixture. Then, 300 µL of PBS was added to each well of the PTEF acceptor plate. The donor and acceptor plates were combined together and incubated for 4 h at room temperature with shaking at 300 rpm. In each plate, SV47 or DB14 and the positive control were tested in duplicate. After incubation, acceptor samples were prepared by mixing 270 µL of the solution from each acceptor well with 130 µL of acetonitrile containing the internal standard. Donor samples were prepared by mixing 20 µL of the solution from each donor well with 250 µL of PBS and 130 µL of acetonitrile containing the internal standard. Then, SV47 or DB14 concentrations in the acceptor and the donor wells were analyzed by LC-MS/MS. The permeability rate (P e in nm/s) was calculated with the following equation: Finally, the permeability of the tested compounds was classified by their P e as high (P e > 10 nm/s), moderate (1 < P e < 10), or low (P e < 1).
Statistical Analysis
Statistical analyses were conducted in R v.3.6.1 [34]. Morphological endpoints were compared between the treatment groups and the control group using Fisher's Exact Test. The morphological Lowest Effect Limits (LELs) were identified as the lowest concentration eliciting a significant difference from control. Significance was defined by the Bonferroniadjusted p-value (0.05/5 = 0.01), which was adjusted for the number of concentrations within each dye. The concentration at which 50% mortality (LC50) was observed and calculated using the drm function within the R drc package.
Behavior was analyzed separately for the light phase and dark phase. Within each phase, the distribution of average movement per fish was compared between the treatment and control using a Kolmogorov-Smirnov test. Behavioral LELs were identified as the lowest concentration eliciting a significant difference from the control. Significance was defined by the Bonferroni-adjusted p-value (0.05/5), which was adjusted for the number of concentrations within each dye.
Morphological Effects
One embryo from the SV47 control group was removed from analysis due to low well quality. Embryos exposed to SV47 showed a concentration-dependent increase in mortality with an LC 50 of 4.37 mg/L (Figure 1a). Embryos exposed to 0.55 and 1.20 mg/L of SV47 had a morphology and behavior consistent with the control (Tables 1 and 2). Developmental progression, axis curvature, jaw malformation, yolk sac edema, pericardial edema, and touch response had an LEL of 3.16 mg/L, with the 3.16 and 4.20 mg/L groups significantly different from the control. In addition, malformed snout and caudal fin have LELs of 4.20 mg/L ( Table 1). The 5.23 mg/L treatment group only had six surviving embryos. Given the small postmortality sample size, we refer to the endpoints observed in all six of the surviving embryos: developmental progression, axis curvature, yolk sac edema, and pericardial edema (Figure 2a). --PIG ----CIRC ----TRUN ----SWIM ----NC ----TR 29 0.006 -- DB14 treatment groups showed no significant difference or dose-response in mortality between treatment groups and the control group (Table 1, Figure 1b). There was no significant effect in morphology in the 0.15, 0.75, or 1.69 mg/L treatment groups. Significantly different morphological endpoints were the same for the 5.37 and 7.54 mg/L treatment groups, with an LEL of 5.37 mg/L for yolk sac edema, axial curvature, eye malformation, snout malformation, jaw malformation, pericardial edema, and pectoral fin malformation (Table 1).
Behavioral Changes
The light-phase movement of the SV47 3.16 mg/L treatment group was similar to the controls (Figure 3), but embryos had a subdued response to the phase change and significantly lower movement during the dark phase relative to the controls ( Table 2, p = 0.002). Embryos in the 4.20 and 5.23 mg/L treatment groups showed almost no movement throughout the assay (Figure 3). The lack of movement in the dark phase observed in the higher doses may be due to physical defects rather than an indication of neurotoxicity given effects seen at lower concentrations [35]. One common phenotype that affects fish buoyancy and motility is impaired swim bladder inflation [36,37], with some textile dyes showing effects on swim bladder function [12,38]. However, no SV47 treatment groups had significant differences in swim bladder function (Table 1). Similarly, Abe et al. showed that zebrafish embryos exposed to large concentrations of the textile dye erythrostominone had no significant decrease in swim bladder function but had decreased dark-phase movement attributed to yolk sac edema and pericardial edema [39]. Our data show embryos in the 3.16, 4.20, and 5.23 mg/L SV47 treatment groups with high instances of yolk sac edema and pericardial edema, which could therefore be a physical obstruction inhibiting swim ability.
Toxics 2021, 9, x FOR PEER REVIEW 7 of 10 erythrostominone had no significant decrease in swim bladder function but had decreased dark-phase movement attributed to yolk sac edema and pericardial edema [39]. Our data show embryos in the 3.16, 4.20, and 5.23 mg/L SV47 treatment groups with high instances of yolk sac edema and pericardial edema, which could therefore be a physical obstruction inhibiting swim ability. Although there were no significant changes in morphology in the 0.15, 0.75, and 1.69 mg/L DB14 treatment groups, the LEL for dark-phase movement was 0.15 mg/L, and the dark-phase movement was lower than the control across all treatment groups (Table 2, Figure 4). In particular, the 0.75 and 1.69 mg/L treatment groups showed a slight response to the phase change but lower movement throughout the dark phases ( Figure 4). Touch response, an indicator of skeletal muscle function or the innervation of the nerves, was not significantly impaired for any DB14 treatment group (Table 1). Contrary to the SV47 results, the 5.37 and 7.54 mg/L DB14 treatment groups were hyperactive during the light phase despite having high rates of yolk sac edema, bent axis, and pericardial edema (Table 2, Figure 2b). Because light-phase movement in the controls was low, it is possible that hyperactivity was observable for periods where lower movement is expected but periods where greater movement is expected to show the inhibitory effects of the malformations. Although there were no significant changes in morphology in the 0.15, 0.75, and 1.69 mg/L DB14 treatment groups, the LEL for dark-phase movement was 0.15 mg/L, and the dark-phase movement was lower than the control across all treatment groups (Table 2, Figure 4). In particular, the 0.75 and 1.69 mg/L treatment groups showed a slight response to the phase change but lower movement throughout the dark phases ( Figure 4). Touch response, an indicator of skeletal muscle function or the innervation of the nerves, was not significantly impaired for any DB14 treatment group (Table 1).
Toxics 2021, 9, x FOR PEER REVIEW 7 of 10 erythrostominone had no significant decrease in swim bladder function but had decreased dark-phase movement attributed to yolk sac edema and pericardial edema [39]. Our data show embryos in the 3.16, 4.20, and 5.23 mg/L SV47 treatment groups with high instances of yolk sac edema and pericardial edema, which could therefore be a physical obstruction inhibiting swim ability. Although there were no significant changes in morphology in the 0.15, 0.75, and 1.69 mg/L DB14 treatment groups, the LEL for dark-phase movement was 0.15 mg/L, and the dark-phase movement was lower than the control across all treatment groups (Table 2, Figure 4). In particular, the 0.75 and 1.69 mg/L treatment groups showed a slight response to the phase change but lower movement throughout the dark phases ( Figure 4). Touch response, an indicator of skeletal muscle function or the innervation of the nerves, was not significantly impaired for any DB14 treatment group (Table 1). Contrary to the SV47 results, the 5.37 and 7.54 mg/L DB14 treatment groups were hyperactive during the light phase despite having high rates of yolk sac edema, bent axis, and pericardial edema (Table 2, Figure 2b). Because light-phase movement in the controls was low, it is possible that hyperactivity was observable for periods where lower movement is expected but periods where greater movement is expected to show the inhibitory effects of the malformations. Contrary to the SV47 results, the 5.37 and 7.54 mg/L DB14 treatment groups were hyperactive during the light phase despite having high rates of yolk sac edema, bent axis, and pericardial edema (Table 2, Figure 2b). Because light-phase movement in the controls was low, it is possible that hyperactivity was observable for periods where lower movement is expected but periods where greater movement is expected to show the inhibitory effects of the malformations.
Analytical Chemistry
Analytical chemistry analysis was performed on the stocks used for the exposures. The results are summarized in Table 3.
Blood-Brain Barrier Permeability
The in vitro BBB model was moderately permeable to SV47 (1.586 nm/s, Table 3) and highly permeable to DB14 (26.259 nm/s, Table 4). Interestingly, the highly permeable dye was the one that presented less morphological effects but more behavioral alterations. While hypoactivity can have many different causes (i.e., morphological deformities, secondary paralysis, impaired neurodevelopment, etc.), it is worth noting that morphological abnormalities were not detected with the DB14 treatment. These results suggest that assays to measure BBB permeability might be a useful complement to zebrafish embryo exposures, particularly when assessing neurodevelopmental endpoints. Understanding the capability of chemicals to cross the BBB can help discern potential neurotoxic effects on developing organisms.
Conclusions
Similar to other anthraquinone dyes, toxicity information for SV47 and DB14 is sparse. With the continued use of anthraquinone dyes in industrial and commercial settings, it is important to fill toxicological data gaps so that we can understand the potential adverse outcomes from their presence in wastewater and aquatic ecosystems. Here, we show that SV47 and DB14 are both found to cause toxic effects in zebrafish embryos. SV47 induced high mortality, with an LC 50 of 4.37 mg/L, and high rates of morphological abnormalities. DB14 induced significant morphological effects at the highest tested concentrations and showed potential for neurotoxicity at all concentrations. Future assessments of SV47 and DB14 should use an integrative approach that combines these phenotypic markers and omics analyses to understand the molecular mechanisms of their toxicity. Our results showed that the zebrafish embryo is a useful model to understand the potential adverse effects of smoke dyes on vertebrates, particularly when paired with other complementary in vitro assays. Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available on request from the corresponding author. | 4,736.2 | 2021-01-01T00:00:00.000 | [
"Environmental Science",
"Biology"
] |
Multisource information fusion method for vegetable disease detection
Automated detection and identification of vegetable diseases can enhance vegetable quality and increase profits. Images of greenhouse-grown vegetable diseases often feature complex backgrounds, a diverse array of diseases, and subtle symptomatic differences. Previous studies have grappled with accurately pinpointing lesion positions and quantifying infection degrees, resulting in overall low recognition rates. To tackle the challenges posed by insufficient validation datasets and low detection and recognition rates, this study capitalizes on the geographical advantage of Shouguang, renowned as the “Vegetable Town,” to establish a self-built vegetable base for data collection and validation experiments. Concentrating on a broad spectrum of fruit and vegetable crops afflicted with various diseases, we conducted on-site collection of greenhouse disease images, compiled a large-scale dataset, and introduced the Space-Time Fusion Attention Network (STFAN). STFAN integrates multi-source information on vegetable disease occurrences, bolstering the model’s resilience. Additionally, we proposed the Multilayer Encoder-Decoder Feature Fusion Network (MEDFFN) to counteract feature disappearance in deep convolutional blocks, complemented by the Boundary Structure Loss function to guide the model in acquiring more detailed and accurate boundary information. By devising a detection and recognition model that extracts high-resolution feature representations from multiple sources, precise disease detection and identification were achieved. This study offers technical backing for the holistic prevention and control of vegetable diseases, thereby advancing smart agriculture. Results indicate that, on our self-built VDGE dataset, compared to YOLOv7-tiny, YOLOv8n, and YOLOv9, the proposed model (Multisource Information Fusion Method for Vegetable Disease Detection, MIFV) has improved mAP by 3.43%, 3.02%, and 2.15%, respectively, showcasing significant performance advantages. The MIFV model parameters stand at 39.07 M, with a computational complexity of 108.92 GFLOPS, highlighting outstanding real-time performance and detection accuracy compared to mainstream algorithms. This research suggests that the proposed MIFV model can swiftly and accurately detect and identify vegetable diseases in greenhouse environments at a reduced cost.
Introduction
A recent report revealed that plant diseases account for over one-third of the annual natural losses in agricultural production [1].Once plants become infected, these diseases can rapidly spread and result in significant production losses.Therefore, early detection and diagnosis of plant diseases are of utmost importance.In the past, agricultural experts were responsible for plant disease detection, requiring extensive professional knowledge.However, this approach proved to be time-consuming, labor-intensive, and prone to errors [2].The traditional method of manual feature extraction for plant disease detection is complex and inefficient, posing challenges for greenhouse cultivation [3].Moreover, certain valuable features that are not readily discernible to the naked eye often go unnoticed [4].Additionally, when confronted with extensive datasets in natural settings, the accuracy of these traditional methods is notably diminished [5].Fortunately, advancements in artificial intelligence and computer vision technology, particularly in deep learning, offer promising solutions across various fields, including agriculture, surpassing traditional methods.[6,7].
In recent years, there has been a growing trend towards applying artificial intelligence (AI) methodologies to various aspects of agriculture, including disease detection.Tang et al. [8] incorporated the attention mechanism into ShuffleNet and achieved an impressive accuracy of 99.14% in identifying multiple crop diseases on the Plant-Village dataset.Ni et al. [9] enhanced the ResNet50 network by introducing the concept of dense connections.Their improved model exhibited good performance on the Al Challenger 2018 dataset.Mohapatra et al. [10] introduced custom-CNN for identifying four types of rice leaf diseases.Their model outperformed others with a higher accuracy of 97.47%.Furthermore, researchers have discovered that employing attention mechanisms can enhance the weight of lesion features, thus improving recognition effect.Chen et al. [11] introduced the SE module, significantly improving the model's sensitivity to channel features.It demonstrated superior performance compared to existing models.He et al. [12] employed a double-layer Faster R-CNN to detect brown planthoppers at different quantities and stages.Wang et al. [13] proposed an S-RPN network, integrating attention mechanisms into residual networks.On their self-built AgriPest21 dataset, they obtained an average accuracy (mAP) of 78.7%.Jiao et al. [14] proposed an adaptive feature fusion module within FPN to extract more comprehensive pest features, along with an adaptive enhancement module to reduce information loss.Li et al. [15] put forward the DAC-YOLOv4 algorithm, which accurately detects strawberry powdery mildew.This method successfully identifies diseased leaves and areas even in complex backgrounds and calculates the disease index based on the incidence of strawberry powdery mildew, providing valuable references for subsequent treatments.Sun et al. [16] proposed VegDenseCap, utilizing vegetable leaf images as input.The disease features are then described in natural language, achieving an average accuracy of 88.0% (mAP).Additionally, Li et al. [17] improved YOLOv5s, resulting in a remarkable mAP of 93.1% for vegetable disease detection.Bora et al. (2023) [18] proposed a system that achieved disease detection rates of 99.84%, 95.2%, 96.8%, and 93.6% for tomato leaves, stems, fruits, and root positions, respectively.Zhang et al. ( 2023) [19] presented experimental results on 3123 tomato leaf images, comprising 1850 camera-captured images and 1273 obtained from the internet, demonstrating that the proposed M-AORANet achieved a recognition accuracy of 96.47%.Sunil et al. (2023) [20] applied a Multi-Feature Fusion module (MFFN) to classify a publicly available tomato disease dataset, attaining training, validation, and external testing accuracies of 99.88%, 99.88%, and 99.83%, respectively.While the studies mentioned above predominantly used samples with simple backgrounds, their adaptability to complex backgrounds is still limited.Presently, datasets for agricultural disease detection models are predominantly classified into two categories (Fig. 1): those captured in natural environments, featuring backgrounds, and those obtained under controlled conditions, devoid of backgrounds.As depicted in Fig. 1, images obtained from natural environments exhibit intricate backgrounds, contributing to models with enhanced robustness and generalization.In contrast, images acquired in controlled environments exhibit minimal background interference, potentially yielding models that are less effective in natural settings.Only a few studies have addressed disease identification in complex environments, but their network accuracy has not met the desired expectations, indicating certain limitations.
Compared to traditional methods of plant disease detection, deep learning has shown significant advantages in the field [21].However, the effectiveness of deep learning models largely depends on the training dataset [22].Due to the significant variability of different diseases in real-world environments, it is challenging for training datasets to cover all scenarios, leading to insufficient sample quantities and imbalanced distributions [23].Additionally, there is difficulty in establishing unified standards for annotating disease training datasets, which can result in misclassifications when using end-toend prediction methods like deep learning.Considering that plant diseases often occur alongside various contextual information, utilizing multiple sources of information during disease occurrences can aid in more accurate category judgments.Wang et al. (2020) [24] proposed a context-aware attention network that encodes various types of contextual information into image annotations.Zhao et al. (2020) [25] developed a deep learning system called the Multi-Context Fusion Network (MCFN), which utilizes contextual features collected from imagecapturing sensors as prior information to assist in crop disease classification.They reduced false alarms in the proposed ContextNet and designed a deep fully connected network to fuse visual and contextual features for crop disease prediction.Zhou et al. (2021) [26,27] proposed a model that explores semantic embeddings of disease images and disease description text, integrating the correlation and complementarity between the two modal data types.The region proposal component guides the model to focus on regions of interest in disease images with complex backgrounds in a weakly supervised manner, thereby avoiding the costly manual annotation of key image regions.The progressive learning network allows the model to progressively learn global features and fine local features.Wang et al. (2021) [28] combined modal information from disease image and disease text, achieving better results on small datasets compared to using image or text models alone.Feng et al. (2022) [29] proposed an end-to-end disease recognition model composed of a lesion region detector and a disease classifier (YOLOv5s + BiCMT), demonstrating that bidirectional cross-modal feature fusion of disease images and text is an effective method for in-field vegetable disease identification, with robust performance.Cheng et al. (2023) [30] introduced a location attention block, which effectively extracts positional information from feature maps and constructs attention maps to enhance the model's feature extraction capabilities in regions of interest.It is evident that integrating deep learning models with multi-source information on plant diseases can lead to a unified solution, thereby improving the accuracy of plant disease detection.
The study was conducted in Shouguang City, located in Shandong Province, China.Known as the "hometown of vegetables" in China, Shouguang City is renowned for pioneering winter warm greenhouses in the country.It serves as the largest production base for greenhouse vegetables in China, cultivating a diverse range of vegetables, including tomatoes, cucumbers, bitter gourds, eggplants, and chili peppers.These crops, along with eggplants, melons, and legumes, are integral to China's "vegetable basket project" and are susceptible to various diseases.The greenhouse environment further increases the risk of disease incidence [31].In recent years, the escalating probability of vegetable diseases due to climate change has necessitated widespread pesticide spraying (Fig. 2).Consequently, residual pesticide levels in vegetables have remained persistently high, posing significant food safety concerns and substantially diminishing the economic viability of vegetable cultivation [32].Therefore, accurate diagnosis of vegetable diseases becomes crucial for effective disease prevention and control.During preliminary visits and research conducted by our project team among vegetable farmers in Shouguang City, the diagnosis and prevention of vegetable diseases primarily rely on experience urrently (Fig. 3), with low timeliness, poor accuracy, and a high demand for personnel with specialized skills, often leading to misdiagnosis and missed detections [33].A common vision emerged -the desire to utilize modern technology for precise diagnosis of vegetable diseases.This scientific problem addresses the application of machine vision methods to intelligently and accurately detect and recognize vegetable diseases in the greenhouse planting environment.
The detection and identification of vegetable diseases play a crucial role in enabling growers to promptly address them and minimize losses [34].However, machine vision-based detection and recognition of vegetable diseases encounter significant challenges in realworld planting environments.These challenges include complex planting conditions, various types of diseases, and subtle differences in symptom manifestation.While deep learning technology has made progress in addressing these issues in recent years, improving the accuracy of vegetable disease detection and recognition to meet the requirements of diverse regions, spaces, and timeframes in greenhouse planting remains a key concern.
This study aims to tackle the limitations of insufficient data volume for vegetable disease images in greenhouse planting environments and the subpar detection performance observed in existing research.To achieve this, we construct a large sample dataset comprising disease images captured in greenhouse planting environments.Additionally, we investigate Space-Time Fusion Attention Network and multi-layer encoding and decoding feature fusion networks.Through this project, we develop a vegetable disease detection method that leverages multi-source information fusion.The performance of the suggested approach is assessed using a dataset created specifically for this research.It is anticipated that this project will make significant strides in the crucial area of image recognition for greenhouse vegetable diseases, thereby providing a scientific theoretical foundation for comprehensive disease prevention and control measures.
Data collection
The collection of image data was collaboratively conducted by multiple researchers and agricultural experts from our team.The data collection took place at the Vegetable Planting Base located in Shouguang City, Shandong Province, China (coordinates: 118.782956E, 36.930686N).The base encompasses a total area of 680,000 acres and cultivates various types of vegetables, including tomatoes, cucumbers, and bitter melons.At various times, under diverse weather conditions, temperatures, lighting, and angles, images of naturally occurring diseases were captured using greenhouse monitoring cameras.Building upon a thorough analysis of the disease pathogenesis, a large-scale dataset (VDGE, Vegetable Disease for Greenhouse Environment) was established.The images in VDGE are formatted as JPEG.Concurrently, leveraging Internet of Things (IoT) technology, with appropriate sensor support, automatic collection of space, temporal, and environmental information, among other multi-source data, was facilitated (Fig. 5).
The collected multi-source information was then automatically transformed into textual data, providing descriptions of the diseases.The backgrounds of the disease images encompass various noises and environmental factors, such as leaves, weeds, soil, and diverse lighting conditions, rendering them suitable for real-world model applications and offering credible experimental data for deep learning modeling.Examples of collected data are shown in Table 1.
Data preprocessing
In the initial image collection, certain images were found to be redundant, blurry, or poorly lit.Consequently, a selection process was undertaken to eliminate Moreover, given the surplus of background information in the images, with disease spots occupying only a fraction of the entire image, manual cropping was necessary.This was done to reduce the data volume for more efficient processing and to minimize interference from non-essential elements.All images were resized to a standardized dimension of 640 × 640.Consequently, we obtained a refined original dataset for further research.
Data annotation
Employing a semi-supervised approach, disease targets within VDGE were labeled.Initially, a small subset of disease data (1000 images) underwent manual annotation, including disease category labels, infected area location information, bounding boxes delineating regions of interest, and a textual description file containing multisource information.Subsequently, a model trained on these annotated disease data assigned temporary pseudolabels to the remaining disease data.These temporary labels were then manually adjusted for certain diseases, followed by continued training of the disease detection Fig. 5 The Internet of Things (IoT) used for Data Collection Fig. 4 The Vegetable Planting Base model.Through iterative refinement, the performance of the labeling model was enhanced, resulting in savings of manpower and cost compared to complete manual labeling.
During the manual labeling process, to ensure accuracy and authority, images were initially classified into their corresponding high-level vegetable categories, such as tomatoes, cucumbers, and bitter gourds.Subsequently, three groups of agricultural experts independently annotated different types of vegetable diseases and multisource information texts.Thus, each data received three labels for both the image and multi-source information text.Considering potential inconsistencies among annotations from different annotators, the following measures were taken: data with completely inconsistent labels among the three were removed, while data with two consistent labels or all three consistent labels were retained, with the majority-consistent label chosen as the final label.Additionally, data expressing completely opposite features in images and multi-source information texts were discarded.Statistics on the volume of the original dataset VDGE after data annotation are shown in Table 2.
By analyzing Table 2, it becomes apparent that the dataset has certain issues.These include a limited total sample size of image data, an uneven distribution of samples across different vegetables, and variations in the number of samples for different diseases within the same vegetable category.Consequently, this study aims to mitigate the impact of these challenges on model performance by employing techniques such as data augmentation, model structure optimization, and other related methods.
Data augmentation
Data augmentation strategies are pivotal in enriching experimental data, facilitating more realistic simulations of intricate object detection scenarios, and enhancing the performance of detection models.To maintain independence between training and test set images throughout the experimental process and bolster the model's generalization capability, the dataset was initially partitioned into training, validation, and test sets using an 8:1:1 ratio before any data augmentation operations were conducted.
In vegetable disease detection scenarios, data augmentation methods such as random cropping, color transformation, and scaling can alter the shape, color, and texture features of the diseases.Therefore, this study employs five specific methods for data augmentation to ensure controlled changes: horizontal flipping, vertical flipping, brightness transformation, contrast transformation, and saturation transformation.The aim is to enhance the randomness of data during model training without excessive augmentation.Different data augmentation methods are randomly combined during the training process, with their respective usage probabilities outlined in Table 3. Figure 6 illustrates the enhancement effect, where A represents the original vegetable disease image, and B, C, D,
Methods
This study presents a novel approach for vegetable disease detection by utilizing a multi-source information fusion method.The proposed method is specifically designed to address the challenges posed by complex unstructured environments commonly found in greenhouse settings, including variations in lighting conditions, occlusion, and overlap.To facilitate this research, a dedicated dataset of vegetable disease images grown in greenhouses was constructed.By leveraging this dataset, the developed method demonstrates enhanced adaptability and robustness in accurately detecting and identifying vegetable diseases.
Space-Time Fusion attention network (STFAN)
Considering the varying types of diseases that affect different vegetables, it is important to account for factors such as the occurrence time, surrounding environment, and spaceal conditions specific to each type of vegetable disease.Therefore, integrating space, temporal and environmental information from vegetable disease images becomes crucial for accurate disease detection.One approach involves initially classifying vegetables based on multi-source information and subsequently developing disease detection models tailored to each vegetable type.This two-step process allows for a more effective and specialized detection approach, thereby improving accuracy and reliability in identifying and combating vegetable diseases.
The Space-Time Fusion Attention Network proposed in this study is depicted in Fig. 7.The network takes into account both efficiency and accuracy by utilizing a backbone network to extract multi-source information from the original image.This extracted information is subsequently input into two fully connected layers, forming the decision layer that outputs the specific vegetable type corresponding to the disease image.This approach enables effective utilization of the multi-source information obtained from the image, allowing accurate separation of different types of vegetable data.In Fig. 6, the first branch focuses on generating the coarse classification results for the image.The remaining branches individually output space, temporal, and environmental information.These branches extract specific features related to these aspects from the input image.By concatenating the multi-source information from each branch, and feeding it into a decision network comprising multi-layer perceptrons, the final vegetable classification result can be obtained.
Firstly, following the network structure outlined in Fig. 6, the process commences with the input of vegetable disease images and multi-source information.By utilizing the Bert model [35] to encode space, temporal and environmental information related to vegetable diseases (referred to as multi-source information), a feature matrix of multi-source information is obtained.The textual information of vegetable disease multi-source information is fed into the model, resulting in an output of encoded vectors for multi-source information.
Secondly, the core concept of multi-source information fusion is achieved through attention mechanisms to integrate visual and multi-source information.This involves merging the encoded knowledge features with the visual features corresponding to the input image, thereby obtaining multi-source information fusion visual features.
Thirdly, the network proceeds to extract multi-source information features.This extraction process is facilitated by various branches, each dedicated to capturing distinct types of information such as space, temporal, and environmental features.Once the multi-source information is obtained from these branches, it undergoes fusion through fully connected layers.These layers amalgamate the extracted features, facilitating the integration and combination of diverse information sources.The outcome of this fusion process yields comprehensive and enriched feature representations that encompass the various aspects of the vegetable disease images.
Finally, a softmax classifier is employed to classify and determine the vegetable type based on the fused features.
The softmax classifier assigns probabilities to each potential vegetable category, indicating the likelihood of the input image belonging to a specific vegetable type.The output with the highest probability denotes the predicted vegetable type associated with the input disease image.
Multilayer encoder-decoder feature Fusion Network (MEDFFN)
After determining the types of vegetables in a vegetable disease image, it becomes necessary to identify the location of the disease.However, most convolutional neural network models reduce the resolution of feature maps in deep convolutional layers to 1/32 or 1/64 of the original image's size.As a result, small targets like diseases become indiscernible on these deep feature maps, where a target of size 32 × 32 or 64 × 64 occupies only a single pixel.Fortunately, we can leverage the environmental information surrounding vegetable diseases as additional multi-source data to aid in disease detection tasks.It is important to note that diseases typically manifest on the vegetables themselves rather than randomly appearing in the sky or elsewhere.Hence, the small-scale multi-source information derived from shallow convolutional blocks, which includes details about the texture, color, shape, and other characteristics of the disease's surrounding environment, can be integrated with the deep higherorder semantic information to generate super-resolution features.This integration process serves two purposes.Firstly, it prevents the loss of important details in deep features by incorporating the fine-grained information from shallow convolutional blocks.Secondly, it ensures an appropriate receptive field size, enabling accurate disease detection.
This study introduces a multi-layer encoding and decoding feature fusion network, illustrated in Fig. 8.A novel module called CSTB (Convolutional Swin Transformer Block) is proposed, which combines convolutional modules with the Swin Transformer architecture.This module is utilized to construct a multi-layer encoding and decoding feature fusion network.To enhance the feature information of interest and suppress redundant information, the encoder incorporates an upsampling layer, while the decoder includes a downsampling layer.These layers work together to provide improved local disease feature details for the encoding and decoding sequence features.By leveraging this approach, the network can effectively fuse and integrate information from multiple layers, leading to enhanced performance in disease object detection.
As depicted in Fig. 9, the hybrid model, Convolutional Swin Transformer Block (CSTB), consists of multi-layer convolutions and Swin Transformer Block (STB).The encoding process utilizes a patch merging layer, while the decoding process employs a patch embedding layer.The input CSTB undergoes a feature forward pass determined by a 1 × 1 convolution, followed by three stacked convolutional modules.This module facilitates channel dimension operations, both upsampling and downsampling, while preserving the spatial dimension in the output.It effectively integrates information across channels.By employing multi-layer convolution modules, the model can learn complex and abstract feature information, extract more detailed spatial features, and provide STB with structural priors.Subsequently, the output passes through either the patch merging layer or the patch embedding layer in the forward direction.The patch merging layer is utilized for downsampling in the encoding process, while the patch embedding layer is employed for upsampling during the decoding process.
Once the encoding has been downsampled using the patch merging layer or the decoding has been upsampled through the patch embedding layer, it is then forwarded into the two-layer Swin Transformer Block (STB), as depicted in Fig. 10.This module comprises two stacked layers of Swin Transformer Layers (STL).Each STL is composed of layer normalization, a local window multihead attention module (W-MSA), residual connections, and linear layers.Specifically, two consecutive Swin Transformer Layers utilize a multi-head self-attention module based on local windows.The calculation formula for two consecutive Swin Transformer Layers can be expressed as follows: (1) In the equation, Z l and z l represent the output of the local window multi-head attention module and linear layer in the first STL layer, respectively.Similarly, Z l+1 and Z l+1 represent the output of the local window multi- head self-attention module and linear layer in the second STL layer, respectively.The function WMSA(•) denotes the local window multi-head attention operation, LN represents layer normalization, and W(•) represents the linear layer.Unlike conventional Transformer, this model employs a multi-head self-attention mechanism within nonoverlapping local windows.This approach enhances the extraction of local feature information.For the local window multi-head self-attention, let's consider a 2D feature map X?R C×H×W , where H and W denote the vertical and horizontal dimensions of the feature map correspondingly.To implement this, the feature map is split into non-overlapping windows of size M × M.Then, we flatten and transpose each window to obtain the feature X i ?R M 2 ×C .Subsequently, we apply multi-head self- attention operations to the flattened features within each window.Assuming the number of heads is k, and the feature dimension of a single head is d k = C/k , the formula for calculating the k-th multi-head self-attention within a non-overlapping window is as follows: In the equation, W q i , W k i , W v i represent the query, key, and value weight matrices for the k-th multi-head selfattention, respectively.Y i k represents the output of the k-th multi-head self-attention operation, which is then concatenated and layer normalized to obtain the final output, denoted as X k .The calculation formula can be expressed as follows: In the formula, Concat(•) represents the concatenation operation, and LN represents layer normalization.After passing through the two STB modules, the features are then forwarded to the next stage, which is the CSTB module.In this module, the features need to be reshaped in order to restore the required image feature dimensions before being input into the convolutional layer of the next CSTB stage.Specifically, the output sequence dimensions of the second STB are (1, H × W, C).The reshaping process involves restoring the image feature dimensions to (C, H, W) before feeding them into the convolutional layer of the subsequent CSTB stage.
Boundary structure loss function (BSLF)
To address the challenges of missed and false detections in small-scale disease detection, a boundary structure loss function (BSLF) is introduced.This loss combines the boundary intersection over union ratio loss (IOU) [35], structural similarity loss (SSIM) [36], and the widely used cross-entropy loss (BCE) [37].
The following equation represents the calculation formula for the loss function: In the equation above, L bce , L iou , L ssim represent the cross-entropy loss, boundary intersection over union ratio loss, and structural similarity loss, respectively.λ 1 , λ 2 , λ 3 are weight coefficients, which are set to 1.
The cross-entropy loss is commonly used in binary classification or segmentation tasks to measure the discrepancy between the predicted values and the ground truth labels.It is described by the following equation: In the equation above, G (x,y) ?(0,1) represents whether the pixels at coordinates (x, y) belong to the object in the ground truth labels of vegetable diseases.S (x,y) rep- resents the predicted probability that the pixels at coordinates (x, y) belong to the disease target.
Due to the challenge of class imbalance commonly encountered in disease detection, cross-entropy loss, which estimates overall classification accuracy for all pixels equally, may not effectively handle this issue.To address this, the boundary intersection over union (IOU) ratio loss is introduced to penalize inaccurate classification and improve regional consistency and boundary response.The IOU loss is defined as follows: Similar to the cross-entropy loss, G (x,y) ?(0,1) denotes whether the pixels at coordinates (x, y) belong to the object in the ground truth values of vegetable diseases.S (x,y) represents the predicted probability that the pixels at coordinates (x, y) belong to the disease target.
Structural similarity loss, originally introduced for image quality assessment, is utilized to capture the structural characteristics within an image.In this context, it is incorporated into the training loss to guide the network in learning the structural information of defective objects based on the provided labels.Let x = x j : j = 1, • • • , N 2 and y = y j : j = 1, • • • , N 2 represent the pixel values of the N×N feature map for the predicted probability S and the corresponding real label G, respectively.The loss associated with structural similarity can be defined as follows: In the given equation, µ x , µ y and σ x , σ y represent the mean and standard deviation of x and y, respectively.σ xy denotes the covariance between x and y.C 1 is assigned a value of 0.012, and C 2 is set as 0.032.
Multisource Information Fusion Method for Vegetable Disease Detection (MIFV)
Based on the principles of deep learning, we analyze the relationship between space-time fusion attention network and multi-layer encoding and multilayer encoderdecoder feature fusion network.We explore detection and recognition methods for disease types and positions under challenging conditions like uneven lighting, partial occlusion, and leaf overlap.To further improve disease detection and recognition, a multisource information fusion method for vegetable disease detection (MIFV) method specifically designed for vegetable disease detection (Fig. 11) is introduced.According to Fig. 11, a multi-layer encoding and decoding feature fusion network is employed for the detection of diseases on specific vegetables.This indicates that there exist significant variations in disease detection models across different vegetables.However, it should be noted that Space-Time Fusion Attention Network do not guarantee the accurate classification of vegetable disease images in every real-world scenario.Consequently, to mitigate the impact of image misclassification and enhance the system's accuracy and robustness, a pretraining model in the form of a Space-Time Fusion Attention Network is utilized to train a multi-layer encoding and decoding feature fusion network.During the training process, fine-tuning is required for the classification branch of the multi-layer encoding and decoding feature fusion network.In other words, the multi-layer encoding and decoding feature fusion network specific to each type of vegetable needs to undergo a certain number of training iterations using data from other types of vegetables.This step ensures that the Space-Time Fusion Attention Network can still yield accurate detection outcomes even in cases of misclassification.
Experimental environment
In this study, the MIFV model is developed and trained using the Python deep learning framework.The experimental setup involves using an NVIDIA GeForce 3060 Ti graphics card with 32GB of memory.For model training, specific parameters are defined.The batch training size is set to 8, indicating that 8 samples are processed in each iteration.The random gradient descent (SGD) optimizer is employed, with a momentum parameter of 0.937, enabling faster convergence towards optimal solutions.The total epoch count for training is set to 200.
Evaluating indicator
This study used AP (Average Precision), mean Average Precision (mAP), recall rate (Recall), model parameter (M), computational complexity (GFLOPs) and detection speed (FPS) as evaluation indicators for the target detection model.
The calculation formula for mAP is: The formula includes the following elements: K represents the count of detected categories; mAP denotes the mean AP value, with higher values indicating superior detection performance.AP refers to the AUC (Area Under the Curve) of the PR curve constructed by employing Recall as the x-axis and Precision as the y-axis for a specific category across all predicted images.The calculation formula for Precision, Recall and AP are as follows: In the provided formula, TP signifies the count of detection frames that fulfill the criteria of having an IOU value greater than or equal to the specified threshold.FP, on the contrary, represents the quantity of detection frames with an IOU value lower than the prescribed threshold.FN denotes the number of targets that were not correctly identified.
Frames Per Second (FPS) is a measure of a model's inference velocity.A model is considered to satisfy realtime detection criteria when it achieves an FPS exceeding 30.Additionally, Giga Floating Point Operations Per Second (GFLOPs) and the model's parameter volume, are metrics that gauge the model's computational complexity.Lower values of GFLOPS and parameter volume signify that the model demands less computational resources.
Selection of learning rate
The learning rate is a pivotal hyperparameter that significantly influences a model's performance.This section delves into the optimization of this parameter by evaluating the model's behavior across a spectrum of learning rates: 0.1, 0.05, 0.01, and 0.001, under otherwise identical conditions.The objective is to enhance the model's learning efficacy on the training set and its recognition accuracy on the test set.The variation in the loss function across these learning rates is depicted in Fig. 12(a).It is evident that at learning rates of 0.1 and 0.05, the loss function remains largely unchanged, indicating that the step size is too large for the function to converge.This underscores the necessity of selecting a moderate learning rate that balances convergence and the rate of convergence.A comparison between the 0.01 and 0.001 learning rates reveals that the latter offers superior convergence properties and speed.Additionally, Fig. 12(b) illustrates that the accuracy fluctuates markedly under the 0.1 and 0.05 learning rates.In contrast, the highest model accuracy is achieved with a learning rate of 0.001.Consequently, the learning rate is ultimately set to 0.001.
Model training
During the model training process, we employed the STFAN as a pretraining model and utilized the learned features to train the MEDFFN.Initially, during the pretraining phase of STFAN, we observed a continuous decrease in the loss function, accompanied by a steady increase in accuracy, as depicted in Fig. 13.This serves as evidence of the effectiveness of STFAN in feature learning.
Subsequently, we proceeded to the fine-tuning phase of MEDFFN.During this stage, particular attention was directed towards fine-tuning the classification branch to mitigate the potential impact of misclassifications from STFAN on the final detection results.Specifically, we devised a targeted fine-tuning strategy, wherein each vegetable category's MEDFFN underwent multiple training sessions, encompassing both intra-category and intercategory vegetable data.This approach aimed to enhance Fig. 12 Comparison of the loss function and mAP at different learning rates the model's robustness against misclassifications.Throughout the fine-tuning process, the loss function steadily decreased, accompanied by a gradual improvement in the mAP metric, as illustrated in Fig. 14, vividly demonstrating the enhancement in model performance.
To comprehensively assess the performance of the MIFV algorithm proposed in this study, we conducted tests on the test set.Through the analysis of vegetable disease detection results, the detection and false alarm situations of different types of diseases can be evaluated.Utilizing the proposed MIFV model for the detection of various types of vegetable diseases separately, the precision (P), recall (R), and<EMAIL_ADDRESS>(i.e., the AP value when IOU is set to 0.5) are presented in Table 4.
As shown in Table 4, overall, the proposed MIFV model achieves precision (P), recall (R), and AP values of 85% or higher across 12 types of diseases and healthy
Comparative experiment
This study selected SSD, Faster RCNN, YOLOv5n, YOLOX-s, YOLOv6-N, YOLOv7-tiny, YOLOv8n, and YOLOv9 for comparison using the dataset constructed internally named VDGE.Table 5 illustrates the specific outcomes.Table 5 clearly demonstrates the effectiveness of the MIFV algorithm proposed in this study.On our self-built VDGE dataset, compared to YOLOv7-tiny, YOLOv8n, and YOLOv9, the mAP has been improved by 3.43%, 3.02%, and 2.15% respectively, showcasing significant performance advantages.
It is particularly worth emphasizing that the MIFV algorithm not only excels in detection accuracy but also demonstrates superior performance in terms of model parameters and computational complexity.Compared to existing algorithms, the MIFV algorithm has made significant strides in reducing model parameters and computational complexity, with model parameters at 39.07 M and computational complexity at 108.92 GFLOPs.This is of great importance for devices with limited resources and for application scenarios that require rapid response.
It can be observed from the table that the SSD (VGG16) algorithm has the highest FPS, reaching 53.6, indicating that its inference speed is extremely fast and well exceeds the standard for real-time processing.The Faster RCNN (ResNet50) algorithm has an FPS of 7.1, which is below the standard for real-time processing, suggesting that it may face issues with slow speed in practical applications.The YOLO series of algorithms perform relatively well in terms of FPS, all surpassing the threshold of 30.In particular, YOLOv5n and YOLOv7-tiny have FPS values of 41.3 and 42.5, respectively, indicating that these two algorithms maintain a high mAP while also exhibiting good real-time performance.The MIFV algorithm has an FPS of 43.6, slightly higher than that of YOLOv7tiny.This indicates that the MIFV algorithm can provide satisfactory inference speed in practical applications, meeting the requirements for real-time detection.Overall, although the MIFV algorithm has the highest mAP, reaching 92.38%, its FPS is also maintained at a high level.This demonstrates that the algorithm ensures high precision while also taking into account inference speed, making it suitable for practical application scenarios.
To substantiate the merits of the proposed MIFV model, this study conducts a comparative analysis with other models, as illustrated in Fig. 15(a) and 15(b), which depict the loss and mAP curves, respectively.
As observed in Fig. 15(a), the proposed MIFV model exhibits a lower loss compared to other models, with an initial loss of 0.040048 that stabilizes around 0.0067.The To provide a more comprehensive understanding and comparison of the performance of different algorithms, we have detailed in Table 6 the detection accuracies of the YOLOv7-tiny, YOLOv8n, and YOLOv9 algorithms across various target categories, and we have presented an intuitive visualization of these results in Fig. 16.These data and charts offer readers a clear perspective for performance comparison, aiding in a deeper understanding of the advantages of the MIFV algorithm in all aspects.In summary, while maintaining high precision, the MIFV algorithm effectively reduces model parameters and computational complexity, providing strong support for its deployment in practical applications.
It can be seen that compared to other algorithms, this research algorithm has achieved certain performance improvements for different types of vegetable diseases.The experiment shows that the network design that fully utilizes multi-source information from vegetable disease images is reasonable and improves detection accuracy.
Ablation experiment
In this study, the MIFV model proposes three significant structural improvements: the STFAN module, MEDFFN module, and BSLF.To validate their effectiveness, ablation experiments were conducted on the VDGE dataset by gradually integrating each module into the Swin Transformer Baseline network, as shown in Table 7.
Based on Table 7, several observations can be made.In Experiment B, the utilization of the STFAN module Figure 17 shows the feature attention heatmaps of four groups pre and post introduction of the STFAN module.The vegetable disease image in its original form is presented in the left column of every group.The attention heatmap prior to incorporating the module is displayed in the middle column, and the right column is the attention heatmap output after passing through the module.The darker the color, the greater the weight, which is more important for detecting vegetable diseases.
Through this module, the network can focus on important areas and improve the performance of vegetable disease detection.
Although the core function of STFAN is classification, we unexpectedly observed a significant enhancement in the model's focusing ability during the experiments.Specifically, STFAN uses a backbone network to extract multi-source information from the original vegetable disease images and outputs the type of vegetable to which the disease image belongs through a decision layer composed of two fully connected layers.This process not only improves the accuracy of classification but also enhances the model's ability to focus on key features in the image.After the introduction of the STFAN module, the model's attention heatmaps showed a clear preference for the disease feature areas, indicating that STFAN indirectly strengthens the model's focus on important features when dealing with multi-source information.The experimental results show that STFAN not only effectively utilizes multi-source information for classification but also enhances the model's ability to focus on key features, which is of great significance for improving the accuracy of vegetable disease detection.The improvement in focusing ability demonstrated by STFAN in classification tasks is due to its enhanced processing of image content during feature extraction and information fusion.
Comparison of performance with and without multisource information
To illustrate the effectiveness of multisource information, Table 8 presents the detection results of the MIFV algorithm with and without the use of multisource Fig. 17 The feature attention heatmaps of four groups before and after adding the STFAN module information, Fig. 18 presents the mAP and loss curves during the training process.The data in Table 8 lead to the conclusion that employing multisource information enhances the performance of disease detection, nearly increasing by 9% compared to the use of disease images alone (from 84.39 to 92.38%).As shown in Fig. 18, the use of multisource information outperforms the non-use in terms of convergence speed and mAP.
Utilizing multisource information is more precise than relying on a single image modality.This underscores the complementary nature of visual information and textual descriptions in the identification process of diseased images.A single image modality extracts visual information from the image through a deep convolutional neural network and predicts its category.However, when the image contains few distinguishable features or is obscured by substantial noise, the addition of multisource information of the disease can enhance the complementarity between features, thereby facilitating the achievement of correct recognition outcomes.
Conclusion
In response to the problem of insufficient utilization of multi-source information of vegetable diseases and large semantic gaps in feature fusion layers in current greenhouse vegetable disease target detection algorithms, which contain redundant information that interferes with the final detection effect, this study proposed the MIFV algorithm.The proposed MIFV algorithm redesigned and optimized the backbone network and feature fusion layers, improved the loss function.The structural design experiment of STFAN shows that multi-source information of vegetable diseases is crucial for detection.The design of MEDFFN indicates that suppressing deep redundant fusion features is also important.The BSLF loss function preserves the boundaries of vegetable disease targets well and effectively detects the contour of disease boundaries.Compared to the latest seven algorithms, the MIFV algorithm model has achieved significant improvement in detection performance on the VDGE dataset, which is conducive to improving the automation and intelligence level of greenhouse vegetable disease detection technology.
Future research directions
This study proposes a Multisource Information Fusion Method for vegetable disease detection based on deep learning.By integrating multiple sources of information related to vegetable disease occurrence during visual extraction, it enhances the detection performance of vegetable diseases in complex scenarios, offering new research avenues in vegetable disease detection.However, there is still room for improvement.
Fig. 2 Fig. 1
Fig. 2 Vegetable disease damage.(a) Widespread dissemination of diseases (b) Extensive spraying of agricultural chemicals Figure 4 illustrates the data collection environment at the base.
Fig. 3
Fig. 3 Diagnosis of vegetable diseases using empirical methods.(a) Diseases on the front surface of leaves (b) Diseases on the back surface of leaves
Fig. 11
Fig. 11 Work flow of Multisource Information Fusion Method for Vegetable Disease Detection
Fig. 14
Fig.14 The curves depicting the variation of the loss function and mAP during the fine-tuning phase of MEDFFN
Fig. 15
Fig. 15 Comparison of Loss and mAP Curves
Fig. 16
Fig. 16 Detection accuracy for different disease categories
1 .Fig. 18
Fig.18 The mAP and loss curves during the training process with and without multisource information
Table 2
Statistics on the volume of the original dataset VDGE after data annotation
Table 1
Examples of collected data E, and F showcase the results after applying the five data augmentation operations.
Table 3
Probability of Data Augmentation methods Fig. 6 Data Augmentation Effect
Table 4
Results of Vegetable Disease Detection
Table 5
Comparison of different algorithms
Table 6
Detection accuracy for different target categories (%)
Table 7
Experimental analysis on component elimination
Table 8
Experimental comparison analysis with and without multisource information | 9,727.2 | 2024-08-02T00:00:00.000 | [
"Agricultural and Food Sciences",
"Computer Science",
"Environmental Science"
] |
Effect of zinc doping on electrical properties of LaAlO3 perovskite
New solid solution with the general formula of LaAl1-xZnxO3-1/2x was prepared by a solid-state reaction route. According to XRD, the crystal structure of LaAlO3 is rhombohedral, while the solid solution possesses cubic symmetry. Homogeneity region of the solid solution LaAl1-xZnxO3-1/2x was narrow and limited to the maximum concentration of 5 mol. %. Computer simulations using crystallochemistry and density functional theory approaches showed that LaAlO3 has high energy barriers for O 2– -ion transport (>2.79 eV). These results are in good agreement with the low values of electrical conductivity obtained experimentally. The electrical conductivity of LaAl1-xZnxO3-1/2x was measured by impedance spectroscopy in the temperature range of 200–1000 °C. The partial substitution of Al 3+ by Zn 2+ was found to increase the electrical conductivity by ~2 orders of magnitude. The electrical conductivity of doped phase LaAl0.95Zn0.05O2.975 as a function of oxygen partial pressure was measured, and the partial contributions (oxygen-ionic and electronic) were determined. It was found that the sample has mixed ionic and p-type electronic conductivity, while the electronic contribution increases with the rise of the temperature. Keywords
Introduction
During the past few decades, the perovskites have been used in various electrochemical devices and their properties have been well described. For example, these materials are promising electrolyte systems for solid oxide fuel cells (SOFCs). The general requirements for an electrolyte are high ionic conductivity, stability in both oxidizing and reducing environments, good mechanical properties and long-term stability. The electrolyte system, namely, yttria stabilized zirconia (YSZ) has been widely investigated for SOFCs, operating at 900-1000 °C [1]. In recent years, the focus of SOFC development has been on lowering the operating temperatures. Perovskites A +2 B +4 O 3 , for example doped BaCeO 3 and BaZrO 3 , are promising materials in this field due to their high proton conductivity. However, the presence of an alkaline earth component in the composition of perovskites A +2 B +4 O 3 can result in the formation of the corresponding carbonates [2][3][4][5], and thus to the degradation of the material.
A new direction of materials development is "alkaline earth elements free strategy", that is, investigation of compounds not containing an alkaline-earth component. The modification of compounds with the general formula of A 3+ B 3+ O 3 is the most simple implementation of this approach [6][7][8][9]. The lanthanum aluminate LaAlO 3 (LAO) can be a promising perovskite material in this trend due to its high chemical stability [10][11][12][13]. The systems based on LaAlO 3 can be good ionic or mixed conductors by adding suitable dopants [12]. Aluminates based on LaAlO 3 have such advantages as low cost of the initial materials, high thermodynamic stability due to the strength of Al-O bonds and wide T-p(O 2 ) regions of ionic conductivity [12].
Complex oxide LaAlO 3 is a tolerant system to the different substitutions. The possibility of introducing various dopants into the La 3+ or Al 3+ −sublattices of LaAlO 3 has been proven in several works. The substitutions of lanthanum by alkaline-earth elements (Ca, Sr, Ba) [7,11,14,15], aluminum by magnesium [7,15,16], and simultaneous cosubstitutions into both sublattices [7][8][9]12,13,15,16] have been made. Thus, it was shown that the acceptor doping of LaAlO 3 produces a deficiency in the oxygen sublattice and, respectively, induces oxygen-ionic transport. It should be noted that the main substitutions are performed for the La-sublattice, and in this case the alkaline earth metal is the dopant, which reduces the chemical resistance of the material.
In this study we used ZnO as a dopant for several reasons: i) as an acceptor dopant, divalent Zn 2+ increases the concentration of oxygen vacancies in the perovskitelattice; ii) in addition, due to the stable oxidation state, the doping will not lead to an increase in the electronic conductivity; iii) zinc belongs to the IIB group in the Periodic Table, it is not an alkaline earth element, the presence of which impairs chemical stability. Also, we assume that the introduction of zinc can reduce the synthesis temperature and will make it possible to obtain dense ceramics, as it was found in the works [17][18][19][20].
Although lanthanum aluminate has been a subject of many studies, the data of its electrical properties are not in good agreement. Thus, it is necessary to systematize the data on the electrical properties of LaAlO 3 . In the present study, we also calculated migration paths and migration energy barrier for oxygen transport. The investigations of electrical properties of LaAlO 3 and Zn-doped at the B-site LaAlO 3 were performed.
Experimental
The LaAl 1-x Zn x O 3-1/2x (where x=0, 0.05, 0.1, 0.15, 0.33) samples were synthesized by solid state method. As initial reagents, preliminary dried oxides of the corresponding elements (99.99% purity, REACHIM, Russia) were used. Aluminum and zinc oxides were dried at 500 °C for 3 h to remove adsorption water. Lanthanum oxide was calcined at 1100 °C for 3 h to decompose the lanthanum carbonates LaOHCO 3 and La 2 O 2 CO 3 in accordance with [21].
The stoichiometric amounts of the oxides were weighed on an analytical balance with an accuracy of ±0.0001 g, mixed and ball-milled in ethanol. The synthesis was started at 700 °C, then the temperature was increased stepwise by 100 °C. All heat treatment steps were carried out with an isothermal holding time of 24 h, cooling with a furnace. After each heat treatment, the samples were milled in a planetary ball mill Pulverisette 6 (Fritsch, Germany) with ethanol and with using the zirconia milling bodies.
Single phase aluminate LaAlO 3 was obtained at 1250 °C. Single phase doped aluminate LaAl 0.95 Zn 0.05 O 2.975 was obtained at lower temperature 1200 °C. The synthesis of the samples LaAl 1-x Zn x O 3-1/2x (x=0.1, 0.15, 0.33) were continued at higher temperature 1300 °C. However, these samples were not obtained as the single phases; also, the sample with x = 0.33 was melted at high temperatures.
Phase composition of the samples was determined by a powder X-ray diffraction method using a diffractometer D8 Advance (Bruker) with Cu Kα radiation in increments of 0.05θ in the range of angles 2θ=10°-120° with exposures of 1s, a voltage of 40 kV and a current of 40 mA. The refinement of unit cell parameters was made using the FullProf software [22].
The surface morphology of the powder samples was studied by means of a high-end imaging desktop scanning electron microscope the Thermo Scientific "Phenom" Pharos (Phenom-World, Netherlands) with FOV: 912 µm, mode: 15kV -map, detector: BSD Full.
Multi-method modeling for the oxygen-ion conductivity for pure lanthanum aluminate LaAlO 3 was performed. We used a combined approach consisting of a crystallochemical analysis of geometric characteristics of free space in crystals, simulation of oxygen transport by the bond valence method (BVSE method) and quantum-chemical modeling of the ionic conductivity within the density functional theory (DFT) method.
The geometrical-topological approach is based on the Voronoi partition [23] and is implemented in the ToposPro software package [24]. Crystallochemical analysis reveals the geometric capabilities of the structure, i.e. a presence of wide voids and channels, which are accessible for anion migration. The criterion R chan (an elementary channel radius) was determined for the geometrical analysis, which characterizes the presence of voids and channels in the structure, as described in [25]. R chan describes the width of the bottleneck between two voids. This criterion is the sum of the radii of the working ions and the environment ions, taking into account the coefficient of ion deformation. This coefficient also takes into account the polarizability of the migration ion when passing through the channel. Based on the set of well-known oxygen conductors, we have chosen the coefficient of deformation for oxygen conductors of 0.8, so that R chan was assumed to be equal to 1.73 Å.
The quantitative semi-empirical evaluation of activation energies of oxygen diffusion was conducted by the bond valence method. This approach is implemented in the SoftBV [26] and 3DBVSMAPPER [27] packages. We use the SoftBV software package developed by the Adams group [26], due to its availability to users. The calculation procedure was carried out as described in [26]. We calculated the migration energies for each species in the structure. This made it possible to reveal that ionic conductivity in LaAlO 3 is due only to oxygen anions. The method is not accurate enough, but allows a quick initial assessment of activation energies for ranking and, next, more precise quantum-chemical modeling of ion transport as described by Nestler et al. [28].
The DFT-calculations were performed for structure relaxation and calculations of oxygen migration energies. The VASP package [29] with the Nudged Elastic Band (NEB) method [30] were utilized. The GGA (generalized gradient approximations) exchange-correlation functional in the form of PBE (Perdew-Burke-Ernzerhof) [31] was applied. When optimizing the structure, the convergence thresholds were used 10 -6 eV and 10 -5 eV/Å for the energy and interatomic forces, respectively. The cutoff energy of plane waves in all calculations was taken equal to 600 eV and uniform Γ-centered k-point mesh for sampling the Brillouin zone with a reciprocal-space resolution of 2π × 0. The theoretical results were compared with the experimentally investigated electrical properties. For electrical measurements, the powder samples were formed into pellets with 10-12 mm in diameter and ~2 mm thickness by pressing at ∼50 MPa. A solution of rubber in hexane was used as a plasticizer. The pellets were sintered at the temperature of 1250 °C (LaAl 1-x Zn x O 3-1/2x ) and 1650 °C (LaA-lO 3 ) for 24 h. Platinum electrodes in the form of finely dispersed paste mixed with an alcohol solution of rosin were applied to the preliminarily polished surfaces of the sintered tablets. The electrodes were burned for 2 h in air at 900 °C.
The relative density of the samples, determined by a hydrostatic method, was found to be 96% (LaAl 0.95 Zn 0.05 O 2.95 ) and 91% (LaAlO 3 ). For this experiment, dried pellets were soaked in kerosene (ρ k =0.8 g/cm 3 ) for 24 hours. For the calculations, the mass of dried samples (m dry ) and the mass of pellets saturated of kerosene (m sat ) were used according to the equation: The conductivity of the samples was characterized by an impedance spectroscopy technique. Measurements were performed by the two-probe method using a Z-1000 P (Elins) impedance spectrometer under varying temperature (200-1000 °C) and partial pressures of oxygen (pO 2 = 1•10 -20 -0.21 atm). The oxygen partial pressure was measured and controlled by an oxygen sensor and a pump made of a solid electrolyte based on yttriumstabilized zirconia ZrO 2 (Y 2 O 3 ).The obtained impedance spectra were analyzed using an equivalent circuits method and refined using Zview software [32].
Structural features of LaAlO 3 and morphology characterization
The XR-diffractogram of LaAlO 3 is presented in the Supplementary (Fig. S1). The obtained phase LaAlO 3 is characterized by the rhombohedral structure, in accordance with the JCPDS card №31-0022 and in agreement with literature data [6,8,10,33]. This is a slightly distorted cubic perovskite with the sp.gr. R3 ̅ c and the unit cell parameters: a = 5.408(5) Å, c = 13.182(3) Å, γ = 120°. Rhombohedral structure is stable modification of LaAlO 3 at room temperature. However, lanthanum aluminate exhibits a reversible phase transition from rhombohedral to cubic symmetry at heat treatment above 400 °C [34][35][36]. The cubic phase is unstable under room temperature. But in some studies, the cubic structure was stabilized at room temperature. A cubic modification was obtained by the mechanochemical [11] and the Pechini methods [15].
The morphology of the sample was investigated using scanning electron microscopy (SEM). Fig. S2a shows the SEM image of the powder sample LaAlO 3 . The grains of the sample were small and had a size of ~1 µm.
Below we present the theoretical calculations of migration paths and a migration energy barrier for the oxygen conductivity for the rhombohedral phase LaAlO 3 , obtained in this work.
Theoretical study of O 2--ion conductivity
Voronoi partition was built for LaAlO 3 using the above described criterion R chan in the ToposPro program. We have found a three-dimensional migration map for oxygen anions in the structure (Fig. 1). The migration energy barrier for oxygen ion diffusion in LaAlO 3 is 1.844 eV according to the BVSE modeling, the corresponding energy profile is shown in Fig. S3. BVSE predict the formation of a three-periodic migration map.
The DFT results show that the oxygen diffusion map consists of two independent paths (Fig. 2a), while only one path (Path 1) is enough for the 3D oxygen diffusion. The DFT-NEB migration energy barriers for the paths 1, 2 are 2.86 and 2.79 respectively, the energy profiles are shown in Fig. 2b. It should be noted that the DFT migration energy values surpass the BVSE ones, similar to already described in the Nestler et al. [28]. It can be caused by strong O-O repulsion as well as many-body effects, which are counted in DFT and not considered in BVSE. But quantitatively both methods provide the similar outlook for oxygen diffusion map as shown in Fig. 3. The oxygen vacancy formation energy was evaluated as 6.15 eV/site according to the DFT data, see the Supplementary for more details. Because of the activation energy for diffusion is usually considered as a sum of the vacancy formation energy and the migration energy, we may conclude that LaAlO 3 should have a poor oxygen conductivity due to very high barriers.
As known from the literature, the energy involved in the process of migration from one site to the unoccupied equivalent site must be low, certainly less than about 1eV [37]. The high quantitative values of the oxygen migration energy prove the necessity of doping perovskite in order to improve the conductive properties. Nevertheless, the implementation of a three-periodic migration map of O 2-anion with the ability to migrate in different directions demonstrates the prospect of creating new perovskites with increased conducting properties.
Computer simulations using crystalochemistry and density functional theory approaches showed that LaAlO 3 has high energy barriers for O 2--ion transport (>2.79 eV). However, computer simulations are carried out for ideal crystals, in according to the occupancy of all atoms at their sites. Therefore, the value of the experimental energy barrier can be less than the theoretical one due to defects and random vacancies in the real crystal.
Structural features of LaAl 1-x Zn x O 3-1/2x solid solution and morphology characterization
The formation of LaAl 1-x Zn x O 3-1/2x solid solution was controlled by XRD. Homogeneity region of the solid solution
Electrical measurements
Electrical properties were studied by the method of electrochemical impedance. As an example, for the sample of x = 0.05 the impedance spectra, recorded at different temperatures, were shown in Fig. 4a. The impedance plot is represented by one distorted semicircle started from the zero point. The impedance spectra were analyzed through the data fitting, using equivalent elementary circuits arranged in series consisting of one resistance (R) and one constant phase element (CPE) in parallel. The capacitance for these semicircles is determined to be ∼10 −11 F/cm. The results of electrical measurements showed that there is not difference in the general view of the impedance spectra of doped and undoped samples. We can assume that this semicircle corresponds to a bulk response. We made this conclusion on the basis of the comparison with the data, presented in [11], since in many respects we have similar results : i) the average grain size of LaAlO 3 was found to be ~1 μm ; ii) the capacitance for high-frequency semicircle is determined to be ∼10 −11 F/cm ; iii) the values of the conductivity of the undoped samples agree well (Fig. 4b).
The observed small second semicircle at low frequencies can be attributed to the grain boundary response. It should be said, according to literature data, the Nyquist plots are typical for the doped LaAlO 3 and exhibit, as usual, two semicircles − the bulk and grain boundary responses. However, the grain boundary resistance is very different from different works, and there is often a situation where the grain boundary semicircle is higher than the resistance of the bulk semicircle. For the investigated Zn-doped composition the observed second semicircle with specific capacitance of ∼2×10 −9 F/cm was small and was visible as separate semicircle at higher temperatures ( Supplementary Fig. S5a). The capacity calculated for this semicircle correlated well with the data presented in [11], where the same second semicircle was assigned to the grain boundary response too. The evolution of impedance spectra for different temperature ranges is shown in Fig. S5 and Fig. S6.
The comparison of data on conductivity and density for the ceramics based on aluminate LaAlO 3 is presented in the Table S1. As seen, the reported conductivity values scatter in a wide range; this implies a strong influence of the phase and elemental impurities, porosity and microstructural characteristics. Fig. 4b compares the temperature dependences of conductivities of undoped LaAlO 3 , prepared in this work with literature data [5,6,10], solid solution LAZ9505 and composition LAZ91. The samples LAZ9505 and LAZ91 showed a high conductivity. The pure LaAlO 3 exhibits a low ionic conductivity due to the high binding strength of Al-O [12]. These data for LaAlO 3 are in good agreement with the literature data, presented in [11], although the reported conductivity values scatter in a wide range (Fig.4b). Some literature data demonstrate a strong contribution of grain boundary resistivity to the total resistivity. For the reasons mentioned above, the bulk properties could not be determined and total contribution (bulk+grain boundary) has been presented [15]. At the same time, the high values of conductivity, measured in [7], are probably doubtful due to incorrect extrapolation of the large semicircle to the high frequencies.
Acceptor-doping of aluminum by zinc leads to an increase by 2 orders of magnitude of the total conductivity over the investigated temperature range. The energies of activation for LAZ9505 and LAO were 1.054 eV and 1.21 eV, respectively. This increase in conductivity of doped sample is due to creation of oxygen vacancies. The substitution of a divalent cation for a trivalent cation produces oxygen vacancy according to the quasichemical equation: Fig. 5a shows the results of the measurements of the conductivity of the sample LAZ9505 as function of oxygen partial pressure in the temperatures range of 500-900 °C. Two areas can be distinguished on the isotherms: a region of electrolytic conductivity as a plateau (i.e. a region where conductivity does not depend on oxygen pressure, pO 2 < 10 −5 atm), and a region at high partial oxygen pressures (pO 2 > 10 −5 atm) for which a positive slope of the dependence is observed.
For pO 2 < 10 −5 atm and the electroneutrality condition It is well established in the literature that doped LaA-lO 3 is a p-type mixed conductor under oxidizing conditions [34], and LaAlO 3 phase exhibits ~10% oxygen-ionic transport numbers in air [34]. Accordingly, doping with zinc didn't change the general character of the conductivity of this phase.
A comparison of the oxygen-ion conductivities of the investigated sample LaAl 0.95 Zn 0.05 O 2.975 with an undoped composition LaAlO 3 , as well as the most conductive composition of a Ca-doped sample, described in [11], is shown in Fig. 5b. As can be seen, doping in both cases leads to an increase in oxygen-ion conductivity, which is a result of the formation of oxygen vacancies (Eq. 3). However, the effect of increasing the oxygen-ionic conductivity upon doping with Ca 2+ is greater. As it is known, two factors determine ionic conductivity, that is, defect concentration and mobility. For the case under consideration, with comparable defect concentrations, obviously, the mobility of oxygen vacancies is different. There are many factors that affect the mobility of oxygen vacancies [38], and in the general case, expansion of the cell volume weakens the metal-oxygen bonding and increases the oxygen vacancy mobility [39]. We believe that due to the smaller lattice parameter and, as a consequence of the smaller volume of the unit cell (V cell = 54.225 Å), the ionic conductivity of the Zn-doped sample is lower than that of the Ca-doped composition (V cell = 54.483 Å) [11].
The oxygen-ionic transport numbers t ion were calculated as a ratio of ionic conductivity to total conductivity σ ion/ σ total . As an example, the Fig. 5c shows calculated data of t ion vs. pO 2 for LaAl 0.95 Zn 0.05 O 2.975 at 500 °C. It was shown that maximum values of ∼1 were reached at the partial oxygen pressures pO 2 < 10 −5 atm. The dependences of the oxygen-ion transport number vs. pO 2 at different temperatures were similar. As can be seen, the sample in air had ion transport numbers of about 20%. These results show that studied phase is mixed ionic-electronic conductor under oxidizing conditions. As for the comparison of the ion transport numbers with other doped phases, based on LaAlO 3 , it is known that an increase in the ion transport numbers can be achieved with an increase in the concentration of the acceptor dopant (due to an increase in the concentration of oxygen vacancies). For example, for the most conductive aluminate-based phases La 1- x Ca x AlO 3-δ , when calcium is introduced from 5 mol. % to 15 mol. %, the ion transport numbers in air increase from 18% to 55% [11]. Thus, for low concentrations of the dopants (5 mol. %), the ion transport numbers are comparable and do not exceed 20%. Unfortunately, Zn-substituted solid solutions with a high concentration of the dopant are not formed; therefore, such doping does not allow a significant increase in the ion transport numbers. However, it should be noted that Zn-doping significantly lowered the sintering temperature of ceramics (1250 °C), for example, Ca-doped ceramics were obtained at 1450 °C [11]. Probably, in the future, codoped phases may be of interest. For example, the codoping of Sr 2+ + Mg 2+ can significantly increase the conductivity, but high temperatures are required to obtain ceramics (Table S1). Therefore, the introduction of low concentrations of Zn 2+ into the B-sublattice of LaAlO 3 whith simultaneous acceptor doping of the Asublattice is a promising method for further investigations.
Conclusions
Zn-substituted LaAl -ion transport and low conductivity. However, substitution by zinc was found to increase the electrical conductivity by 2 orders of magnitude compared to undoped LaAlO 3 . Besides, sintering of Zn-doped phase at 1250 °C yielded dense ceramics with relative density of above 96%. | 5,283.6 | 2021-02-04T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Quijote-PNG: The Information Content of the Halo Mass Function
We study signatures of primordial non-Gaussianity (PNG) in the redshift-space halo field on nonlinear scales using a combination of three summary statistics, namely, the halo mass function (HMF), power spectrum, and bispectrum. The choice of adding the HMF to our previous joint analysis of the power spectrum and bispectrum is driven by a preliminary field-level analysis, in which we train graph neural networks on halo catalogs to infer the PNG f NL parameter. The covariance matrix and the responses of our summaries to changes in model parameters are extracted from a suite of halo catalogs constructed from the Quijote-png N-body simulations. We consider the three main types of PNG: local, equilateral, and orthogonal. Adding the HMF to our previous joint analysis of the power spectrum and bispectrum produces two main effects. First, it reduces the equilateral f NL predicted errors by roughly a factor of 2 while also producing notable, although smaller, improvements for orthogonal PNG. Second, it helps break the degeneracy between the local PNG amplitude, fNLlocal , and assembly bias, b ϕ , without relying on any external prior assumption. Our final forecasts for the PNG parameters are ΔfNLlocal=40 , ΔfNLequil=200 , ΔfNLortho=85 , on a cubic volume of 1Gpc/h3 , with a halo number density of n¯∼5.1×10−5h3Mpc−3 , at z = 1, and considering scales up to kmax=0.5hMpc−1 .
INTRODUCTION
The presence of a certain degree of non-Gaussianity (NG) in the primordial cosmological perturbation field is a general prediction of both inflationary and other early Universe scenarios.In addition, both the level of the predicted NG signal and the shape of the expected NG signatures are significantly model dependent.This makes primordial non-Gaussianity (PNG) a powerful tool to constrain inflation, or alternative primordial models, and to provide clues about physics at very high energy scales.
From an observational point of view, the challenging aspect of any PNG analysis is that the expected NG signatures are very small and the optimal statistic that maximizes their signal-to-noise ratio is unknown from low-redshift observables.Indeed, to date there has been no experimental detection of a PNG signal, although significant constraints have been placed using Cosmic Microwave Background (CMB) data; the CMB is an ideal observable for PNG studies, since it formed at early times, when cosmological perturbations where still in the linear regime, hence preserving the statistical features of the primordial fluctuation field.The most precise results currently come from the analysis of Planck CMB data, which produced an upper bound on the level of PNG at roughly less than 0.1% than the amplitude of the Gaussian component of the field (Akrami et al. 2020).
The open question is whether and how we can obtain more stringent PNG constraints-or achieve a detection-with future cosmological observations.In this respect, it is known that, after Planck, CMB data have nearly saturated its PNG constraining power, with possible improvements of, at most, a factor ∼ 2 for relevant parameters in a majority of scenarios (Finelli et al. 2018;Abazajian et al. 2019).It is therefore necessary to explore different observables.Galaxy clustering is a natural candidate for two main reasons.First of all, in the limit of weak PNG, the bispectrum (i.e., the 3-point function of the Fourier/harmonic modes) of primordial cosmological perturbations contains most of the non-Gaussian information and the three-dimensional galaxy density field contains more bispectrum modes for NG analysis than the two-dimensional CMB map.Furthermore, some models-notably, those producing a "local type" bispectrum, where the signal peaks on squeezed Fourier mode triangles-generate a characteristic scale dependent signature in the galaxy power spectrum on very large scales (Dalal et al. 2008;Matarrese & Verde 2008;Slosar et al. 2008;McDonald 2008;Giannantonio & Porciani 2010;Desjacques & Seljak 2010a), which can be used to constrain NG.
In both cases there are however some important complications to consider.As far as bispectrum analysis is concerned, the big caveat is that the additional modes in the Large Scale Structure (LSS) bispectrum are in the non-linear regime.Hence, they present a "latetime" component generated by the non-linear gravitational evolution of structures, which is hard to disentangle and much larger than the primordial one.Of course, this late-time 3-point signal is interesting in itself since it carries a lot of information about cosmological parameters and structure evolution (Hahn et al. 2020;Hahn & Villaescusa-Navarro 2021); however, as long as we are focused on PNG, it is a massive source of contamination, with an amplitude ∼ 1000 times larger than the primordial signal of interest.The scale-dependent power spectrum signature on large scales clearly does not present this problem and was considered for a long time a cleaner LSS probe of PNG, although limited to a subset of all possible PNG scenarios.However, a significant issue has been recently re-pointed out also in this area (Reid et al. 2010;Barreira 2020Barreira , 2022)), namely the degeneracy produced by the breaking of the universality relation that was generally used to link the NG galaxy bias parameter b φ to the linear bias parameter b 1 .This is due to halo/galaxy assembly bias effects and, if not addressed in any way, it allows us only to constrain the b φ f NL combination.
A key objective in cosmological PNG studies is thus developing optimal data analysis strategies to overcome, at least partially, the aforementioned issues.As long as the b φ (b 1 ) relation is concerned, an active effort is being put into characterizing it as well as possible via numerical studies of N-body simulations (Barreira 2020(Barreira , 2022;;Lazeyras et al. 2023;Sullivan et al. 2023), in order to produce accurate priors.Another logical line of attack, which we start exploring in this work, is that of going beyond a power spectrum + bispectrum analysis and include extra summary statistics, which could help disentangle the PNG signal from late-time evolution effects.The open question, with no straightforward answer, is of course, which summary statistics are best suited to this purpose?In this paper we explore the halo mass function (HMF) as an interesting candidate.This choice was not casual but was driven by training graph neural networks to perform field-level likelihood-free inference on halo catalogues from Quijote-png simulations.The analysis of the outcome of those calculations led us to the conclusion that the model was extracting information from the abundance of halos, as we explain in section 3.1.Therefore, the halo mass function can be seen as a machine learning-driven statistic that stands ahead of others.
Furthermore, our choice is also justified at a theoretical level, since the HMF has been known for a long time to be sensitive to non-Gaussian initial conditionswhich are able to skew its distribution by changing the abundance of massive halos-and it was proposed as an interesting complementary PNG probe to the bispectrum in a number of papers (Matarrese et al. 2000;Sefusatti et al. 2007;Grossi et al. 2007;Pillepich et al. 2010;Desjacques et al. 2009;Grossi et al. 2009;Desjacques & Seljak 2010b;LoVerde & Smith 2011;Palma et al. 2020).On top of this, a major advantage of the HMF is that it directly depends on the PNG amplitude parameter f NL .Therefore, it does not exhibit the b φf NL degeneracy that affects the scale-dependent power spectrum signature.
This work belongs to the Quijote-png series (Coulton et al. 2023a;Jung et al. 2022a;Coulton et al. 2023b;Jung et al. 2022b), where we aim to build a simulationbased pipeline to optimally extract NG information, pushing our analysis to smaller, non-linear scales.This kind of approach is complementary to a perturbation theory-based, likelihood analysis of power spectrum and bispectrum (Moradinezhad Dizgah et al. 2021;Cabass et al. 2022a,b;D'Amico et al. 2022).See also Giri et al. (2023), for an alternative simulation-based approach, which uses large scale modulation of small scale power.
The paper is structured as follows: in section 2 we briefly describe the simulation dataset used in our analysis; in section 3.1 we describe our preliminary field-level analysis; in section 3.2 we recall and summarize the main methodological aspects of our data analysis pipeline to extract relevant summary statistics and compute the corresponding Fisher matrix; section 3.3 is devoted to a specific discussion of the HMF-the main new ingredient with respect to our previous analyses-and of how we extract it from simulations; our numerical Fisher forecasts are described in section 4, where we also discuss the improvements coming from complementing the initial power spectrum + bispectrum analysis with HMF estimates; finally, we draw our conclusions in section 5.
SIMULATIONS
In this work, we use the publicly available halo catalogues derived from the Quijote suite of N-body simulations (Villaescusa-Navarro et al. 2020).1These simulations have been produced using the codes 2LPTIC (Crocce et al. 2006) and 2LPTPNG (Scoccimarro et al. 2012;Coulton et al. 2023a) 2 to generate initial conditions at z = 127, Gadget-III (Springel 2005) to follow their evolution up to z = 0 and the Friends-of-friends algorithm to identify the halos in each simulation (Davis et al. 1985).
We report the cosmological parameters of these simulations in table 1.As described in section 3.2, we use 15000 simulations at the fiducial cosmology to evaluate covariance matrices, and paired sets of 500 catalogues where one parameter is displaced by a small step from its fiducial value to compute derivatives with respect to all parameters considered in the analyses.As in Coulton et al. (2023b); Jung et al. (2022b), we focus on the following cosmological parameters {σ 8 , Ω m , n s , h}3 and PNG amplitudes {f local NL , f equil NL , f ortho NL }, including a simplified bias parameter M min (the minimum mass of halos included in the analysis).To ensure that the initial condition generation method has not generated unphysical higher-order N-point functions, which could impact the results presented here, we performed further validation of the initial conditions by examining the primordial trispectrum.As is discussed in appendix A, we find no evidence of large, unphysical trispectra in the initial conditions.
We focus our analyses at redshift z = 1, for which all power spectra and (modal) bispectra have been computed in Jung et al. (2022b).Results at lower redshifts, z = 0.5 and z = 0, are also shown in appendix B.
Field-level analysis
As we discussed in the introduction, the problem of finding an optimal summary statistic that minimizes the error bars on a given cosmological or PNG parameter is unsolved.An alternative to using summary statistics is to perform field-level analysis.The goal with this kind of analysis is to maximize the amount of information that can be extracted without relying on summary statistics.While there are many types of methods to perform such analysis, in our case we made use of graph neural networks (GNNs) (Battaglia et al. 2018).The advantages of GNNs over other methods are that they 1) do not impose a cut on scales; 2) symmetries (e.g.rotational and translational invariance) can be easily implemented; and 3) can be more interpretable than other methods.Because of this, we decided to train GNNs to perform field-level likelihood-free inference.
As a starting point, we run 1,000 simulations; each containing 512 3 particles in a periodic box of size 1 h −1 Gpc.Each of those simulations has a different initial random seed but also a different value of f local NL in the range −300, +300.The value of the cosmological parameters was the same in all simulations.We then trained a GNN to perform field-level likelihoodfree inference on the value of f local NL .The architecture and training procedure are the same as those outlined in de Santi et al. (2023); Shao et al. (2022); Villanueva-Domingo & Villaescusa-Navarro (2022).
From this exercise, we found that our model was able to infer the value of f local NL with an error of σ(f local NL ) ∼ 35, at z = 0.In an attempt to understand the behavior of the network, we trained a deep set model (Zaheer et al. 2017) where the only information we made use of the halos was their masses, not their spatial positions.By training such a model, we found that the performance of this model was almost identical to the one of the GNNs.We thus concluded that the network was likely not using the clustering of the halos to perform the inference.Therefore, the network should be using the abundance of halos to infer f local NL .To verify this, we trained a simple model consisting of fully connected layers on the halo mass function of the halo catalogues from the simulations.We found that this model performed almost as well as the GNN.From this exercise, we reached the conclusion that the halo mass function is a summary statistic that contains lots of information, likely more than clustering-based statistics as the GNN did not use those to perform the inference.
We emphasize that we trained the GNN using halo catalogues from simulations that only vary f local NL .Therefore, our results did not account for degeneracies with cosmological parameters that could degrade the constraints, as we shall see below.
This motivated a further analysis-illustrated in the following sections-in which we explicitly extract the power spectrum, bispectrum and HMF from the Quijote dataset, as well as their covariance and response to variations in both cosmological and PNG parameters, in order to perform a full Fisher matrix forecast on nonlinear scales.
Fisher information
In this section, we recall the main ingredients of our Fisher analysis pipeline, which was previously used in Jung et al. (2022b).
The Fisher information matrix, defined as allows us to estimate the variance, σ 2 (θ i ) = (F −1 ) ii , of the optimal unbiased estimator of a given summary statistic s with covariance C assuming the statistic is Gaussian distributed,4 and neglecting the dependence of C itself on parameters (Carron 2013).
In this work, both the covariance and derivatives are computed from the simulations described in section 2. The covariance matrix is evaluated using where n r is the number of realizations at fiducial cosmology (15000 here).Then, to obtain an unbiased estimate of the precision matrix, we apply the Hartlap correction factor (Hartlap et al. 2007) where n s is the length of the summary statistic vector s (note however that this correction is very small here as n s ∼ 10 2 while n r = 15000).The derivatives are calculated using finite difference: where we use the sets of 500 simulations where one parameter θ i is displaced by ±δθ i with respect to its fiducial value.However, it was noticed in Coulton et al. (2023b); Jung et al. (2022b) that this number of realizations was not sufficient to obtain fully converged derivatives of the halo power spectrum and bispectrum, leading to spuriously low predictions when analyzing jointly cosmological parameters and PNG amplitudes.To overcome this issue, a conservative approach to Fisher matrix computations was developed in Coulton & Wandelt (2023); Coulton et al. (2023b), which is based on computing the Fisher matrix from maximally compressed statistics instead of working with the summary statistics directly.
As shown in Heavens et al. (2000); Alsing & Wandelt (2018), the compressed quantity defined by si = conserves all the statistical information about the parameter θ i contained in the data vector s, if s follows a Gaussian likelihood (hence, the same assumption as for the Fisher matrix in eq. 1).This compression uses the same ingredients as for the Fisher matrix computation (covariance and derivatives of s), with the addition of the mean s that is trivial to evaluate from the simulations at fiducial cosmology.Repeating the process for all parameters of interest in θ, one can then compute the Fisher matrix of the compressed statistics s by substituting it to s in eq. ( 1).In practice, one has to separate the initial dataset into two subsets.The first is used to perform the compression (i.e.compute the derivatives in eq. 5) and the second is compressed (i.e.s in eq. 5) and is then used to calculate derivatives ∂s/∂θ i and covariance Ĉ of the compressed statistics, to obtain a conservative estimation of the Fisher matrix.In this work, we use 80% and 20% of the simulations for the two steps respectively, which have been verified to give optimal and numerically stable results.We repeat the procedure for many random splits of the data (between the two steps) and average the results to minimize the intrinsic variance of the method.Finally, as shown in Coulton & Wandelt (2023), computing the following combination of the standard (overoptimistic) and compressed (conservative) Fisher matrices where G corresponds to the geometric mean defined by gives unbiased estimates of Fisher error bars with a much smaller number of simulations.An illustration of the different convergences for the three methods is provided in appendix C.
Halo mass function
In addition to the halo power spectrum and bispectrum, we consider the halo mass function (HMF) defined as the number of dark matter halos per unit of comoving volume per unit of logarithmic mass bins.
We measure it in the Quijote simulations using 15 logarithmic bins corresponding to halo masses M between approximately 2.0 × 10 13 and 4.6 × 10 15 M /h (note however that we do not use the first two bins in the analyses presented in section 4).To be exact, we use the same binning as in Bayer et al. (2021), where the counted halos contain each between 30 and 7000 dark matter particles. 5 In figure 1, we show the impact of the three shapes of PNG on the halo mass function.Both the local and equilateral shapes increase the number of massive halos for a positive f NL value (and decrease it for a negative f NL ) and have very degenerate signatures, while for orthogonal PNG it is the opposite.For less massive halos, the effect of PNG changes sign (with the switch occurring for higher masses for orthogonal PNG, which is the only one which appears in the mass range of the plot at z = 1).This effect was already present on early works on the HMF with PNG simulations (see e.g.LoVerde et al. 2008) and is due to the fact that, at fixed Ω m , more massive halos can only appear at the expense of less massive halos and matter in smaller structures.
Constraints from the HMF
As a preliminary exercise, in figure 2, we show the constraining power of the halo mass function on PNG amplitudes f NL of the three shapes, assuming exactly known cosmological parameters.As expected, the HMF is, in this case, extremely sensitive to the presence of PNG, leading to even tighter constraints than the power spectrum and bispectrum.For example, our Fisher forecast on PNG of the local type is σ(f local NL ) ∼ 30 at z = 0, which is in very good agreement with the GNN and deep sets results σ(f local NL ) 35 (see section 3.1), and is more than two times smaller than the equivalent power spectrum + bispectrum forecasted error bar.
However, it is well known that there are large degeneracies between f NL and several cosmological parame-5 The mass of a halo is given by M = N mp where N is the number of dark matter particle it contains and mp is the mass of a dark matter particle.However, mp depends on the cosmological parameter Ωm, which requires to include the correction term − 1
∂ HMF
∂ lnN when computing the derivative ∂ HMF ∂ Ωm (see Bayer et al. 2021, for details).This derivative can also be evaluated by finite difference, between bins of N .at z = 0 and z = 1.For internal comparison, the derivative with respect a given parameter θ is multiplied by the finite difference ∆θ, used for its numerical estimation (see table 1 for details).The vertical scale is logarithmic, except in the range [−10 −8 , 10 −8 ], where it is linear.Note that, in some cases, we have a change of sign in the fNL derivatives, implying an opposite effect of PNG on the abundance of high mass and low mass halos respectively.This is consistent with previous findings in the literature, as pointed out in the main text.The decreasing behaviour of all derivatives at high M is related to the exponential decay of the HMF in this mass range; note that a plot of the logarithmic derivatives would display clear differences between them, also at high M .The numerical results displayed here have all been cross-validated in the simulation-independent, halo-model based analysis that we describe in section 4.4.
When we jointly analyze all parameters, these degeneracies increase the errors significantly (by roughly one order of magnitude at z = 1, and slightly less at z = 0, where the change of sign of f NL derivative-seen in figure 1-helps distinguish it from the response to variations in other cosmological parameters), making them larger than those achievable from the power spectrum and bispectrum combination.
Joint constraints with the power spectrum and bispectrum
While, as expected, the HMF alone does not produce competitive f NL constraints in comparison with the power spectrum and bispectrum, it does remain interesting to investigate whether a combined analysis of all three statistics can produce significant improvements; this is the main point of the present work.Complementing our previous power spectrum + bispectrum analysis with the HMF can in principle benefit us in two ways.First of all, it directly adds extra information about the f NL parameter; also, it could be useful to help break the ).These constraints are derived from the Quijote suite of halo catalogues at z = 0 and z = 1, each having a 1 (Gpc/h) 3 volume.The solid lines (with triangle markers) are computed for each primordial shape independently, assuming a fixed cosmology (at fiducial values), while for the dash-dotted lines we marginalize over the cosmological parameters σ8 and Ωm.This highlights the large degeneracies between the parameters at the level of the halo mass function.For comparison, we also show the corresponding constraints from the power spectrum and bispectrum (horizontal solid lines and dash-dotted lines for the independent and joint cases respectively), as computed previously in Jung et al. (2022b) (Mmin = 3.2 × 10 13 M /h).
If we consider the unmarginalized HMF results, we see that the fNL constraining power is higher at z = 1 for the local and equilateral case, despite the smaller number of halos at this redshift; this is clearly due to a stronger response of the HMF to variations in fNL at higher redshift, consistent with previous findings (see, e.g., figure 4 in LoVerde et al. 2008).
The shape is due to the change of sign in the fNL derivative at different masses, discussed in the main text and in figure 1.
important degeneracy between f NL and the so-called b φ bias parameter.Before presenting our results, let us review and discuss the latter point in more detail.In the presence of local PNG, the halo density fluctuation field δ h (z) can be written to leading order as follows (Dalal et al. 2008 where δ m is the matter density fluctuation, D(z) is the growth factor and b 1 , b φ are bias parameters, defined respectively as the response of δ h to mass density δ m and primordial potential φ.It is evident, in this relation, that the scale-dependent signature depends on both b φ and f NL , and that the two parameters are completely degenerate.This issue can be avoided if one assumes-as it was generally done-the universality relation between b 1 and b φ , that is where δ c is the critical density for collapse.However, it has been recently pointed out in Barreira (2020Barreira ( , 2022) ) that such a relation does not accurately describe the bias of either galaxies, selected by stellar mass, or halos, selected by concentration.Therefore, b φ is not exactly determined anymore and this reintroduces the b φf NL degeneracy problem.To overcome the issue, different studies have been focusing on using simulations to produce accurate priors on b φ (Lazeyras et al. 2023) and on exploiting the multi-tracer technique (Barreira & Krause 2023;Sullivan et al. 2023;Karagiannis et al. 2023).In the present context, the idea is instead to try and break the degeneracy by exploiting the information in the HMF-which selects all halos in each given mass bin-and its direct dependence on f NL and not on b φ .
For clarity, we split the discussion of our results into two parts: initially, we assume universality in the b φ (b 1 ) relation using eq.( 9) and we measure the sheer extra information content in the HMF, in absence of the b φf NL degeneracy 6 ; later on, we instead treat b φ as a free parameter.
Fixing b φ
The outcome of the first part of the analysis (assuming universality in b φ (b 1 ) is illustrated in figure 3 and 4 (see also table 2).We see that, by adding the HMF, error bars on σ 8 and f equil NL roughly become two times smaller than the power spectrum + bispectrum result.Moreover, there is also a noticeable improvement for Ω m and f ortho NL .For f local NL there is instead no clear improvement; this seems due to the fact that in this case the information content is totally dominated by the power spectrum contribution, via scale dependent bias; such contribution is instead smaller for the orthogonal shape and absent for the equilateral case, making the HMF inclusion more important for these scenarios and especially for the equilateral one.
Note that we consider only halos with masses above ∼ 4 × 10 13 M /h in the HMF, which is larger than the fiducial M min = 3.2×10 13 M /h used to study the power spectrum and bispectrum.This means that the HMF is not sensitive at all to small variations of M min around 6 Or, equivalently, we forecast the power spectrum + bispectrum + HMF constraining power on the b φ f NL parameter combination the fiducial value.However, through cross-correlated terms with the other summary statistics, error bars on M min are almost two orders of magnitude smaller 7 .In appendix C, we verify the numerical stability of our results by varying the number of simulations used.
It is interesting to check which halo mass range gives the largest contribution to the observed improvements.To this purpose, we repeat the analysis by sub-dividing halos in a "low mass" (4×10 13 < M < 1.7×10 14 M /h), "intermediate mass" (1.7×10 14 < M < 7.5×10 14 M /h) and "large mass" (M > 7.5 × 10 14 M /h) interval and check the contribution of each group separately.Our results are displayed in figure 5 where we see that the low mass range carries most of the information.This is somewhat counter intuitive, since the effect of f NL is expected to be larger in the tails of the distribution.
7 An important caveat here is that it is important to verify whether this conclusion holds when considering a more complex bias model, which includes higher order bias parameters; this will be done as part of a future work on mock galaxy catalogues, by including numerical derivatives with respect to HOD parameters Accounting for the effects of b φ in our methodology is not straightforward, since b φ cannot be explicitly in-cluded as an input parameter in our simulations and this does not allow us to directly compute the numerical derivative ∂s/∂b φ .To circumvent this issue in a simple way and be able to perform a first test of the ability of the HMF to remove degeneracies between b φ and f local NL , we then decide here to work in the conservative assumption that these two parameters are fully degenerate at the level of the halo power spectrum and bispectrum.In other words, we assume that ∂s/∂b φ ∝ ∂s/∂f local NL , where s is either the power spectrum or the bispectrum.
For the HMF, we instead set the derivative with respect to b φ equal to zero, as it does not depend on this parameter, and compute the f local NL derivative as usual.In figure 6, we show the 1-σ Fisher constraints obtained in this assumption and compare them with the "ideal" (b φ fixed) constraints derived in the previous section, for different k max (see also table 2).
The most important result here is that the inclusion of the HMF makes it possible to break the b φ -f local NL degeneracy to a level which allows us to produce meaningful f local NL constraints without resorting to any prior information on b φ .The final f local NL forecast is however degraded by a factor ∼ 2.5 with respect to the idealized, b φ fixed case that was shown in figure 11.In order to achieve this constraining level it is also crucial to include the information from the power spectrum and bispectrum at non-linear scales (k between 0.2 and 0.5 h Mpc −1 ), as it helps break degeneracies with several cosmological parameters (Ω m in particular).
We corroborate our findings with a simulationindependent analysis based on the halo model (for a review, see Cooray & Sheth 2002;Asgari et al. 2023).Within this framework, we describe the HMF and halo power spectrum following Takada & Spergel (2014), up to k max = 0.2 h Mpc −1 .We use the halo mass function and bias from Tinker et al. ( 2010) using directly M 200,m as the mass definition in the mass integration.In the power spectrum analysis of the simulations the halos are considered point-like, thus we use a Dirac delta as halo profile; thanks to the low k max we use, the 2-halo term dominates the signal and this approximation is appropriate.The effect of PNG-here we only consider the local model-is included as a correction to the HMF parametrized according to LoVerde & Smith (2011), and through the scale dependent halo bias shown in equation ( 8).While aware that the M 200,m mass does not match the FOF mass used in the rest of the paper, we still consider as observable the HMF divided in 10 bins logarithmically spaced between 3.2 × 10 13 M /h and 3.2 × 10 15 M /h.We bin the halo power spectrum in 30 bins logarithmically spaced between 6.3 × 10 −3 h Mpc −1 and 0.2 h Mpc −1 .We choose a relatively low k max to ensure that non-linearities are negligible at this stage.In the HMF-halo power spectrum covariance, for which we again follow Takada & Spergel (2014), only the Gaussian terms are included at present.A more refined analysis, including a wider range of scales and masses, the complete covariance, uncertainties on the parametrization of the HMF and, crucially, the bispectrum will be presented in a future work (Ravenni & et al. in prep.).
The results are shown in figure 7, which highlights a very good agreement between our preliminary theoretical computations and the purely simulation-based forecast.This result confirms that a joint analysis including the HMF is an interesting approach, which deserves further investigation and could be adopted as a complementary strategy to those already implemented in the literature to address the b φ -f local NL degeneracy issue.
Removing degeneracies with Planck priors
As highlighted in section 4.2, removing degeneracies of the HMF using the information from the halo power spectrum and halo bispectrum improves significantly the constraints on PNG of the equilateral type.In this section, we push the idea further by assuming strong, but realistic, priors on cosmological parameters, based on CMB measurements from Planck.
We use the same Gaussian likelihood based on the Planck CMB data (Aghanim et al. 2020) 8 in addition to our HMF, power spectrum and bispectrum measurements to derive 1-σ Fisher constraints (see also table 2).For both f local NL and f equil NL it improves these constraints, while the effect is smaller for f ortho NL .Note also that the effect is the strongest when the HMF is also considered in the analysis, meaning it removes degeneracies between PNG and cosmological parameters at the level of the HMF.Concerning numerical convergence with the number of simulations used to compute the derivatives, including these Planck priors also improves it significantly, where only f equil NL is not optimally constrained for the power spectrum + bispectrum case, and all parameters have converged when we add the HMF information.
CONCLUSION
In this work we presented a combined analysis of the power spectrum, bispectrum, and mass function of dark matter halos in the Quijote-png simulation suite.Our main goal was that of verifying whether adding the HMF to our previous joint power spectrum and bispectrum analyses (Coulton et al. 2023a;Jung et al. 2022a;Coulton et al. 2023b;Jung et al. 2022b) could lead to improved constraints on primordial non-Gaussianity.The main underlying reason behind this analysis is that the HMF turned out to be the statistics used by a sophisticated graph neural network when carrying out a preliminary field-level likelihood-free inference calculation.Furthermore, the HMF tail has been known for a long time to be strongly sensitive to PNG.Finally, the HMF not only carries complementary information to the power spectrum and bispectrum, but also does not suffer from the b φ -f local NL , assembly bias-PNG degeneracy that has been recently pointed out in Barreira (2020Barreira ( , 2022) ) as an important issue in the analysis of local PNG.
Our results show that the HMF can indeed play a significant role in tightening the expected PNG bounds and breaking parameter degeneracies, when its contribution is added to those of the power spectrum and bispectrum.In the first part of our analysis we remove a priori the b φ -f local NL degeneracy by assuming universality in the b φ (b 1 ) relation, i.e, we set b φ = 2δ c (b 1 −1).In this case, we see that the HMF is able to improve equilateral f NL constraints by roughly a factor 2 and orthogonal f NL constraints by 15%.Constraints on PNG of the local type are instead unchanged, since in this idealized scenario the local PNG information is dominated by the large scale power spectrum modes, via scale dependent bias.
In the second part of the analysis, we treat instead b φ as a free parameter and assume that the responses of the halo power spectrum and bispectrum to changes in b φ and f local NL are identical, that is, we assume that these two parameters are fully degenerate in a joint analysis of power spectrum and bispectrum.Starting with this setup, we then see that the additional inclusion of the HMF is able to break the b φ -f local NL degeneracy at a significant level, without the need to rely on any prior on b φ or any other external information.More precisely, our final f local NL constraints after marginalizing over b φ and other standard cosmological parameters are now degraded by a factor ∼ 2.5, compared to the ideal case in which b φ is fixed by the universality relation.We confirmed these results with a semi-analytical, halo model based evaluation of the Fisher matrix, in which we restrict ourselves to the power spectrum and HMF, after verifying that for local PNG these two observables give the dominant contributions to the final sensitivity.We note that to achieve the claimed level of precision on f local NL , it is important to include non-linear scales in the analysis, up to k max = 0.5 h Mpc −1 since they help break additional important degeneracies that affect the HMF constraining power.We also stress that Quijote-png simulations have a cosmological volume of 1 (h Gpc) −3 , making it not straightforward to generalize our forecasts to, e.g., a Euclid-like or other coming survey settings.For the same reason, a direct comparison with other forecastssuch as those based on the multi-tracer methodology and placing suitable priors on b φ -are not at the moment easy to make.In a forthcoming publication, Ravenni & et al. (in prep.), we will produce more detailed semianalytical predictions for future surveys, based on the halo model.
The results presented here have to be considered as preliminary also as they rely on a simplified bias model for our tracers and they do not account for systematic effects in the determination of the HMF from actual observations.Indeed, the dark matter mass of a halo is a quantity notoriously difficult to measure observationally, especially for high-redshift objects.Halos are complex and dynamic structures, which are almost exclusively probed by the signal broadcasted by the baryons they host.(Dark) Mass measurements tend to require sophisticated and labor-intensive observations, which is unfeasible for a large number of objects, as needed for the HMF.Moreover, the sample completeness (for the host halo, not the tracers!) need to be known exquisitely well, which may constitute a formidable challenge.Among the most promising approaches are the Sunyaev Zeldovich effect-selected clusters (signal at mm wavelengths) (Mroczkowski et al. 2019), X-ray clusters (Pratt et al. 2019) and (optical) gravitational lensing mass determination (e.g.Murray et al. 2022).For example, cluster catalogs will increase drastically with a suite of forthcoming experiments; eROSITA (Predehl et al. 2021), Simons Observatory (Ade et al. 2019), Euclid (Laureijs et al. 2011), Roman (Akeson et al. 2019) and Rubin (Ivezić et al. 2019).Cluster masses will not be measured directly but inferred through proxies; these proxies, however, will be provided as a product of these surveys, and are expected to be or be made robust and reliable.An important ingredient for any HMF analysis would be to quantify robustly the probability distribution of the proxies as a function of the true halo mass.This can then simply be folded in the error budget and the uncertainty propagated through to the inferred parameters.
The results shown in this paper clearly show that a joint analysis of the HMF, power spectrum and bispectrum of LSS tracers is a promising approach to constrain PNG, hence providing another motivation for further investigation in this direction and for addressing the aforementioned observational issues. .The significance of the detection of the trispectrum in the initial conditions for the three types of primordial non-Gaussianity.This is computed using 200 simulations of each type of primordial non-Gaussianity as τ NL (Kogo & Komatsu 2006).In many inflationary models, τ NL is generated with local non-Gaussianity and thus, the trispectrum seen here is physical.
These trispectra measurements suggest that unphysical higher order N-point functions are not significant in our simulations.
B. ANALYSES AT OTHER REDSHIFTS
We have performed a similar analysis using the Quijote snapshots at z = 0.5 and 0 to verify that our conclusions hold at other lower redshifts.As can be seen in figure 10, this is indeed the case.For all parameters, the relative improvements due to including the halo mass function in the Fisher analysis are of the same order (note however that the difference between the halo power spectrum and bispectrum results is more pronounced at lower redshifts).
C. CONVERGENCE OF NUMERICAL DERIVATIVES
In figure 11, we study the impact of varying the number of simulations used to compute numerical derivatives on the 1-σ Fisher constraints, both with and without including the HMF in the analyses.This shows that the parameters for which the improvement due to the HMF is the largest (i.e.σ 8 and f equil NL ) have also a better numerical convergence with the number of simulations (smaller difference between standard and conservative Fisher methods).
Figure 1 .
Figure 1.The halo mass function derivatives with respect to the parameters σ8, Ωm, f local NL , f equil NL , f ortho NL
Figure 2 .
Figure2.The 1-σ Fisher error bars on fNL (local, equilateral and orthogonal) from the halo mass function, as a function of the maximum mass Mmax of halos considered (Mmin ∼ 4.1 × 10 13 M /h).These constraints are derived from the Quijote suite of halo catalogues at z = 0 and z = 1, each having a 1 (Gpc/h) 3 volume.The solid lines (with triangle markers) are computed for each primordial shape independently, assuming a fixed cosmology (at fiducial values), while for the dash-dotted lines we marginalize over the cosmological parameters σ8 and Ωm.This highlights the large degeneracies between the parameters at the level of the halo mass function.For comparison, we also show the corresponding constraints from the power spectrum and bispectrum (horizontal solid lines and dash-dotted lines for the independent and joint cases respectively), as computed previously inJung et al. (2022b) (Mmin = 3.2 × 10 13 M /h).If we consider the unmarginalized HMF results, we see that the fNL constraining power is higher at z = 1 for the local and equilateral case, despite the smaller number of halos at this redshift; this is clearly due to a stronger response of the HMF to variations in fNL at higher redshift, consistent with previous findings (see, e.g., figure4inLoVerde et al. 2008).The shape is due to the change of sign in the fNL derivative at different masses, discussed in the main text and in figure1.
Figure 3 .
Figure 3. Ratio of 1-σ Fisher error bars on cosmological parameters and PNG amplitudes from the halo mass function, halo power spectrum and halo bispectrum at z = 1, assuming b φ fixed.This illustrates how including the halo mass function tightens the constraints on several parameters (σ8 and f equil NL in particular).Note that the values of these error bars are given in table 2 and figure 11.
Figure 4 .
Figure 4.The impact of the HMF on the 1-σ constraints on cosmological parameters and PNG amplitudes from the halo power spectrum and bispectrum at z = 1, assuming b φ fixed.However, this is balanced by the fact that, within the analyzed mass range and considering our mass binning choice, we have significantly more halos in the lowest mass interval (∼ 95%, ∼ 5% and 0.01% of the halos are in the low, intermediate and large mass bins respectively).4.4.Breaking the b φ -f local NL degeneracy with the HMF
Figure 5 .
Figure 5.The impact of different mass bins of the HMF on the 1-σ constraints on cosmological parameters and PNG amplitudes from the halo power spectrum and bispectrum at z = 1, assuming b φ fixed.Note that we restrict only the mass range for the HMF.
Figure 6 .
Figure 6.The Halo Mass Function can break the b φ -f local NL degeneracy in the power spectrum and bispectrum.As in figure 3, we show normalized 1-σ Fisher error bars derived from the HMF, halo power spectrum and bispectrum at z = 1.Here, we assumed that f local NL and b φ are fully degenerate at the power spectrum and bispectrum level, while the HMF does not depend on b φ .
Figure 7 .
Figure 7. Similar to figure 6, considering only {σ8, f localNL } and bias parameters.The 1-σ Fisher constraints include the information contained in the HMF and the power spectrum information up to kmax = 0.2 h Mpc −1 computed using the halo model on the left, and from simulations on the right.Note that both methods give σ(f local NL ) ∼ 50 and similar σ(σ8) (less than 20% difference).
Figure 8 .
Figure 8. Similar to figure 3, where we include Planck priors on the cosmological parameters {σ8, Ωm, ns, h} and we assume b φ fixed.
Figure9.The significance of the detection of the trispectrum in the initial conditions for the three types of primordial non-Gaussianity.This is computed using 200 simulations of each type of primordial non-Gaussianity
Table 1 .
The parameters of the Quijote and Quijote-png halo catalogues used in this work.
Table 2 .
The 1-σ constraints on cosmological parameters and PNG amplitudes at z = 1 obtained by combining the information of the halo power spectrum, bispectrum and mass function, each measured from the Quijote and Quijote-png simulations. | 10,166.8 | 2023-05-17T00:00:00.000 | [
"Physics"
] |
Overactive autophagy is a pathological mechanism underlying premature suture ossification in nonsyndromic craniosynostosis
Nonsyndromic craniosynostosis (NSC) is the most common craniosynostosis with the primary defect being one or more fused sutures. In contrast to syndromic craniosynostosis, the etiopathogenesis of NSC is largely unknown. Here we show that autophagy, a major catabolic process required for the maintenance of bone homeostasis and bone growth, is a pathological change associated with NSC. Using calvarial suture mesenchymal cells (SMCs) isolated from the fused and unfused sutures of NSC patients, we demonstrate that during SMC differentiation, the level of the autophagosomal marker LC3-II increases as osteogenic differentiation progresses, particularly at differentiation day 7, a stage concurrent with mineralization. In fused SMCs, autophagic induction was more robust than that in unfused SMCs, which consequently led to enhanced mineralized nodule formation. Perturbation of autophagy with rapamycin or wortmannin promoted or inhibited the ossification of SMCs, respectively. Our findings suggest that autophagy is essential for the osteogenic differentiation of SMCs and that overactive autophagy is a molecular abnormality underlying premature calvarial ossification in NSC.
In addition, it is required for the osteogenic differentiation of human mesenchymal stem cells/osteoblasts 14,24 . Other than its role in bone homeostasis, autophagy in chondrocytes also mediates the pro-growth effect of FGF signaling, an important regulatory pathway related to craniosynostosis 25 .
However, little is known regarding the role of autophagy in calvarial ossification and cranial bone diseases. Autophagy has been described in mandible-derived bone mesenchymal/stromal stem cells 26 , which are involved in intramembranous ossification similar to that observed in calvaria-derived bone mesenchymal stem cells. Interestingly, mandible-derived bone mesenchymal stem cells/multipotent stromal cells exhibit a higher level of autophagic activity and anti-aging capacities than those of tibia-derived bone mesenchymal stem cells 27 , which are involved in the endochondrial ossification process. This suggests that the intramembranous ossification process might be more dependent on autophagy. Therefore, it is likely that overactive autophagy is a pathological mechanism of premature suture ossification in NSC. In the current study, we provide the first evidence suggesting a direct role for autophagy in the calvarial ossification process, using calvarial SMCs isolated from the fused and unfused sutures of NSC patients. Results indicate that overactive autophagy is a likely mechanism underlying the pathogenesis of craniosynostosis.
Materials and Methods
Patients and specimens. All calvarial tissue fragments were collected from human donors undergoing cranial surgery for nonsyndromic monosutural craniosynostosis at the Shanghai Children's Medical Center. The characteristics of patients participating in this study and the experiments for which samples were used are shown in Table 1. Patients were 7 to 14 months of age (mean 11.2 months). Only nonsyndromic monosutural patients were chosen for this study. A matched pair of suture tissues, consisting of one prematurely fused suture and one unfused suture, was taken from each patient. Written informed consent was obtained from all participants' legal guardians. Ethical clearance was obtained from the Ethics and Research Committees of Shanghai Children's Medical Center in China, and all experiments were performed in accordance with relevant guidelines and regulations.
SMCs isolation and culture. The methods for SMCs isolation and culture are described in previous reports 11 . In brief, the suture complex, consisting of the suture mesenchyme plus 3 mm of bone on either side of unfused sutures or the fused bony ridge plus 3 mm of bone on either side of fused sutures, was dissected from all specimens, and the overlying pericranium was removed. Calvarial specimens were then washed extensively in phosphate-buffered saline (PBS) supplemented with 1% penicillin/streptomycin (Sigma-Aldrich, St. Louis, MO, USA), cleaned of any soft tissue residues, minced into tiny pieces and blocks, and placed into 100-mm-diameter plates. When culturing cranial SMCs, tissue pieces and blocks were maintained in standard culture medium (Dulbecco's modified Eagle medium) supplemented with 10% fetal calf serum, L-glutamine (1 g/L; Life Technologies, Grand Island, NY, USA), and 1% penicillin/streptomycin, and were allowed to attach to the culture flasks. Cells were incubated as a monolayer in a humidified atmosphere containing 5% CO 2 at 37 °C. When cells reached 60-80% confluence, they were subcultivated for multiple passages (spending <15 days in primary culture) and used in experiments at confluence. The culture medium was replaced every 3 days.
To test the osteogenic potential of SMCs and the effect of rapamycin and wortmannin treatments, cells were seeded in 24-well plates at a density of 50,000 cells/well in 600 μL of medium. After reaching 70% confluence, cells were treated with new standard culture medium or with rapamycin or wortmannin for 24 h. Then, culture medium was replaced with differentiation medium. Mineralization was analyzed after culturing in differentiation medium for 14 days. Culture medium was changed every 3 days. After washing with PBS three times, cells were fixed in 95% ethanol for 30 min and then stained with 1% Alizarin Red S2 dye (9436-25 G Amresco, Cleveland, OH, USA) in 0.05 M tris-HCl (pH 8.0). Cells were then incubated at 37 °C for 30 min and washed with deionized water, and representative photographs were taken. The formation of mineralized nodules, defined as the percentage of mineralization area, was quantified using Image J densitometry. To minimize the variation between individuals, we normalized the mineralization area by dividing the mineralization area percentage of each group by the mineralization area percentage from the corresponding untreated and unfused sample to get the relative mineralization ratio. Three independent experiments were repeated for each condition.
Antigen identification by flow cytometry. Cell surface antigen phenotyping was performed on human SMCs. Cells from prematurely fused and unfused sutures were cultured for two passages and harvested using 0.25% trypsin. After washing in PBS, cells were incubated for 30 min at room temperature in the dark using the Human multipotent mesenchymal stromal cell (MSC) Analysis Kit (BD Pharmingen, San Diego, CA, USA) according to the manufacturer's guidelines. The kit contained the following: mouse anti-human CD90 FITC, CD44 PE, CD105 PerCP-Cy5.5, CD73 APC, κ PE and PE hMSC Negative Cocktail (CD34 PE, CD11b PE, CD19 PE, CD45 PE, and HLA-DR PE), and PE hMSC Negative Isotype Control Cocktail (mIgG1, κ FITC, mIgG1, κ PerCP-Cy5.5, mIgG1 κ APC mIgG1, κ PE, and mIgG2a). Cell status was determined using a FACS flow cytometer (BECTON DICKINSON, Newark, NJ, USA) and analyzed using FlowJo VX software.
RNA extraction, reverse transcription, and PCR. RNA was extracted using TRIZOL Reagent (Life, CA) according to the manufacturer's protocol, and then 1 µg purified RNA was reverse transcribed into cDNA using a PrimeScript RT Reagent Kit (Takara, Japan) according to the manufacturer's instructions. Quantitative PCR was performed using Power SYBR Green PCR Master Mix (Applied Biosystems, UK) and the primers are listed in Table 2.
Evaluation of cell viability.
assay kit (Sigma, Steinheim, Germany) was used to assess cell viability as follows. Cells were seeded at a density of 10,000 cells/well in 100 μL of medium in 96-well plates. Cells were then treated with rapamycin or wortmannin for 24 h, or bafilomycin A1 (BafA1) for 3 h. After treatment, MTT solution was added to the culture medium to a final concentration of 500 μg/mL, and the cells were incubated for a further 2 h at 37 °C in the dark. The supernatant was then removed, dimethyl sulfoxide was added to the wells to dissolve the formazan formed during the MTT assay, and the plates were shaken gently at 37 °C for 15 min. The absorbance of the resulting solution was measured at 570 nm using the GloMax-Multi Detection System (Promega, Madison, WI, USA). Rapamycin and wortmannin were purchased from Sigma-Aldrich (St. Louis, MO, USA), and BafA1 was purchased from Cayman Chemical Company (Ann Arbor, MI, USA).
Western blot analysis. Cells were washed twice with cold PBS and then harvested by trypsinization with 0.25% trypsin. For total protein isolation, cells were lysed in lysis buffer (Beyotime, Haimen, China) on ice for 30 min and centrifuged at 13,400 × g for 30 min at 4 °C. Total protein concentration was determined using a bicinchoninic acid protein assay kit (Bio-Rad, Hercules, CA, USA) according to the manufacturer's instructions, and then equal amounts of protein were separated by 10% sodium dodecyl sulfate-polyacrylamide gel electrophoresis and transferred to a nitrocellulose filter membrane. After blocking in tris-buffered saline (pH7.5) containing 0.1% tween 20 (TBST) and 5% nonfat milk for 1 h, membranes were incubated with primary antibodies (1:1000
Statistical analyses.
Results are presented as the mean ± standard deviation (SD). The significance of differences among groups was determined by one-way ANOVA followed by Tukey's post-hoc test. Statistical significance was defined as described in the figure legends.
Mesenchymal cell populations isolated from fused and unfused cranial sutures are identical.
Abnormal osteogenic activity in cranial SMCs is generally considered a common cause of craniosynostosis. Hence, we isolated mesenchymal cells from the fused and unfused sutures of patients with nonsyndromic monosutural craniosynostosis to investigate disease pathogenesis. Flow cytometry was first used to characterize the identity of isolated cell populations. Results showed that greater than 90% of SMCs from both fused and unfused sutures expressed typical human MSC markers including CD90, CD105, and CD73 (Fig. 1A). Expression levels of these markers were similar between fused and unfused SMCs (Fig. 1B). To further characterize these cells, we examined the expression of the osteogenic markers ALP, BSP, and COL1-A1 by qPCR. Indeed, these markers were expressed in isolated SMCs and no significant differences in expression levels were observed between the fused and unfused cranial SMCs, indicating that they have osteogenic capability and exist in a similar osteogenic differentiation state (Fig. 1B). However, the isolated fused and unfused SMCs gradually lost growing capability within 2 months.
Autophagic activity is enhanced in SMCs from the fused suture. Autophagy has been shown to be essential for bone mineralization 28 . Therefore, we hypothesized that hyperactive autophagy might play a role in the premature calvarial ossification that leads to craniosynostosis. To this end, we examined the level of LC3-II protein, a common marker for evaluating autophagic activity, during the osteogenic differentiation of SMCs. Consistent with a previous report using the UMR-106 osteoblastic cell line 28 , LC3-II protein levels were not changed in SMCs at differentiation day 3, but were significantly increased at differentiation day 7 ( Fig. 2A,B). As expected, we noted that LC3-II levels in SMCs from the fused suture were higher than those of SMCs from the unfused suture at differentiation day 7 ( Fig. 2A,B). This suggests that fused SMCs have the propensity for enhanced autophagy during osteogenesis.
To investigate whether increased LC3-II in the fused SMCs was due to abnormal autophagosome production or autophagosomal consumption, we treated the cells with the specific lysosomal proton pump inhibitor BafA1, which can block autophagosome/lysosome fusion. Indeed, inhibition of autophagosome maturation led to a marked increase in LC3-II levels in both fused and unfused SMCs, irrespective of osteogenic differentiation induction. However, this increase was particularly striking in the fused SMCs at differentiation day 7, which was significantly higher than that in unfused SMCs at the same stage of osteogenic differentiation ( Fig. 2A,B). These results indicate that SMCs in the fused suture exhibit enhanced autophagosome production during osteogenic differentiation.
Induction or inhibition of autophagy can enhance or repress the osteogenic differentiation of
SMCs. Having determined that the fused SMCs exhibit enhanced autophagy during osteogenic differentiation, we wondered whether this abnormality is associated with enhanced ossification. After 2 weeks of differentiation, calvarial SMCs were stained with Alizarin Red S2 to reveal bone mineralization. Indeed, the fused SMCs formed more bone nodules than the unfused SMCs (Fig. 3A,B). Moreover, nodules from the fused SMCs stained darker (Fig. 3A), suggesting enhanced mineralization. These data indicate the fused SMCs have augmented osteogenic capability.
To determine if disturbed autophagy can affect osteogenesis in SMCs, we treated the cells with the autophagy inducer rapamycin (5 µM) or the autophagy inhibitor wortmannin (1 µM) for 24 h before transferring them to osteogenic differentiation medium. After 14 days in osteogenic differentiation medium, SMCs was stained with Alizarin Red S2. Indeed, rapamycin treatment significantly enhanced bone nodule formation in both the fused and unfused groups (Fig. 3A,B), whereas wortmannin treatment significantly decreased osteogenic activity in both groups (Fig. 3A,B). These results indicate that autophagy is essential for the osteogenesis of human SMCs. However, we did not note a significant difference in bone nodule formation between the fused and unfused groups with either rapamycin or wortmannin treatment (Fig. 3A,B).
To verify the effect of rapamycin or wortmannin on autophagic activity, we examined LC3-II protein expression in treated SMCs at differentiation day 7. As expected, LC3-II was increased in response to rapamycin in both the fused and unfused groups, whereas wortmannin reduced the levels of this protein in both groups (Fig. 4A,B). Consistent with the effect of rapamycin and wortmannin on ossification outcome, we did not identify a significant difference in LC3-II protein levels between the fused and unfused groups after treatment with rapamycin or wortmannin.
Discussion
NSC is a common inborn heteroplasia. Recently, local tissue-specific differences in the activity of cellular networks have been associated with intramembranous calvarial ossification 11 . FGF signaling, an important regulatory factor related to craniosynostosis, regulates bone growth through autophagy 24 . Thus, we proposed a new idea whether there was a relationship between autophagy and local premature suture ossification. Although mandible-derived bone MSCs exhibit stronger autophagy and anti-aging capacities than tibia-derived bone MSCs 22 , the role of local differences in autophagy in the pathogenesis of premature suture ossification is poorly understood. Here, we confirm that autophagic activity is involved in the development and maintenance of cranial sutures, and reveal that autophagy plays a role in premature suture ossification. Our findings provide evidence of a potentially novel mechanism for NSC development.
Autophagy is a major catabolic process required for the maintenance of tissue homeostasis, particularly under conditions of stress 22 . It has been shown to be involved in various aspects of bone growth and health 29 . Here we show that autophagy is also essential for osteogenesis in human SMCs. As previously reported for the UMR-106 cell line and rodent primary osteoblasts, we observed that LC3-II levels are not changed during the early differentiation stage. A significant increase in LC3-II protein levels was not observed until differentiation day 7, which represents a time point after the initiation of mineralization 28 . This suggests that the induction of autophagy is associated with SMC ossification. Modulation of autophagy using rapamycin or wortmannin indeed enhanced or repressed SMC ossification, respectively. Our findings indicate that the induction of autophagy is also required for mineralization during human SMC differentiation. In addition to fusion of the autophagosome with the lysosome to degrade its content, exocytosis of the autophagic vacuole was previously shown to be an unconventional protein secretion pathway 21 . Studies have shown that mineralization can be initiated with cells 30 . Therefore, it has been proposed that autophagic vacuoles serve as a pathway to secret apatite crystals from osteoblasts 28 . Our work suggests that this mineralization mechanism might also be conserved in human cells.
During osteogenic differentiation, autophagic induction in the fused SMCs is activated to a level higher than that in the unfused SMCs, and consequently, more mineralized nodules were observed in the fused group after 14 days of culture in mineralizing conditions. Our findings indicate that overactive autophagy is a novel pathological mechanism resulting in premature ossification in NSC patients. It is notable that the fused and unfused suture tissues in this study were obtained from the same NSC patient. Hence either somatic mutations or exogenous factor-induced epigenetic changes might be the underlying cause. Our work suggests that mutations or epigenetic changes in autophagy-related genes should be explored to understand NSC etiology.
To verify the role of autophagy in regulating the osteogenic differentiation of SMCs, we used rapamycin and wortmannin to modulate autophagy. Although we noted that activation or inhibition of autophagy could significantly promote or repress mineralization in both types of SMCs, we did not observe a difference between the fused and unfused SMCs after rapamycin or wortmannin treatment. One possibility is that these treatments might function downstream of primary pathological defects, which cancels out the upstream difference. Full-length blots are presented in the Supplementary Fig. 3. Data are expressed as the mean ± SD of three independent experiments. *P < 0.05; **P < 0.01. | 3,789.8 | 2018-04-25T00:00:00.000 | [
"Biology",
"Medicine"
] |
Scalable neutral H2O2 electrosynthesis by platinum diphosphide nanocrystals by regulating oxygen reduction reaction pathways
Despite progress in small scale electrocatalytic production of hydrogen peroxide (H2O2) using a rotating ring-disk electrode, further work is needed to develop a non-toxic, selective, and stable O2-to-H2O2 electrocatalyst for realizing continuous on-site production of neutral hydrogen peroxide. We report ultrasmall and monodisperse colloidal PtP2 nanocrystals that achieve H2O2 production at near zero-overpotential with near unity H2O2 selectivity at 0.27 V vs. RHE. Density functional theory calculations indicate that P promotes hydrogenation of OOH* to H2O2 by weakening the Pt-OOH* bond and suppressing the dissociative OOH* to O* pathway. Atomic layer deposition of Al2O3 prevents NC aggregation and enables application in a polymer electrolyte membrane fuel cell (PEMFC) with a maximum r(H2O2) of 2.26 mmol h−1 cm−2 and a current efficiency of 78.8% even at a high current density of 150 mA cm−2. Catalyst stability enables an accumulated neutral H2O2 concentration in 600 mL of 3.0 wt% (pH = 6.6).
H ydrogen peroxide (H 2 O 2 ) is a valuable chemical for a variety of industrial applications, as well as a potential energy carrier alternative to oil or hydrogen in fuel cells. H 2 O 2 is currently manufactured by a large-scale indirect anthraquinone process and the under-developed direct synthesis from a H 2 and O 2 mixture 1 . The anthraquinone process involves multiple redox reaction steps and requires expensive palladiumbased hydrogenation catalysts. Furthermore, energy-intensive distillation for obtaining high concentration H 2 O 2 is necessary to minimize transportation and storage costs. Direct synthesis via H 2 and O 2 is more straightforward but potentially explosive. Electrochemical H 2 O 2 production through the oxygen reduction reaction (ORR) in an electrolyzer or fuel cell is an attractive and cost-effective route due to its mild operation conditions, on-site production, and tunable concentration 2 . However, it is still a great challenge to develop efficient and stable electrocatalysts that are selective toward the two-electron ORR.
Incorporation of an efficient and stable catalyst into a protonexchange membrane electrolyzer or fuel cell is a promising route to commercialization. Many potential ORR electrocatalysts, mainly including carbon-based materials and noble metal-based materials, have been reported for H 2 O 2 production in alkaline or acidic electrolyte 3 . Carbon-based electrocatalysts typically perform well in alkaline solution but show low intrinsic activity and stability in acidic media 4 . Bimetallic noble metal alloys, such as Au-Pd, Pt-Hg, Pd-Hg, and Au-Pt-Ni, catalyze ORR through two-electron pathways with selectivity as high as 95% [5][6][7] . The goal of secondary metal incorporation is to change the electronic structure of the primary catalytic site and optimize the binding strength of reaction intermediates 8 . An ideal two-electron ORR electrocatalyst should possess a suitable binding strength for OOH* (not too strong or too weak) and suppress the O-O bond breakage in OOH* to O*. However, stability of the bimetallic alloys is a concern, particularly for medicinal or water treatment applications. Elemental leaching hinders the long-term ORR stability and the leached ingredient (particularly toxic Hg) devalues the H 2 O 2 product and increases the separation cost 9,10 . Apart from the metal alloying strategy, incorporation of nonmetal elements such as phosphorus, sulfur, and boron into metals to form multicomponent alloys has been demonstrated to be an attractive and effective way to improve the electrocatalytic activity of metal catalysts [11][12][13][14][15] . Particularly, our previous work found that electronegative phosphorus (P) was able to regulate the binding strength of intermediates in ORR and improve the four-electron ORR activity for cobalt phosphide 16 . Since Pt is the most widely used material for four-electron ORR, it is highly desirable to investigate if P alloying is able to alter the electronic structure of P-rich platinum phosphide and shift the reaction pathway from a four-electron to a two-electron pathway.
Ultrasmall nanoparticle catalysts not only have a high surface to volume ratio which reduces cost for precious metal catalysts by increasing the per mass surface area, but also lead to higher exposure of low-coordinated edge sites for improved electrocatalytic activity 17 . However, small nanoparticle electrocatalysts are prone to aggregation during long-term electrochemical operation, which lowers surface area, reduces available active sites and consequently causes electrocatalytic activity degradation 18 . Encapsulation of nanoparticles in a porous ultrathin shell of a stable metal oxide can largely preserve the catalytic activity while increasing the resistance against aggregation 19 . Atomic layer deposition (ALD), a thin-film deposition technique that allows growth of conformal coating through a self-limiting vapor growth process, has been employed to deposit ultrathin metal oxide layers to overcoat and stabilize nanoparticle catalysts for optimizing both activity and durability [20][21][22] . Therefore, ALD is of interest to prevent aggregation of ultrasmall platinum phosphide nanocrystals and preserve their ORR activity and selectivity during long-term electrocatalysis.
Generally, the ORR activity of an electrocatalyst is initially evaluated by the rotating-ring disk electrode (RRDE) technique, which provides only an upper limit to the activity and selectivity of two-electron ORR due to rapid transportation of H 2 O 2 from disk to ring 2 . In real devices, such as those based on a membrane electrode assembly (MEA) architecture, additional transport factors must be considered. These include the slow diffusion rate of H 2 O 2 from the catalyst and gas diffusion layers to the output stream and the chance for further H 2 O 2 reduction or chemical decomposition 23 . Yamanaka and Wilkinson's groups have reported MEA-based water electrolyzers and fuel cell reactors for production of small amounts of neutral H 2 O 2 by continuously feeding gaseous O 2 into the cathodic chamber [24][25][26][27] . However, the long-term stability for efficient O 2 -to-H 2 O 2 production at high current levels is still a large challenge due to the severe H 2 O 2 accumulation at the interface between ORR catalyst layer and proton-exchange membrane, particularly if there is no solvent flow to remove the concentrated product. To reach a high concentration at a large scale will require incorporation of an efficient two-electron ORR catalyst into a system with sufficient long-term stability in the presence of high H 2 O 2 content to allow for continuous recycling of the H 2 O 2 product to reach medical level concentrations.
Herein, monodisperse colloidal platinum diphosphide nanocrystals (PtP 2 NCs) with an uniform size of 3 nm are directly synthesized by a hot-injection method using platinum(II) 2,4pentanedionate and tris(trimethylsilyl)phosphine. Unlike ORR catalyzed by Pt NCs which follow a conventional four-electron pathway, the ultrasmall PtP 2 NCs proceed through a two-electron pathway with a nearly zero overpotential to initialize the O 2 -to-H 2 O 2 reaction and achieve a maximum selectivity of 98.5% at 0.27 V vs. RHE. DFT calculations reveal that changes in electron density and increased Pt atom separation due to P incorporation leads to a weaker adsorption of the key OOH* intermediate and inhibition of subsequent O-O breakage of OOH* to form the O* intermediate. The ultrasmall PtP 2 NCs are treated by ALD of an alumina overcoat and post-annealing to suppress aggregation and maintain electrocatalytic stability. The resulting catalyst is employed in a PEMFC to achieve a steady neutral H 2 O 2 formation rate of 2.26 mmol h −1 cm −2 and the accumulated H 2 O 2 concentration reaches 3 wt% in 65 h and as high as 1.21 M in 600 mL after continuous cycling for 120 h.
Results
Synthesis and characterization. To synthesize ultrasmall and highly monodisperse platinum phosphide NCs, platinum(II) 2,4pentanedionate and tris(trimethylsilyl)phosphine ((Me 3 Si) 3 P) are employed in a hot-injection synthesis to allow for separate control of the nucleation and growth processes. In a typical preparation, 0.3 mmol of platinum(II) 2,4-pentanedionate (0.118 g) was initially mixed with 8 mL oleylamine (OAm), 0.5 mL oleic acid (OA), and 8 mL octadecene (ODE). Oxygen and impurities were removed by placing the solution under vacuum at 120°C for 1 h. In a nitrogen atmosphere, the solution was then heated to 220°C at a rate of 10°C/min. Meanwhile, the P precursor was prepared by placing 1.2 mL (Me 3 Si) 3 P dissolved in hexane (10 wt%) and 1.0 mL ODE under vacuum to remove the hexane at room temperature. The (Me 3 Si) 3 P solution was quickly injected at 220°C and for 15 min the temperature was maintained. Inductively coupled plasma mass spectroscopy (ICP-MS) gives an atomic ratio of platinum to phosphorus of 0.498 (Supplementary Table 1), and energy-dispersive X-ray spectroscopy (EDS) of platinum phosphide NCs shows a similar Pt:P ratio of 0.509 ( Supplementary Fig. 1), confirming the formation of PtP 2 . The XRD pattern of PtP 2 NCs matches the cubic structure of bulk PtP 2 (ICDD PDF: 01-080-2220) ( Supplementary Fig. 2). The central Pt atoms are surrounded by 6 phosphorus atoms, which are situated at the corners of a slightly distorted octahedron. Similarly, the phosphorus atoms are surrounded by one phosphorus and three platinum neighbors ( Supplementary Fig. 3). The transmission electron microscopy (TEM) image of the assynthesized PtP 2 NCs shows a spherical morphology with average size of 3 ± 0.2 nm (Fig. 1a). A well-resolved lattice fringe with interplane distances of 0.33 nm is observed, corresponding to the (111) crystallographic plane of the cubic PtP 2 (Fig. 1b). The (111) plane, associated with other planes, such as (200), (211), and (222), are shown on the corresponding selected-area electron diffraction (SAED) image (inset of Fig. 1b), indicating good crystallinity of the as-synthesized PtP 2 NCs. The well-defined spherical geometry and high monodispersity of the PtP 2 NCs is clearly observed from the high-angle annular dark-field scanning TEM (HAADF-STEM) image (Fig. 1c). The elemental mapping of the PtP 2 NCs shows that the Pt and P elements are evenly distributed throughout the whole nanocrystal region ( Fig. 1d-f).
X-ray absorption spectroscopy was carried out to reveal the local geometric and electronic structures of PtP 2 and Pt NCs. Figure 1g shows the Pt L 3 -edge X-ray absorption near-edge structure (XANES) spectra of PtP 2 NCs, Pt NCs, and Pt foil. The rising edge of PtP 2 NCs shows a positive shift compared with that of Pt NCs and Pt foil due to the increased valence oxidation state after incorporation of P into Pt. This result can be ascribed to an electron density shift from metallic Pt to local P atoms with high electronegativity. The donor-acceptor nature of electron density distribution in PtP 2 NCs is further confirmed by the X-ray photoelectron spectroscopy (XPS) of Pt 4f ( Supplementary Fig. 5). The binding energy of Pt 4f 7/2 for PtP 2 NCs is positively shifted (0.9 eV) from that of Pt 4f 7/2 for Pt NCs. This shift is larger than that of conventional metal alloying, suggesting that the stronger electron delocalization in PtP 2 NCs may have greater influence on the intrinsic electronic properties and reaction intermediates adsorption/desorption behavior 28 . The intensity of the Pt L 3 white line is a qualitative indicator of electron vacancies in the 5d orbitals of Pt atoms. The white line intensity for PtP 2 NCs is higher than that for Pt NCs and Pt foil, which is attributed to an electron density shift from Pt to P which creates electron vacancies in Pt and increases probability for electron transition from 2p to the unoccupied 5d orbital 29 . The Fourier transforms of the k 3 -weighted extended Pt L 3 -edge X-ray absorption fine structure (EXAFS) spectra were shown in Fig. 1h. The EXAFS fitting results are summarized in Supplementary Fig. 6 and (Fig. 2a). A remarkable ring current in the potential range of 0.1-0.708 V vs. RHE is observed on PtP 2 NCs, compared to a negligible current measured for the Pt NCs control. The slightly higher onset potential of the PtP 2 NCs than the thermodynamic limit of 0.70 V vs. RHE could potentially be ascribed to a Nernstrelated potential shift. The PtP 2 NCs achieve a maximum H 2 O 2 selectivity of 98.5% at 0.27 V vs. RHE, and the corresponding electron transfer number (n) is 2.03 ( Supplementary Fig. 8), while the Pt NCs follow a typical four-electron pathway during ORR process. This indicates that phosphorus incorporation can regulate the electronic structure of surface Pt active sites and therefore alter the ORR pathway. Figure 2b summarizes the mass activity of different electrocatalysts for O 2 -to-H 2 O 2 conversion, and further details of these calculations are available in Supplementary Table 3. The remarkable mass activity and low overpotential of PtP 2 is superior to most reported electrocatalysts. While it is inferior to the state-of-the-art Pt-Hg and Pd-Hg alloys, replacement of Hg with minimal loss in efficiency is promising since the potential for Hg to leach directly into a medicinal product is a considerable barrier for practical application.
To directly compare stability, highly monodispersed Pt-Hg nanocrystals were also synthesized ( Supplementary Fig. 9). The PtP 2 NCs show very similar mass activity to the-state-of-art Pt-Hg NCs ( Supplementary Fig. 10), but the leaching of heavy metals is greatly reduced as determined by ICP-MS. The concentration of Hg leached from Pt-Hg NCs is 74.6 × 10 3 ppb after ORR for 6 h in 0.1 M HClO 4 , which is three orders of magnitude higher than the Pt and P leached from PtP 2 NCs (Supplementary Table 4). This severe leaching phenomenon limits the wide application of H 2 O 2 produced by the Pt-Hg nanoparticle electrocatalyst, particularly for medicine or water purification. In general, the chemical stability of bimetallic Pt-Hg alloy catalysts is highly dependent on their synthesis routes and surface properties and further studies need to be done to systematically establish Hg leaching discrepancy between the discussed Pt-Hg NCs and the reported electrodeposited Pt-Hg nanoparticles 6 .
In situ attenuated total reflection infrared spectroscopy (ATR-IR) was carried out to investigate adsorbed oxygen intermediates on the supported PtP 2 catalyst during ORR in O 2 -saturated 0.1 M HClO 4 (Fig. 2c). As detailed below, the in situ observation of OOH ad and HOOH ad during ORR confirms the associative two-electron pathway for PtP 2 . In accordance with previous literature, the bands at 1435 and 1330 cm −1 are assigned to the functional groups of the carbon support, and the bands at 1126 and 1052 cm −1 are ascribed to the ClO 4 − species 30 . The absorption band at 1488 cm −1 , present at all applied potentials, is assigned to the O-O stretching mode of adsorbed molecular oxygen (O 2,ad ). This assignment agrees with previous report that the band of adsorbed O 2 is observed around 1468 cm −1 for Pt/C 31 . The band intensity shows a continuous decrease with increase of overpotential due to O 2 consumption as well as substitution by the newly formed oxygen species ( Supplementary Fig. 11a). This band disappears in N 2saturated solution and shifts to 1406 cm −1 in the 18 O 2 isotope spectrum ( Supplementary Fig. 12). The band at 1264 cm −1 can be assigned to the O-O stretching mode of adsorbed superoxide (OOH ad ), which is consistent with that reported for the Au electrode 32 . It appears at 0.7 V vs. RHE and increases with increasingly negative potential ( Supplementary Fig. 11b), which is consistent with the trend of the H 2 O 2 current in the linear sweep voltammograms of PtP 2 NCs. The OOH ad band shows a significant shift to 1193 cm −1 in 18 O 2 ( Supplementary Fig. 10) , while remaining the same in the deuterated medium (Supplementary Fig. 13). As for Pt NCs, the OOH ad band is initially observed at 0.9 V vs. RHE, consistent with its onset potential of four-electron ORR. Lastly, the band at 1396 cm −1 is attributed to the OOH bending mode of adsorbed hydroperoxide (HOOH ad ) 33 . A slight shift is observed for HOOH ad in 18 Supplementary Fig. 12), while the band is not detected in the deuterated medium presumably due to a large shift to lower wavenumber ( Supplementary Fig. 13). The HOOH ad band first appears at 0.7 V vs. RHE for PtP 2 NCs, in accordance with the onset in H 2 O 2 production. Figure 2d shows the normalized in situ Pt L 3 -XANES spectra of PtP 2 NCs recorded at various ORR potentials in 0.1 M HClO 4 . Commercial PtO 2 , PtCl 2 , and Pt foil were used as references and a linear combination of XANES spectra was fitted to the in situ Pt L 3 -edge spectra (Supplementary Figs. 14 and 15). The calculated oxidation states of platinum species in PtP 2 under various potentials are shown in Fig. 2e and summarized in Supplementary Table 5. For the as-prepared PtP 2 NCs, the initial oxidation state of platinum species is calculated to be +3.26, which is attributed to the electron density shift from Pt to P. Under opencircuit potential (OCP) and 0.9 V, a slight change of oxidation state is observed. This is presumably attributed to the formation and dissolution of minor surface oxide based on the small change of white line intensity. At a potential of 0.7 V a negative shift in the absorption edge is observed the average oxidation state decreases to +2.72 since the surface platinum active sites in PtP 2 start to be involved in O 2 activation and H 2 O 2 generation. The oxidation state further decreases to +2.25 by 0.5 V and remains the same to 0.3 V. It should be noted that the oxidation state of +2.25 keeps stable at 0.3 V for 6 h of measurement (Supplementary Fig. 16), indicating that the high P content can stabilize Pt +2.25 in the PtP 2 for sustaining rapid and stable O 2 -to-H 2 O 2 conversion.
The inset of Fig. 2d illustrates the changes in the Pt L 3 -edge XANES spectra with the in situ potential. Here, Δμ is the value obtained by subtracting the Pt L 3 -edge XANES spectrum at 0.54 V from that collected at elevated potentials. The |Δμ| of Pt NCs increase monotonically with potential, while for PtP 2 |Δμ| increases sharply from 0.54-0.7 V but remains unchanged to 0.9 V. The value of |Δμ| is expected to increase with increasing amounts of oxygen species adsorption 34 . The relatively high |Δμ| for PtP 2 within 0.54-0.7 V indicates a high coverage of oxygen intermediates in this region of intermediate activity, potentially due a rate limiting step beyond generation of the initial oxygen intermediates such as *OOH adsorption.
Theoretical DFT calculation for ORR. Two-electron ORR generally follows two hydrogenation steps for H 2 O 2 production, i.e., O 2 → OOH* → H 2 O 2 , while four-electron ORR proceeds with four successive hydrogenation steps for H 2 O generation, i.e., (Fig. 3a). The optimized geometries of OOH*, O*, and OH* intermediates on PtP 2 (111) are shown in Supplementary Fig. 17. Recent theoretical studies have pointed out that the ORR activity for H 2 O 2 production is strongly related to the binding ability of OOH* 6 . Specifically, for an ideal catalyst for H 2 O 2 production, the adsorption of OOH* should be neither too strong nor too weak.
The adsorption configuration of OOH* is determined by the orientation type of the adsorbed oxygen molecule. There are usually two different adsorption configurations, end-on adsorption and side-on adsorption, for O 2 on the catalytic surface of Pt and PtP 2 ( Supplementary Fig. 18). For pure Pt, the optimized adsorption energy (E ads ) of the end-on configuration is more negative than that of side-on configuration, indicating that the former orientation is more favorable and subsequently that associative hydrogenation prevails over the dissociative reaction pathway. For PtP 2 , the adsorption energy of the end-on than that in Pt-OOH* (2.08 Å) (Fig. 3a). This effect is attributed to electron delocalization in phosphorus-rich PtP 2 (Fig. 3c). For the bridge site of PtP 2 (111), the average Pt-O bond length is increased because the Pt-Pt distance is larger due to the high degree of P incorporation (Fig. 3b). A lower overlap among the binding states between Pt 5d and O 2p is observed when OOH* is adsorbed on PtP 2 (111) compared with Pt (111) (Fig. 3d), leading to a weaker binding strength of OOH* over PtP 2 (111) surface. Figure 3f shows the potentialdependent free-energy diagram for two-electron and fourelectron ORR pathways on the PtP 2 (111) surface. At zero electrode potential (U = 0 V) all elementary steps of the ORR are exothermic. At the equilibrium potential (U = 1.23 V), based on the free energies of the intermediates species the first two steps are predicted to be rate determining for the four-electron ORR. At an electrode potential of 0.7 V, the free-energy difference between OOH* to H 2 O 2 is 0.106 eV compared to 0.180 eV for that of OOH* to O*, consistent with the experimental observation that the adsorbed OOH* preferentially undergoes hydrogenation to form H 2 O 2 rather than continuing the dissociation path under a small overpotential. This result can be understood not only by the weakening of the Pt-OOH* bond, but also by the tightening of the O-O bond in OOH* adsorbed to PtP 2 relative to *OOH adsorbed on Pt. For both the top and bridge sites on PtP 2 , the O-O bond length of adsorbed OOH* is shorter than that on Pt, which is beneficial to suppress the OOH*-to-O* dissociation tendency.
ALD overcoat for stabilization of ultrasmall PtP 2 NCs. Although the ultrasmall PtP 2 NCs gave efficient and selective O 2to-H 2 O 2 conversion, both the disk and ring current quickly decayed and around 60% activity was lost within 60 h at an applied potential of 0.4 V vs. RHE (Fig. 4a). Considering that the elemental composition, crystalline structure, and surface electronic structure of PtP 2 all remain the same following the stability test ( Supplementary Fig. 19), the degradation is ascribed to size instability, which leads to nanocrystal aggregation (Supplementary Fig. 20) and a significant decrease in the electrochemical active surface area (EASA, Supplementary Fig. 21). The left shift of Pt L 3 -rising edge of XANES is also attributed to small size nanocrystal aggregation (Fig. 4l). Ultrathin metal oxides by ALD 40 ). ALD of a thin Al 2 O 3 layer was carried out to stabilize the ultrasmall PtP 2 NCs on a commercial carbon support by alternately exposing the sample to cycles of trimethylaluminum (TMA) and water at 175°C (Fig. 4b). Figure 4c shows that the average size of PtP 2 NCs is increased to 5.2 ± 0.4 nm due to minor thermal aggregation during the mild-ALD process. The Al 2 O 3 overcoat thickness is 1.8 ± 0.2 nm after 42 cycles (Fig. 4d, Supplementary Fig. 22a). This overcoat thickness is smaller than that expected for the typical ALD growth rate for Al 2 O 3 of 1.19 Å cycle −1 , ascribed to the site blocking from any hydrophobic organic ligands remaining on the PtP 2 NCs surface ( Supplementary Fig. 23). We determined that 42 cycles of ALD Al 2 O 3 is required to stabilize PtP 2 NCs and maintain ORR durability, but without further processing the ring current shows a 32.5% decrease compared to the uncoated sample (Supplementary Fig. 24). An observed decrease in EASA is consistent with an expected blocking of active sites by the ALD layer (Supplementary Fig. 25). A balance between increasing the stability and maintaining high activity is achieved by annealing the sample following ALD at 600°C in N 2 gas for 2 h. The size dispersity and element distribution are well maintained (Fig. 4e, g-i), while the overcoat thickness is diminished (~0.54 nm) (Fig. 4f, Supplementary Fig. 22b) and the EASA and Brunauer-Emmett-Teller (BET) surface area is almost restored (Supplementary Fig. 25).
The disk and ring current of the annealed sample (Al 2 O 3 / PtP 2 -600) remain the same before and after 60 h of ORR testing in 0.1 M HClO 4 (Fig. 4a), indicating that the Al 2 O 3 overcoat and activation can stabilize the PtP 2 NCs, while maintaining open pathways to the NC surface ( Supplementary Fig. 26). It should be noted that the O 2 -to-H 2 O 2 selectivity is nearly the same after the ALD surface modification, indicating that the ultrathin Al 2 O 3 overcoating has a negligible geometric effect on the electrocatalytic selectivity of PtP 2 electrode (Supplementary Fig. 27). The Pt L 3 -edge XANES and corresponding EXAFS of PtP 2 , Al 2 O 3 / PtP 2 , and Al 2 O 3 /PtP 2 -600 were compared in Supplementary Fig. 28. No change in the absorption edge (E 0 ) and Pt-P bond distance was observed, which suggests that the intrinsic electronic structures of PtP 2 were well maintained after ALD coating and annealing treatment. This could be further supported by the Pt 4f XPS results ( Supplementary Fig. 29). The slight increase for the white line intensity of XANES attributes to the formation of small amount of platinum oxide during ALD process. To further evaluate the effect of the activated coating on the electrochemical properties, CO desorption (Fig. 4k) was studied by electrochemical CO stripping. Prior to the activation step, the shift in the oxidation peak is lost after Al 2 O 3 overcoating and the current decreases suggesting the active surface is blocked. We also note that incorporation of P into Pt facilitates CO desorption, as proven by the negative shift of CO oxidation peak (0.11 V) in the CO stripping test (Fig. 4k). Figure 5a shows a schematic diagram of a PEMFC using commercial Pt/C anode for H 2 oxidation, Nafion 117 membrane for proton transportation and elimination of gas crossover, and our Al 2 O 3 /PtP 2 -600 cathode for two-electron ORR. The details of the expeirmental setup and operation are shown in Supplementary Fig. 31. The Al 2 O 3 / PtP 2 -600 catalyst ink was spray coated onto the carbon gasdiffuse layer (GDL) and hot pressed with the Nafion membrane to form the MEA. The overall MEA is compactly connected and no voids are observed between the interfaces (Fig. 5b, c). The Pt, P, and Al elements are well distributed across the MEA (Fig. 5d-f). The optimized conditions (e.g., mass loading, catalyst support, water flow rate, and operation temperature) for H 2 O 2 production in PEMFC are summarized in Supplementary Table 6.
The optimized mass loading of Al 2 O 3 /PtP 2 -600 is determined to be 0.8 mg cm −2 ( Supplementary Fig. 32), as lower loading leads to kinetics loss and higher loading causes high O 2 gas mass transport reisistance 41 . The current efficiency (CE%) and H 2 O 2 production rate (r(H 2 O 2 )) at 50 mA cm −2 is 60.8% and 0.57 mmol h −1 cm −2 , respectively. A high CE is achieved despite the more challenging kinetics for H 2 O 2 production at neutral conditions compared to the commonly used acidic conditions. At high current density, cathode flooding is typically observed in carbon-based GDE due to the loss of hydrophobicity during PEMFC operation 42 . For the PEMFC with 20 wt% teflon-treated GDL, the operating current density can be increased up to 125 mA cm −2 with significantly improved r (H 2 O 2 ) (1.51 mmol h −1 cm −2 ) compared to that with the nonteflon-treated GDE ( Supplementary Fig. 33). Both the highest CE% and r(H 2 O 2 ) are achieved at a water flow rate of 10 mL min −1 (Supplementary Fig. 34). Increasing the water flow rate within 2-10 mL min −1 is beneficial to remove the generated H 2 O 2 and minimize its thermochemical decomposition and/or further electroreduction 27 (Fig. 5g). The difference in CE for of O 2 -to-H 2 O 2 in RRDE and MEA system is attributed by the transport efficiency of H 2 O 2 away from the electrode surface 2 .
In the RRDE, the small amount of generated H 2 O 2 molecules are rapidly transported away from the disk electrode and oxidized at the ring electrode, leading to a low steady-state surface H 2 O 2 concentration. By contrast, the H 2 O 2 molecules produced at the catalyst/membrane interface in the MEA system need a longer time to diffuse though the catalyst layer and gas diffusion layer before removal into the water stream, which causes a higher local concentration of H 2 O 2 at the vicinity of catalyst surface and increases the possibility of further H 2 O 2 reduction 27 . Moreover, nearly no degradation of the H 2 O 2 concentration (14.7 mmol L −1 , pH = 6.8) is observed at a constant potential of 0.4 V in 120 h (Fig. 5h). The compact interfaces for both cathode/electrolyte and anode/electrolyte are well maintained after 120 h of measurement (Supplementary Fig. 35). For comparison, a Pt-Hg NC-based MEA was fabricated in the same way and run in the PEMFC under the same conditions. The concentration of leached Hg is 5.9 × 10 3 ppb in neutral H 2 O 2 catholyte solution (Supplementary Table 7), and approximately 38% degradation for H 2 O 2 concentration was observed after 6 h of PEMFC operation without recycling of the product (Supplementary Fig. 36
Synthesis of platinum diphosphide (PtP 2 ) NCs. A solution of platinum(II) 2,4pentanedionate (0.3 mmol), OAm (8 mL), OA (0.5 mL), and ODE (8 mL) was placed into a round bottom flask with a stir bar and degassed at 120°C under vacuum for 1 h. To prepare for injection of the P source, the solution was then heated to 220°C under nitrogen. Meanwhile, the P precursor was prepared by placing 1.2 mL (Me 3 Si) 3 P dissolved in hexane (10 wt%) and 1.0 mL ODE under vacuum to remove the hexane at room temperature. The (Me 3 Si) 3 P solution was quickly injected at 220°C and for 15 min the temperature was maintained. To facilitate Ostwald ripening, during cooling the system was kept at 120°C for 10 min prior to cooling to room temperature. To purify, the precipitate was collected following centrifugation at 6000 rpm for 6 min and redispersed with hexane. To further purify the NCs, aggregation was induced with a 1:6:1 (v:v:v) hexanes:acetone:methanol solution followed by centrifuged and resuspension with hexane and this procedure was then repeated for a total of four times. The final suspension yield a solution with NC density by weight of 2 mg/mL. For comparison, Pt NCs were synthesized in a similar co-heating way without (Me 3 Si) 3 where i d and i r are the disk and ring currents, respectively. N is the Pt ring current collection efficiency. The N value in our system was calibrated in 0.1 M HClO 4 with a 10 mM K 3 Fe(CN) 6 electrolyte and is approximately 0.25 ( Supplementary Fig. 38).
For the CO striping test, the electrodes were initially immersed in the CO-saturated 0.1 M HClO 4 by purging with 10 wt% CO in N 2 gas for 30 min and then set to 0.10 V vs. RHE for 15 min to form a CO adsorption layer on the catalyst surface. Then the electrolyte was purged by N 2 gas for 10 min to remove the remaining CO in solution. The CO stripping CVs were obtained in a potential range of 0-1.2 V with a scan rate of 20 mV/s. Electrochemical impedance spectroscopy was performed on a Reference 600 (Gamry Instrument Inc.) with the working electrode biased at OCP, while sweeping the frequency from 10 5 to 0.1 Hz with a 10 mV AC dither. To determine the electrochemical capacitance, CV scans in the non-faradaic potential region were conducted and the capacitive current was obtained at the middle potential value for each scan rate. CV was carried out in a nitrogen-purged 5 mM K 3 Fe(CN) 6 /0.1 M HClO 4 solution with platinum foil as the counter electrode. EASA values were calculated using the Randles-Sevcik equation 43 : where I p is peak current (A), n = 1, D = 4.34 × 10 −6 cm 2 s −1 , A is the EASA (cm 2 ), C is the concentration of potassium ferricyanide (5 × 10 −6 mol cm −2 ), and υ is the scan rate (5 mV s −1 ). Conversion from vs. Ag/AgCl to vs. RHE was done by adding 0.197 + 0.059 × pH. For in situ ATR-FTIR measurements, a diamond-like carbon was coated onto a Si wafer (5 × 8 × 1 mm 3 ) to prepare the internal reflection element (IRE). The coated IRE was ultrasonicated for 2 min with 30% concentrated H 2 SO 4 followed by rinsing with DI water before experiments. A 50 µL of 2 mg mL −1 catalyst ink (no Nafion binder) was dropcast on the IRE and dried under air at room temperature. A glassy carbon paper was placed on top of the catalyst layer for good electrical contact. Glassy carbon rod connected to the IRE, Pt gauze, and Ag/AgCl in 3 M KCl were used as the working electrode, counter electrode, and reference electrode, respectively. An FTIR spectrometer with a MCT detector was used for the in situ ATR-FTIR measurements. Solutions were saturated either with O 2 for ORR or with Ar as a control. Gamry Reference 600 potentiostat during recording of the IR spectra.
ALD Al 2 O 3 overcoat for stabilization. The ALD Al 2 O 3 overcoat for supported PtP 2 was grown in a GEMSTAR-6 atomic layer deposition (ALD) system using trimethylaluminum (TMA) and distilled water (H 2 O) at 175°C. The precursors were kept in the chamber for 2.2 s and a 28 s purge was used. To ensure the deposition occurred with typical growth per cycle, a silicon wafer with native oxide was included alongside the sample as a control and the Al 2 O 3 thickness on the wafer was determined by the X-ray reflectivity. After 42 cycles, the overcoated PtP 2 was activated at 600°C for 2 h in tube furnace under N 2 gas flow (Al 2 O 3 /PtP 2 -600). For comparison, the pure Al 2 O 3 thin film with around 2 nm thickness on silicon was fabricated by ALD for 20 cycles.
Scalable H 2 O 2 production in fuel cell. The MEA for testing the activity in a H 2 -O 2 fuel cell was prepared using Al 2 O 3 /PtP 2 -600 catalyst on GDL as cathode, Pt/ C catalyst on GDL as anode, and Nafion 117 membrane. To prepare the cathode, a catalyst ink composed of Al 2 O 3 /PtP 2 -600 dispersed in a water-ethanol mixture with ionomer (Nafion solution, 5 wt%) was sprayed on Teflon-treated or non-Teflon-treated GDL. Anode was prepared with commercial Pt/C (20 wt%) catalyst in the same manner as the cathode. The catalyst loading amount for cathode and anode is 0.8 mg PtP2 cm −2 and 0.3 mg Pt cm −2 , respectively. A hot press (120°C and 40 MPa for duration of 5 min) was used to press the components together with a Nafion 117 membrane. The MEA was then assembled in a single fuel cell consisting 4 cm 2 serpentine flow fields. Humidification of the MEA was performed for 60 min by flowing N 2 with 100% relative humidity at a cell temperature of 80°C. The flow rates for H 2 and O 2 gases are 150 and 200 mL min −1 , respectively. The flow rate of external neutral water was controlled by a peristaltic pump. The pure water flow through the cathode chamber is beneficial for the removal of generated H 2 O 2 molecules and to decrease the thermochemical decomposition and/or further electroreduction of H 2 O 2 . In the product recycling mode of operation, initially the system is run for 1 h run to accumulate 600 mL H 2 O 2 solution which is then continuously cycled back through the system without any separation of the H 2 O 2 . All the conditions, such as mass loading, catalyst support, water flow rate, and operation temperature, were optimized for H 2 O 2 production in the PEMFC. For quantitative analysis of H 2 O 2 concentration, the interaction of the H 2 O 2 with a modified iodate solution was monitored with the UV-vis spectrscopy method 44 . Briefly, solution A for the I 3 − method consisted of 33 g of KI, 1 g of NaOH, and 0.1 g of ammonium molybdate tetrahydrate diluted to 500 mL with water. The solution was stirred for~10 min to dissolve the molybdate. Solution A was kept in the dark to inhibit the oxidation of I − . Solution B, an aqueous buffer, contained 10 g of KHP per 500 mL. The pH was measured using a pH meter. Equal weights of A and B was subsequently mixed, followed by addition of the H 2 O 2 solution. The absorbance of the resulting solution was measured at a maximum wavelength of 351 nm.
Based on the obtained concentration of flow H 2 O 2 solution, the CE of H 2 O 2 production can be calculated by the following equation: where F is Faraday's constant (96485 C mol −1 ), Q is the water flow rate (L s −1 ), C is the H 2 O 2 concentration (mol L −1 ), and I is the current (A). The corresponding H 2 O 2 production rate can be expressed as following equation: where A is the MEA area (4 cm 2 ). Full details of experimental procedures can be found in the Supplementary Information.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Received: 14 October 2019; Accepted: 6 July 2020; ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17584-9 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. | 9,104.2 | 2020-08-06T00:00:00.000 | [
"Chemistry",
"Materials Science"
] |
Binding of Ovarian Cancer Antigen CA125/MUC16 to Mesothelin Mediates Cell Adhesion*
Mesothelin is a glycosylphosphatidylinositol-linked cell surface molecule expressed in the mesothelial lining of the body cavities and in many tumor cells. Based on the finding that a soluble form of mesothelin specifically binds to ovarian carcinoma cell line OVCAR-3, we isolated cDNAs encoding a mesothelin-binding protein by expression cloning. The polypeptides encoded by the two cloned cDNA fragments matched to portions of CA125, an ovarian cancer antigen and a giant mucin-like glycoprotein present at the surface of tumor cells. By flow cytometric analysis and immunoprecipitation, we demonstrate that CA125 binds to mesothelin in a specific manner. Binding of CA125 to membrane-bound mesothelin mediates heterotypic cell adhesion as anti-mesothelin antibody blocks binding of OVCAR-3 cells expressing CA125 to an endothelial-like cell line expressing mesothelin. Finally, we show that CA125 and mesothelin are co-expressed in advanced grade ovarian adenocarcinoma. Taken together, our data indicate that mesothelin is a novel CA125-binding protein and that CA125 might contribute to the metastasis of ovarian cancer to the peritoneum by initiating cell attachment to the mesothelial epithelium via binding to mesothelin.
CA125 is a tumor antigen originally defined by the monoclonal antibody OC125 (1) that is routinely used for diagnosis of ovarian cancer and to monitor the recurrence after therapy (2,3). CA125 is expressed on the cell surface, and, in addition, soluble proteolytic fragments are also released into the extracellular space. The primary structure of CA125 was established recently, indicating that it is a type I transmembrane protein with a short intracellular and a giant extracellular domain, the latter with 22,097 amino acid residues. The extracellular part is composed of an amino-terminal part spanning 12,070 residues (4), followed by more than 60 tandem repeats of a 156amino acid motif and a 229-residue linker to the transmembrane domain (5). Both the amino-terminal part and the repeat domains are rich in serine and threonine residues and are highly glycosylated. The carbohydrate content was estimated to be 24 -28%, with O-linked and N-linked glycans (6). Because highly O-glycosylated repeats are the landmark of the mucin family of glycoproteins, CA125 was also named MUC16 (7). The mucin-like repeats contain homology to the so-called SEA module, a domain that was reported to be susceptible to proteolytic cleavage and subsequent self-association (8). An additional potential proteolytic cleavage site in CA125 was reported to be located immediately membrane-proximal (5).
Although the structure of CA125 has been elucidated, a functional role for this molecule in the physiological context or in cancer remains unknown. However, a number of publications have pointed out several properties of CA125 that may be of relevance for its biological function. First, because of its expression in embryonic membranes and adult derivatives of the fetal periderm, CA125 has been suggested to play role as a lubricant, preventing adhesion of membranes (9). Anti-adhesive properties have also been assigned to branched O-glycans on leucosialin/CD43 and other mucins (10). In accordance with these findings, CA125 protein coated on plastic culture dishes interferes with the attachment of a variety of cell lines to the plastic dishes (11). Second, close analysis of the glycans present on CA125 revealed the presence of several glycan structures that have been implicated in immune suppression (6), raising the possibility that CA125 might help protect the embryo from maternal immune rejection and play an immunoevasive role in ovarian cancer. Furthermore, mucins can bind to various sugar-binding molecules, such as selectins (12,13) and galectins (14). In fact, galectin-1 was recently shown to bind to CA125 specifically (15). Finally, in an in vitro Matrigel invasion assay, CA125 from human peritoneal fluid was shown to enhance the invasiveness of a benign endometriotic cell line, EEC 145, but it did not affect the invasiveness of a variety of non-endometrioid cell lines (16), raising the possibility that CA125 plays a role in endometriosis. However, this study did not address the question of how soluble CA125 might bind to EEC145 cells to exert this bioactivity.
Taken together, recent evidence suggests that CA125 may exert a number of different functions in parallel. Some of these functions may be mediated by specific molecular interactions, others by the physical properties of this huge, glycosylated molecule. Interestingly, several other mucins have been implicated in invasion and metastasis of cancer, partly because of similar functions. For example, MUC1 induces T cell apoptosis (17) and increases invasiveness (18), MUC18 has been implicated in tumor angiogenesis (19), MUC2 enhances colon cancer metastasis to the liver (20), although it appears to inhibit initial neoplasia as MUC2-deficient mice develop colorectal cancer (21), MUC8 is up-regulated in metastatic medulloblas-toma (22), and MUC3B is up-regulated in intestinal metaplasia (23).
Mesothelin is another tumor antigen that was originally identified by the antibody CAK-1 on mesothelial cells, mesotheliomas, and ovarian cancers (24,25). It is a secreted protein anchored at the cell membrane by glycosylphosphatidylinositol (GPI) 1 linkage. The amino-terminal 31-kDa fragment of the 69-kDa protein is shed by proteolytic cleavage, leaving a membrane-bound 40-kDa peptide. Both fragments contain N-glycosylation sites. The soluble human amino-terminal 31-kDa fragment was reported to have megakaryocyte potentiating activity in a mouse bone marrow colony assay (26) and was named megakaryocyte potentiating factor (MPF). However, there is no report in the literature to our awareness that demonstrates megakaryocyte potentiating activity either with human MPF on human cells or with mouse MPF on mouse cells. A soluble splice variant of the 40-kDa carboxyl-terminal fragment called "soluble mesothelin/MPF-related" was found in sera of patients with ovarian carcinoma (27). This slightly longer splice variant lacks the hydrophobic GPI anchor motif as the result of a shift in the reading frame.
In addition to mesothelioma and ovarian cancer, mesothelin has recently been found to be overexpressed in cancers of the pancreas (28), stomach (29), lung (30), and endometrium (31). At least in pancreatic cancer, expression of mesothelin is partly the result of hypomethylation of its promoter region (32). In a murine cell line, mesothelin has been shown to be a target gene of the Wnt/-catenin pathway (33). Expression in the mouse embryo was reported to be high on days 7 and 17 of gestation, but absent on day 11 and low on day 15, suggesting developmental regulation (34). Mouse and human mesothelin sequences are 59% identical over the entire length of the protein.
There is no obvious sequence motif except for a signal peptide on the amino terminus and a GPI anchor motif at the carboxyl terminus (25,26). Mesothelin-deficient mice were reported to be healthy and fertile. They show normal platelet counts and no obvious phenotype (34). Accordingly, the biological function of mesothelin is still uncertain.
To get more insight into the biological function of mesothelin/ MPF, we have here succeeded in isolating its receptor/binding protein. We show that mesothelin binds to CA125 and that this interaction mediates cell adhesion. Moreover, we demonstrate that CA125 and mesothelin are co-expressed in advanced stage ovarian adenocarcinoma. Taken together, our data suggest a role for CA125 and mesothelin in metastases formation of ovarian carcinoma.
EXPERIMENTAL PROCEDURES
Cell Culture and Media-NIH:OVCAR-3 (OVCAR-3) cells were maintained in RPMI medium 1640 (RPMI) supplemented with 15% fetal bovine serum (FBS), 1 mM sodium pyruvate, 10 g/ml bovine insulin, and antibiotics. LO is a murine endothelial-like cell line derived from the mouse AGM region (35). LO cells were maintained in Dulbecco's modified Eagle's medium (DMEM) with 15% FBS, 10 g/ml oncostatin M, 1 mM sodium pyruvate, and antibiotics. Human lymphoma cell lines K569 and U937 cells were maintained in RPMI with 10% FBS and antibiotics. COS7 and human colon carcinoma Caco-2 cells were maintained in DMEM with 10% FBS and antibiotics. Human umbilical cord vascular endothelial cells (HUVEC) were maintained in endothelial cell basal medium-2 (modified MCDB 131), purchased from Cambrex and supplemented as recommended by the manufacturer. Hybri-doma cells were maintained in RPMI with 10% FBS, 50 M -mercaptoethanol, 85 g/ml hypoxanthine, 24 mg/liter thymidine, and hybridoma supplement (Sigma). Cells were incubated in a 5% CO 2 culture incubator at 37°C. Inhibition of O-glycosylation in OVCAR-3 cells was carried out by adding 5 mM benzyl-2-acetamido-2-deoxy-␣-Dgalactopyranoside to the culture medium over night.
Antibodies and EST Clones-Anti-murine mesothelin monoclonal antibodies were generated in Wistar rats (Nihon SLC) immunized with 10 7 LO cells as described (35). Flow cytometric screening against mesothelin-transfected COS7 cells identified a monoclonal antibody against mesothelin. This antibody, named B35, was produced in nude mice and purified with a protein G-Sepharose column (Hitrap, Amersham Biosciences) according to the instructions from the manufacturer and diluted to 1 mg/ml in phosphate-buffered saline (PBS) without preservatives.
Anti-mesothelin antibody 5B2 was purchased from Novacastra Laboratories (Newcastle Upon Tyne, United Kingdom), anti-CA125 antibodies OC125 and M11 were from Dako Japan (Kyoto, Japan), anti-MUC1 antibody from Pharmingen (San Diego, CA), and M2 anti-FLAG tag antibody from Sigma. All these antibodies with the exception of M2 are human-specific antibodies generated in mice.
Flow Cytometry and Fluorescence-activated Cell Sorting-Cells were harvested from culture dishes with enzyme-free cell dissociation buffer (Invitrogen) and 10 6 cells were incubated on ice for 30 min with 0.5 g of monoclonal antibody or isotype control in 50 l of PBS, followed by washing and labeling with fluorescein-and/or phycoerythrin-conjugated cross-species adsorbed secondary antibodies (Chemicon and Cedar Lane Laboratories, respectively). To assess ligand binding, incubation with M2 antibody was preceded by incubation in 50 l of conditioned culture supernatant from FLAG-tagged soluble mesothelinor mock-transfected COS7 cells and washed, if applicable. To assess blocking activity of antibody for ligand binding, a 0.2 volume conditioned medium of COS7 transfected with the soluble FLAG-tagged mesothelin cDNA was preincubated with 0.8 volume of hybridoma supernatant (or fresh culture medium as a negative control) for 15 min, then used for cell incubation for 30 min, followed by incubation with M2 and fluorescence-labeled antibody consecutively. Analyses were carried out using a FACSCalibur flow cytometer (Becton Dickinson Immunocytometry Systems, San Jose, CA). Cell sorting was carried out with a FACSVantage cell sorter (Becton Dickinson Immunocytometry Systems).
Library Construction, Expression Cloning, and Sequencing-Messenger RNA was extracted from one confluent 10-cm culture dish of OVCAR-3 cells using the FastTrack 2.0 kit (Invitrogen, Tokyo, Japan) according to the instructions from the manufacturer. Five g of poly(A ϩ ) RNA was used for constructing a cDNA library primed by a random hexamer primer using the Time Saver kit (Amersham Biosciences).
Expression cloning of cDNA encoding a binding partner of mesothelin was carried out by using COS7 cells as previously described (37), except that fluorescence-activated cell sorting was employed instead of plate panning. The DNA sequences of the cDNAs were determined by using a dye terminator cycle sequencing kit (PerkinElmer Life Sciences) and an automated DNA sequencer (Applied Biosystems, Foster City, CA).
Expression of Mesothelin in COS7 Cells and Immunoblotting-Twenty g of expression vector containing truncated CA125 and/or mesothelin coding cDNA was electroporated into COS7 cells (10 7 cells/ ml, 0.8 ml, at 220 V, 960 F). After 2 days of incubation, cells were lysed in 1 ml of lysis buffer (PBS with 50 mM HEPES, 100 mM NaF, 4 mM EDTA, 2 mM sodium vanadate, 0.5% Nonidet P-40 and a mixture of protease inhibitors (phenylmethylsulfonyl fluoride and leupeptin)), yielding ϳ13 mg of total protein. 100 l of cell lysate were put aside as controls. Three g of OC125 antibody was added to the remaining lysate, followed by the addition of protein G Sepharose (Amersham Biosciences). Proteins in the immune complexes as well as control lysates (15 l or ϳ0.2 mg of total protein) were subjected to SDSpolyacrylamide gel electrophoresis on a 10% gel and transferred to a polyvinylidene difluoride membrane (Millipore, Bedford, MA). The blot was incubated with 5B2 antibody, followed by anti-mouse antibody conjugated with horseradish peroxidase (Amersham Biosciences, Buckinghamshire, United Kingdom). The immunocomplex was detected on Hyperfilm (Amersham Biosciences) using an enhanced Luminol oxidation reagent (PerkinElmer Life Sciences).
was carried out in triplicates using a protocol adapted from Cannistra et al. (38). LO cells were grown to confluence in 6-well culture plates. Thirty minutes prior to the addition of OVCAR-3 cells, LO medium was exchanged for OVCAR-3 medium supplemented with the appropriate amount of blocking or control antibody.
OVCAR-3 cells were dissociated from culture dishes with enzymefree cell dissociation solution and added on top of the LO cells at 10 6 cells/well. Culture plates were spun at 800 rpm for 3 min to bring OVCAR-3 cells in contact with LO cells, then incubated at 37°C for 60 min to adhere. Non-adherent cells were removed by repeated washing in PBS with strong finger tapping to agitate the wells. All bound cells were then dissociated with enzyme-free cell dissociation solution, counted, and analyzed by flow cytometry. MUC1 antibody was used to identify OVCAR-3 cells, B35 antibody to identify LO cells.
Alternatively, mouse embryonic diaphragm cells were used instead of LO cells. Diaphragms were dissected from embryos of C57BL/6J mice at day 14.5 post coitus. Cells were dispersed with 0.05% (w/v) trypsin and 0.5 mM EDTA in PBS at 37°C for 10 min and by repeated pipetting, and then filtered through a 40-m mesh to obtain a single cell suspension. Cells were cultured in 6-well plates, one embryo equivalent per plate, in the same medium as LO cells but without any growth factors. On day 5 of culture, when culture had reached confluence, the adhesion of OVCAR cells to the cultured diaphragm cells was assessed exactly as described above. To block binding, 6 g/ml antibody B35 was used.
Cell binding was likewise tested in the inverse configuration. Detached LO cells or cultured embryonic diaphragm cells were added on top of confluent OVCAR-3 cells, attached by centrifugation in LO medium with or without 6 g/ml B35 antibody, washed with PBS, and analyzed by flow cytometry as above. To test whether divalent ions are required for the binding, non-attached cells were washed out with PBS supplemented with 1 mM EDTA or EGTA.
Immunohistochemistry and Measurement of CA125 Serum Concentration-This study was approved by the local ethics committee, and informed consent was obtained from each subject. Samples were collected from patients undergoing surgery for ovarian tumor. Serum concentration of CA125 in each patient was determined before operation by chemiluminescent enzyme immunoassay with the Lumipulse CA125 II kit (Fuji Rebio) according to the instructions from the manufacturer. Of the 18 patients in this study, 9 had serous papillary adenocarcinomas, 3 had mucinous cystadenocarcinomas, 2 had clear cell carcinomas, 1 had an endometrioid adenocarcinoma, 3 had serous adenomas, and 1 had a mucinous adenoma. Type and stage of tumors were determined according to FIGO (39). All specimens were fixed with 10% buffered formalin for 5 h immediately after resection and were embedded in paraffin.
Immunostaining was performed with some modifications as previously described (40). Four-micrometer sections were processed for immunohistochemical procedures based on the Labeled Polymer method (Dako). Briefly, sections were treated with 3% hydrogen peroxide in absolute methanol for 30 min to quench endogenous peroxidase activity. After antigen retrieval with Target Retrieval Solution (Dako), sections were preincubated in 0.01 M PBS containing 10% normal goat serum (Jackson Immunoresearch, West Grove, PA) at room temperature for 1 h, and then incubated in primary antibodies containing 0.5% bovine serum albumin at room temperature for 2 h. Primary antibodies 5B2 and M11 were both used at dilution 1:20. After washes with 0.1 M PBS, the sections were incubated in goat anti-mouse immunoglobulins conjugated with peroxidase-labeled dextran polymer (EnVisionϩ, Dako) at room temperature for 30 min. After washes with 0.1 M PBS, the horseradish peroxidase reaction was developed in 0.1 M Tris-buffered saline, pH 7.4, containing 0.05% 3,3Ј-diaminobenzidine tetrahydrochloride (Sigma), 0.02% nickel sulfate, and 0.01% hydrogen peroxide. Methyl green was used for counterstaining. Only in cells where CA125 has been co-transfected can mesothelin be precipitated using the OC125 antibody. The lower molecular weight species is preferentially precipitated, indicating that the glycosylation pattern of mesothelin may affect binding.
Statistical Analysis-SAGEmap gene expression data were analyzed by pairwise linear regression and analysis of variance using the spreadsheet software Excel (Microsoft, Redmond, WA). Fisher's exact test was used to test the association of tissue mesothelin expression with histological grade. Data from multiple experiments are expressed as mean (Ϯ standard deviation).
Identification of CA125 as a Mesothelin
Counter-receptor-To identify a counter-receptor of mesothelin, an expression construct of murine mesothelin fused to the FLAG peptide at the COOH terminus, mMes-f, was electroporated into COS7 cells. A double band of 40 and 46 kDa could be detected in the culture supernatant by Western blotting with M2 antibody that recognized the FLAG epitope (data not shown). Considering that the theoretical molecular mass of the epitope-tagged carboxyl-terminal fragment of mesothelin is 38.6 kDa, these two bands are in agreement with two differentially glycosylated forms of mesothelin as has been observed previously (25), being released into the supernatant because the fusion with the FLAG tag had destroyed the GPI linkage motif. Using culture supernatant with the recombinant mMes-f protein, we searched for cell lines that bind mesothelin by flow cytometry and found that OVCAR-3, an ovarian cancer line, showed strong specific binding (Fig. 1). The binding could be blocked significantly with B35, a monoclonal antibody specific for murine mesothelin that we had previously identified from a panel of monoclonal antibodies against LO cells.
To isolate a cDNA for the mesothelin-interacting protein, we constructed a cDNA expression library of OVCAR-3 cells. The cDNA library was transfected into COS7 cells by spheroplast fusion, and COS7 cells expressing a mesothelin-binding protein were enriched by flow cytometric cell sorting.
Plasmid DNA recovered from the sorted COS7 cells was subjected to a second cycle of selection. After four cycles of selection, two cDNA fragments of 1.1 and 1.6 kb were enriched. Sequencing analyses of the cloned cDNA fragments revealed that these two clones represented overlapping fragments of the same gene, corresponding in sequence to bases 63444 -64531 and 63354 -64956 of CA125 (GenBank TM accession AF414442). As illustrated in Fig. 2, the cloned cDNA fragments comprise 2.5 and 3.5 units of the mucinous repeats, respectively. The 23 carboxyl-terminal amino acids of the longer clone are part of a short non-repetitive sequence interspersed between the last two repeats.
As expected, flow cytometric analysis revealed that COS7 cells transfected with either cloned cDNA but not mock-transfected COS7 cells could bind mMes-f protein, but not to an irrelevant FLAG-tagged protein (data not shown). Although our CA125 cDNA clones contain neither a signal peptide nor a putative transmembrane domain coding region, their protein products were evidently present on the cell surface of transfected COS7 cells.
Binding Specificity-To test whether human mesothelin binds to CA125 in the same way as we had observed for mouse mesothelin, we constructed an expression construct of the carboxyl-terminal fragment of human mesothelin, termed f-␦hMes, in which an amino-terminal FLAG tag is fused to human mesothelin glutamic acid 298, just below the proteolytic cleavage site. The f-␦hMes expression vector was transfected into COS7 cells, and the recombinant protein could be detected at 42 and 48 kDa in cell lysates (Fig. 3B), indicating differential glycosylation as the calculated molecular mass of the recombinant protein plus GPI anchor is 40 kDa. A small amount of the recombinant protein could also be detected in the culture supernatant (data not shown). The conditioned supernatant was incubated with OVCAR-3 cells. Specific binding was observed by flow cytometry using M2 antibody as shown in Fig. 3A.
To create a CA125 expression construct extending our 1.6-kb cDNA clone to the 3Ј end, we identified an 1.9-kb EST clone in GenBank TM that covers the 3Ј end of the CA125 open reading frame and overlaps with our 1.6-kb clone. We obtained the EST clone from the I.M.A.G.E. Consortium and fused it with a FLAG epitope tag and our 1.6-kb clone on the 5Ј side. The resulting recombinant protein, termed f-MucTM, includes the 1100 carboxyl-terminal amino acid residues of CA125 (Fig. 2).
Lysates of COS7 cells transfected with the f-MucTM and f-␦hMes expression constructs were immunoprecipitated with OC125 antibody and subjected to Western analysis using the mesothelin-specific antibody 5B2. As controls, COS7 cells transfected with either construct or mock-transfected COS7 cells were used. The results, shown in Fig. 3B, indicate that mesothelin can be precipitated from transfected COS7 cells by antibody OC125 only in the presence of CA125 protein. These TABLE I Specificity of mesothelin binding to CA125 Shown are the results from flow cytometric experiments with the respective antibodies or ligands. Binding of epitope-tagged recombinant mesothelin (both mouse and human) was detected by tag-directed antibody (M2). Ϫ, negative (no shift); ϩ, positive; ϩϩ, strongly positive (Ն 100-fold shift in fluorescence intensity). Note that only OVCAR-3 cells bind to mesothelin. Although OVCAR-3 cells express MUC1 in addition to CA125, K562 cells also express MUC1 but do not bind to mesothelin. In addition, cell lines known to express MUC17 and MUC18 as well as the mucin-like glycoproteins CD43 and CD68 do not bind to mesothelin. Thus, mesothelin does not bind to a general carbohydrate epitope found in different mucins but rather binds specifically to CA125.
FIG. 4. Heterotypic cell adhesion mediated by mesothelin. OVCAR-3 cells were added to a monolayer of LO cells. After washing, OVCAR-3 cells bound to LO cells were counted as described under "Experimental Procedures." Addition of B35 anti-mesothelin antibody (solid squares) blocks OVCAR-3 cell binding to mesothelin expressing LO cells in a dose-dependent manner, whereas isotype control antibody (open circles) does not affect cell binding.
results confirm our finding from the flow cytometric analyses that human mesothelin binds to CA125.
Next, we investigated whether mesothelin binding is specific to CA125 or shared by other glycoproteins of the mucin family. We tested several cell lines, which are known to express various mucin molecules, for binding to mesothelin as well as for expression of CA125 and MUC1. The results, summarized in Table I, show that mesothelin does not bind to mucins in general, indicating that binding to CA125 is specific.
CA125 and Mesothelin Mediate Heterotypic Cell Adhesion-CA125 is presented on the surface of ovarian cancer cells. Mesothelin is expressed by the cells which form the mesothelial lining of the peritoneal cavity, a preferred site of metastases formation of ovarian cancer. To test whether binding of CA125 and mesothelin might play a role in heterotypic cell adhesion, a process that is crucial to initiate metastases, we developed a cell adhesion assay. LO cells grow as adherent cells that express mesothelin abundantly, whereas OVCAR-3 cells are also adherent cells that express CA125. OVCAR-3 cells were detached from culture dishes, and 10 6 cells were added on top of confluent LO cells. Cells were then brought in close contact by gentle centrifugation. After brief incubation and extensive washing, adherent OVCAR cells were counted by flow cytometry. Under the conditions used, 8.9 (Ϯ0.8%) of input OVCAR-3 cells were found to be attached to LO cells, and this binding was inhibited by anti-mesothelin antibody B35 in a dose-dependent manner (Fig. 4). In contrast, antibodies against irrelevant antigens or isotype control antibody did not affect the binding at all. These results clearly demonstrate that mesothelin is specifically involved in the attachment of OVCAR-3 cells to LO cells.
We repeated the cell adhesion assay with a confluent culture of cells derived from mouse embryonic diaphragms. As the diaphragm constitutes the rostral border of the peritoneal cavity, we reasoned that it should contain a substantial fraction of mesothelial cells. In fact, 10.2 (Ϯ3.2%) of freshly obtained diaphragm cells were found to express mesothelin by flow cytometry. After 5 days in culture, the cells became confluent and now 14.4 (Ϯ1.4%) expressed mesothelin. 11.1 (Ϯ2.3%) of 10 6 OVCAR-3 cells were found to adhere to cultured embryonic diaphragm cells, but only 5.3 (Ϯ1.6%) adhered after the addition of antibody B35 (data not shown). Thus, mesothelin-mediated cell adhesion of OVCAR-3 cells is not an artifact of LO cells.
In the reverse experiment, when LO cells were attached to a confluent culture of OVCAR-3 cells, 56 (Ϯ7%) of input LO cells were found attached. Washing with EDTA or EGTA did not reduce cell adhesion at all, indicating that the binding is independent of Ca 2ϩ , but in the presence of antibody B35, only 3.3 (Ϯ0.7%) of input LO cells were found attached. When cultured embryonic diaphragm cells were attached to confluent OVCAR-3 cells, the mesothelin expressing diaphragm cells were found to attach three times more efficiently to OVCAR-3 cells than the mesothelin negative cells, even though in the presence of antibody B35, mesothelin positive and negative cells attached to OVCAR-3 cells equally well. Taken together, these results suggest that both CA125 and mesothelin are present on the apical side of cells and mediate apical-to-apical cell binding.
CA125 and Mesothelin Are Co-expressed in Advanced Ovarian Carcinomas-In a first approach to investigate the molecular interaction between CA125 and mesothelin in the pathological context of cancer, we investigated the expression of both antigens in consecutive paraffin sections from biopsies of ovarian tumors.
As summarized in Table II, samples were obtained from 18 different patients with various subtypes of ovarian adenocarcinoma and adenoma. Immunohistochemistry revealed CA125 staining in 13 of 15 of the malignant samples, including two borderline malignancies, but not in the benign adenomas. In contrast, mesothelin was detected in five of the eight serous papillary adenocarcinomas, but not in other tumor types including the borderline malignancies. Both of two grade 1 serous papillary adenocarcinomas were mesothelin-negative, whereas five of the six serous papillary adenocarcinomas with grade 2 or higher stained positive for mesothelin, the outlier being a stage Ia tumor (Table II, in Fig. 5 to illustrate different patterns of co-expression of CA125 and mesothelin. Some samples (e.g. Fig. 5 patients 2711 and 4079) clearly show mesothelin staining in a more restricted part of the tumor than CA125, a pattern that would be expected if tumors acquire mesothelin expression at a later stage of malignant transformation than CA125 expression. The CA125 concentration in the patients' serum was deter-mined prior to surgery and was elevated (Ն35 IU/ml) in all but three patients, two of them with stage I and only one with an advanced (stage IIIc, grade 3) tumor. Notably, that patient expressed CA125 and mesothelin in the tumor tissue in an overlapping fashion (Fig. 5, patient 4193). This observation suggests that mesothelin could be responsible for trapping CA125 in the tumor tissue in this patient. In addition, we analyzed co-expression of CA125 and mesothelin in libraries of the SAGEmap project (41). An unambiguous Unigene ID (Hs.155981 and Hs.98502) and SAGE (serial analysis of gene expression) tag (CCCCCTGCAG and CCTGATCTGC) could be identified for mesothelin and CA125, respectively. Of the 154 libraries in SAGEmap (as of July 21, 2003), 20 contained two or more tags for mesothelin. Seven of the 20 mesothelin-positive libraries contained two or more tags for CA125. Of 123 mesothelin-negative libraries, only one contained two and none more than two CA125 tags. (Eleven libraries were not classified as either mesothelin-positive or -negative because they contained exactly one mesothelin tag. None of those 11 contained more than one CA125 tag either.) Table III lists the 20 libraries containing two or more tags of either mesothelin or CA125 plus the human reference RNA library. High expression of both mesothelin and CA125 was observed in a mesothelioma of the peritoneum, three ovarian serous adenocarcinomas, a pool of ovarian carcinoma cell lines, and a pancreas epithelium ductal adenocarcinoma.
To confirm the observed co-expression of mesothelin and CA125 in SAGEmap libraries, we statistically compared the expression patterns of the respective tags with a number of SAGE tags of other cancer markers and genes, which might have a similar regulation of expression. First, we analyzed the expression of galectin-1 (tag GCCCCCAATA) because it is the only other protein that is known to bind specifically to CA125 (15), and the expression of MUC1 (tag CCTGGGAAGT), a mucin family member implicated in cancer progression, also known as CA15-3 (17,18,42,43). Pairwise regression analyses over expression levels in all 154 SAGE libraries showed that CA125 and mesothelin have a Pearson correlation coefficient of r ϭ 0.43 at a high significance (p ϭ 3 ϫ 10 Ϫ8 ), whereas MUC1 expression is less strongly correlated with CA125 expression (r ϭ 0.25, p ϭ 0.002) and galectin-1 expression shows no significant correlation with CA125 expression (p Ͼ 0.05). Even though galectin-1 was found in most CA125-positive SAGE libraries, it was expressed at similar levels in CA125-negative libraries in an almost ubiquitous manner. Mesothelin expression showed no significant correlation with either MUC1 or galectin-1 expression. Furthermore, neither CA125 nor mesothelin expression was significantly correlated to CEA/ CEACAM5, another mucin and well known marker of colon cancer (44), or to Claudin 4, S100A4, stratifin/14 -3-3, or trefoil factor 2, genes that are activated through hypomethylation in concert with mesothelin in pancreatic cancer (32), or to BMP4 or PTX3, two genes that were reported to be up-regulated in concert with mesothelin by Wnt-1 in a murine cell line (33) (Wnt-1 itself does not have a corresponding SAGE tag). A highly similar expression pattern was observed, however, between CA125 and WFDC2 (whey acidic protein four-disulfide core domain 2), which was recently reported to be a specific marker of ovarian cancer (45) (correlation r ϭ 0.44 for WFDC2 and CA125, r ϭ 0.31 for WFDC2 and mesothelin). These results demonstrate that CA125 and mesothelin show a remarkably similar expression pattern even when compared with other genes that are also known as cancer markers. DISCUSSION CA125 is one of the most commonly used diagnostic antigens of ovarian cancer, although its biochemical nature has long FIG. 5. Tissue staining of serous papillary adenocarcinoma samples with CA125 and mesothelin. Adjacent tissue sections from adenocarcinoma samples from patients were stained with M11 anti-CA125 or 5B2 anti-mesothelin antibody. Patient number and antigen stained for are indicated in each picture. For patient data, see Table II. Sample 2711, a stage IIa tumor, shows pervasive expression of CA125 but an inhomogeneous, spotty expression of mesothelin. Similarly, sample 4079 shows a stage IV tumor with pervasive CA125 staining whereas mesothelin seems to stain only a part of the tumor, although a larger part than in sample 2711. Samples 4595, 4193, and 4876 show three stage IIIc tumors with clear CA125 staining around cystic spaces and different patterns of mesothelin expression; 4595 is mesothelinnegative, whereas samples 4193 and 4876 show mesothelin staining around cystic spaces in close resemblance to the CA125 staining pattern. been elusive. Only very recently, its primary structure was elucidated, demonstrating that CA125 shows several unusual features. First, it is an extremely large glycoprotein consisting of more than 22,000 amino acid residues (4). Second, the extracellular domain contains more than 60 tandem repeats of a 156-amino acid motif. These repetitive sequences as well as the remainder of the extracellular part of the protein are rich in serine and threonine residues, resulting in the addition of O-linked sugar chains (5). Third, CA125 is secreted via the endoplasmic reticulum (ER) and Golgi apparatus by a signalpeptide independent mechanism (15). Although the function of CA125 still remains unknown, CA125 is expected to interact with other molecules as O'Brien et al. (46) co-immunoprecipitated CA125 with two unidentified proteins of ϳ35 and 45 kDa from peritoneal fluid of ovarian cancer patients. In the present study, we demonstrate the binding of CA125 to mesothelin, a glycoprotein which is present in peritoneal fluid of ovarian cancer patients (27) and has a molecular mass of 42-45 kDa because of proteolytic cleavage and glycosylation (27).
Mesothelin is a glycoprotein on the cell surface and has been known as a tumor antigen of mesotheliomas as well as ovarian and pancreatic adenocarcinomas (24,28). In this study, we isolated two cDNA fragments encoding a mesothelin-binding protein, and both cDNA sequences match portions of CA125. The binding of mesothelin to CA125 was demonstrated by flow cytometry as well as immunoprecipitation experiments. As the cloned cDNA fragments encode only a few units of the repeating motif of CA125, this repeating motif must be responsible for the binding to mesothelin. As CA125 is reported to contain more than 60 units of this motif, mesothelin binding is most likely highly multivalent.
Just like the clones we isolated, full-length CA125 lacks a signal peptide (4). A truncated carboxyl-terminal fragment of CA125, which includes the region encoded by our cloned cDNA fragments, has been reported to be secreted via the ER-Golgi pathway, implying a signal peptide-independent mechanism of CA125 protein insertion into the ER (15). Provided both CA125 fragments we cloned are secreted by the same mechanism as full-length CA125, the putative minimal recognition motif for ER insertion should be fully contained in our 1.1-kb fragment, i.e. between tyrosine 21081 and threonine 21444. It is possible that the putative recognition motif for ER insertion exists in other repeats as well. However, the fact that we pulled out two overlapping clones covering this small portion of CA125 strongly suggests that this sequence mediates both protein secretion and binding to mesothelin. Because the CA125 cDNA fragments were cloned by binding of mesothelin to COS7 cells transfected with the cDNA library, the CA125 peptides encoded by two independently cloned cDNAs must be attached to the cell surface. However, neither of the cloned fragments contained a putative transmembrane domain. Although the mechanism of their binding to the cell surface is unclear, it is possible that CA125 fragments were retained on the cell surface through binding to galectin-1 that is expressed in COS7 cells (data not shown). Inhibition of O-glycosylation of OVCAR-3 reduced the binding of mesothelin but not CA-125specific antibody M11 to the cells, indicating that glycosylation of CA125 is important for binding to mesothelin (data not shown).
We also found that the anti-mesothelin antibody B35 blocked the attachment of OVCAR-3 cells expressing CA125 to mesothelin-positive LO cells, indicating that binding between CA125 and mesothelin mediates cell-cell adhesion. Likewise, binding of OVCAR-3 cells to a heterogeneous primary cell culture containing mesothelial cells from the diaphragm could be partially blocked by the same antibody, demonstrating that heterologous cell adhesion through mesothelin is independent of the cellular background and therefore specific. Because of the specificity of our antibody, these cell binding experiments had to be carried out in a mouse-human cross-species system. We have therefore in addition demonstrated biochemically that human mesothelin binds to human CA125. Taken together, these results argue that the molecular binding of CA125 to mesothelin is involved in cellular adhesion. The apical-to-api- cal nature of this cell adhesion, which is evidenced by the efficient attachment of both CA125-expressing and mesothelinexpressing cells to an intact monolayer of mesothelin-or CA125-expressing cells, respectively, is reminiscent of throphinin/tastin-mediated trophoblast adhesion to the endometrium during embryo implantation (47), which is also calcium-independent.
Binding of CA125 to mesothelin is of particular interest with respect to the characteristics of ovarian cancer, the most lethal among gynecological tumors (48). The high death rate is partly the result of the fact that ovarian cancer often metastasizes throughout the peritoneal cavity before diagnosis. Such metastatic implants are attached to the peritoneal mesothelium, which lines the abdominal cavity, omentum, and bowel serosa. The cancer often remains confined to the abdominal cavity, eventually causing death resulting from bowel obstruction (49 -51). As hematogenic or lymphatic transport is not required, factors that promote localized attachment and detachment have been suggested to be important determinants of ovarian cancer metastasis (52). Cannistra's group (38) devised an in vitro binding assay for ovarian cancer cells using confluent monolayers of normal peritoneal mesothelial cells. Using monoclonal antibodies raised against ovarian cancer cells, they reported that CD44H and integrin  1 , expressed on ovarian cancer cells, bind to hyaluronic acid and fibronectin, respectively, expressed on mesothelial cells (38,53). However, they also observed residual specific cell binding that could not be blocked by the ovarian cancer-directed antibodies they used (53). As CA125 and mesothelin, expressed on ovarian cancer cells and on mesothelial cells, respectively, can interact with each other and mediate heterotypic cell attachment in vitro, the residual binding might be a result of binding between CA125 and mesothelin. Consequently, mesothelin might be an additional promising drug target to prevent metastasis in ovarian cancer patients at risk.
Contrary to the broad expression of CA125 in ovarian tumors from borderline malignancies to adenocarcinomas, tissue staining patterns of mesothelin suggest that mesothelin expression occurs at an advanced stage of malignant progression of the tumors. However, the association between advanced histological grade (Ն2) and mesothelin expression in serous papillary adenocarcinoma tissues observed in this study was statistically not significant (p ϭ 0.11) because of the small number of samples. Although we observed mesothelin expression only in the serous papillary subtype of ovarian adenocarcinomas, Frierson et al. have reported mesothelin expression in endometrioid and undifferentiated ovarian carcinomas in a large scale tissue microarray study (31). Because that study investigated neither CA125 expression nor tumor stage and grade, it remains to be determined, with a statistically amenable number of cases, whether or not mesothelin expression is indicative of more advanced malignancy of ovarian carcinomas than CA125. This should add a biological basis to recent proposals for the combined test for CA125 and mesothelin in patient sera (27).
An unresolved clinical issue is the poor correlation between CA125 found in cancer tissue and CA125 concentration in patient serum. The number of patients whose tumor tissue stains positive for CA125 is ϳ90% in serous ovarian adenocarcinoma, as well as in endometrioid endometrial carcinoma. However, the numbers of patients whose serum CA125 levels are elevated are only 80 and 21% for ovarian cancer and endometrioid endometrial carcinoma, respectively (54,55). It has been reported that basement membranes surrounding the tissues in which the tumors arise, as well as peritoneal barriers, hinder such high molecular weight proteins as CA125 from entering the circulation (56). However, this retention mecha-nism alone cannot fully explain the lack of serum CA125 in some patients with advanced stage disease where the basement membrane of the tissue of origin has ruptured, and it has thus been proposed that an unidentified mechanism for CA125 tissue retention must exist, being active with differential efficiency in different gynecological cancers (55). In our study, there is only one advanced stage ovarian cancer patient with normal serum CA125 but positive CA125 tissue staining. In this patient (patient 4193 in Fig. 5 and Table II), CA125 staining precisely co-localized with mesothelin staining, raising the possibility that mesothelin may be able to trap CA125 in the tissue when it is overexpressed in the same location. If this finding can be confirmed in a larger study of ovarian cancer samples from patients with normal CA125 serum levels, it will give a second biological rationale to combined CA125 and mesothelin serum testing.
The SAGE data base analysis revealed co-expression of mesothelin and CA125 genes in a peritoneal mesothelioma, three ovarian, and one pancreatic adenocarcinoma. Protein co-expression was observed by antibody staining in five serous papillary adenocarcinomas. Furthermore, human peritoneal mesothelial cells have been reported to express CA125 (57) as well as mesothelin (24). In contrast, in our cell binding assay, we showed that CA125 on cancer cells mediates cell attachment to mesothelin expressing cells. We did not investigate how different levels of co-expression of both molecules might modify this cell binding, nor did we investigate what influence soluble fragments of CA125 and mesothelin in the peritoneal fluid might have either on the detachment of tumor cells from the ovarian carcinoma or on their attachment to mesothelial cells. Yet, the fact that OVCAR-3 cells do express some mesothelin (24) and the multivalent nature of the mesothelin binding site on CA125 prompt us to speculate that mesothelin co-expressed with CA125 on ovarian tumor cells may not competitively inhibit but rather promote attachment to mesothelial cells by forming a secondary anchor which retains CA125 molecules even after proteolytic cleavage.
In conclusion, the binding between CA125 and mesothelin described herein may be of importance in metastasis formation of ovarian cancer, and it gives a rational basis to combined CA125 and mesothelin serum testing. The clinical relevance of our findings needs to be confirmed in animal models and with larger clinical data sets. | 9,294.6 | 2004-03-05T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Digitalization and SMEs development in the context of sustainable development: A China perspective
Worldwide economies are determined to achieve sustainable development. In this pursuit, the role of SMEs and ICT has emerged as an inevitable choice for sustainable development. The literature on the impact of SMEs and ICT on sustainable development, particularly in China's context, is scarce. Therefore, the analysis aims to investigate the impact of SMEs and ICT on sustainable development in China for the period of 1998–2020. We have applied the ARDL model for empirical analysis. The short and long-run estimates attached to SMEs are significant and positive, confirming that SMEs help to achieve sustainable development. Similarly, the estimates attached to ICT are positive and significant both in the short and long run, confirming the beneficial role of ICT in achieving sustainable development. The estimates attached to institutional quality and R&D control variables are positive and significant in the long run, but only R&D estimates are significant in the short run. In particular, digitalization and SMEs development provide a win–win situation for China to mitigate climate change in the long run and become more environmentally sustainable.
Introduction
Sustainable development represents the equilibrium between economic, social, and environmental dimensions, striving for longterm prosperity and universal well-being.It encompasses the reduction of greenhouse gas emissions, the preservation of natural resources, the promotion of social inclusivity, respect for human rights, and the establishment of sustainable infrastructure and institutions.This global endeavor aligns with the United Nations Sustainable Development Goals, a framework dedicated to eradicating poverty, safeguarding the planet, and fostering prosperity for all [1,2].In this context, the digital transformation of SMEs is gaining remarkable prominence, signifying a pivotal nexus in the pursuit of sustainable development on a global scale.This study endeavors to unravel the intricate interplay between SMEs, digitalization, and their profound influence on sustainable development, particularly within the dynamic landscape of China.
SMEs hold immense potential to advance sustainable development by adopting eco-friendly business practices that reduce their environmental footprint, uphold principles of social responsibility, and contribute to the well-being of local communities [3].By weaving sustainability into their operations, SMEs can sharpen their competitive edge, nurture customer loyalty, and elevate their reputation in an increasingly conscious market [4,5].SMEs play a pivotal role in ushering society towards a sustainable future.SMEs are indispensable for employment, food production and distribution, construction, healthcare, and essential services [6].Collectively, they wield substantial economic influence and are indispensable for driving environmental and societal transformations.In a broader context, environmentally-conscious SMEs contribute to safeguarding the climate, preserving the environment, and promoting biodiversity through their array of offerings, services, and operational approaches [7].However, they pursue these sustainability objectives in diverse ways.Some SMEs prioritize the reduction of their production process's ecological footprint, emphasizing resource-efficient methodologies.Conversely, others concentrate on eco-friendly end-products and extend green services, such as renewable energy solutions [8].
Simultaneously, digitalization emerges as a catalytic force in optimizing resource utilization, waste reduction, and the democratization of education and healthcare access while facilitating the transition to low-carbon economies [9].Nevertheless, it is paramount that the dividends of digitalization are distributed equitably and the ecological and societal ramifications of digital technologies are scrupulously scrutinized and counteracted.In consonance with the deliberative choice of firms to embrace digitalization, the digital perspective and environmental consciousness have ascended to critical significance in contemporary corporate strategy [10].These cutting-edge digital technologies offer unprecedented opportunities for expanding business portfolios and enhancing growth prospects [11].On the other hand, the eco-centric approach underscores the strategic commitment to infuse sustainability imperatives into a firm's tactical, procedural, and creative actions [12].
The rise of digitalization has diverse economic impacts, touching upon economic growth, financial development, educational outcomes, and environmental sustainability [13].As global digitalization spreads, it offers opportunities for inclusive and sustainable development.However, these sustainable outcomes must strike a balance across the economic, social, and environmental dimensions [14].In terms of the environment, digitalization can have both positive and negative effects.On the positive side, it can reduce CO2 emissions by lowering transaction and travel costs.Digitalization also enhances energy efficiency, smart cities, transportation systems, and industrial processes [15].Yet, it can lead to increased energy consumption and CO2 emissions.The impact on environmental sustainability can vary, leading to discussions of an inverted U-curve relationship (Khan et al., 2020).Regarding social development, digitalization, particularly through mobile technology, has transformed lives, impacting economic well-being and human development [16].It can promote inclusive human development, education, and even healthcare accessibility.However, the effect of digitalization on inclusive human development varies depending on various factors and dynamics.It also affects health systems by decentralizing healthcare and improving access.Policies should focus on promoting digital inclusion while safeguarding human rights, privacy, and online security (Adam and Alhassan, 2021).From an economic perspective, digitalization can foster sustainable development.It can drive economic growth, productivity, and financial development [17].Moreover, globalization can be bolstered, further stimulating economic growth.However, without economic transformation, digitalization may have detrimental effects on economic growth [18].
In the latest literature, Luo et al. (2022) reported that digitalization enhances sustainable development in indirect ways, such as by improving the industrial structure, enhancing the degree of economic openness, and escalating the market potential, as industrial structure, economic openness, and market potential advance the impact of digital economy on sustainable development in China.He et al. [19] described that digitalization has positively enhanced the sustainable development of China's Marine Manufacturing Industry.The study reported a positive impact of digital technology on China's Marine Manufacturing Industry in which digital trade played a mediating role.Dong & Ullah [20] study proved that digitalization encourages long-run sustainable development in China.The study suggested that digitalization encourages the use of internet and IoT to decouple environmental pollution and sustainable development.Lee et al. [18] also reported the positive influence of digitalization on green growth in China.While, Li et al. (2022) demonstrated that SMEs development is positively related to the sustainable development of their host country's performance.However, technological advancement and demonstration effect play mediating roles.Zhang et al. [21] highlighted the significant role of SMEs to employment generation, regional development, and poverty reduction, aligning with the sustainable development goals.Xiang et al. [22] demonstrated the importance of environmentally friendly practices in improving the competitiveness of SMEs and contributing to overall sustainable development.
The motivation for the study lies in the persistent need to understand the dynamics between SMEs, digitalization, and sustainable development, particularly in the context of China.In recent decades, the association between enterprises, technological advancements, and sustainable development has gained significant importance, yet there exists a prominent gap in understanding the detailed implications within the SMEs and ICT sectors, particularly for a rapidly growing economy like China.The study highlights the importance of ICT and SMEs in shaping economic trajectories and their consequences for sustainable development.Previous studies have examined the impact of digitalization on environmental perspectives; there is a noticeable gap in understanding the impact of digitalization on sustainable development, especially in China.Still, there is a lack of comprehensive research on the impact SMEs development on sustainable development.Prior literature has overlooked the short-run results.This study addresses these gaps by exploring the impact of digitalization and SMEs development on China's sustainable development.The choice of the sample is placed on China as it is rapidly developing economically and technologically.China is a key carbon emitter addressing environmental problems via digitalization.Data has been collected from the World Bank, Freedom House Report, and National Bureau of Statistics of China for the period 1998 to 2020.The study employs ARDL method for empirical estimations.The main contribution of the study is that this study first assesses the impact of digitalization on sustainable development.Secondly, this provides the link between SMEs development and sustainable development.Thirdly, this study offers short and long-run results.Lastly, the findings of this study can guide policymakers in developing strategies and policies that support the digital transformation of SMEs.These policies may include investments in digital infrastructure, digital literacy programs, and regulatory frameworks to create a conducive environment for SMEs.
I. Ozturk et al.
Theoretical framework, model, methodology, and data
SMEs make up 90 percent of all international firms and enterprises, and almost 50 percent of the global workforce is engaged in SMEs [23].Although SMEs are critical in the development of an economy, they often have to face numerous challenges and barriers when it comes to implementing sustainable business practices and efficiently administrating natural resources.The challenges are many but not limited to scarcity of capital, shortage of technical expertise, and restricted access to markets and information [24].The importance of Environmental, social, and governance (ESG) practices and administration of natural capital in SMEs have come under the spotlight in various academic works.These works also underscore the possible advantages of executing sustainable practices.Successful adoption of ESG practices may augment shareholders' trust, control environmental impacts, and enhance competitiveness [25].Achieving excellence in the administration of natural resources may help reduce waste, foster resource efficiency, and protect the ecosystem.Sustainable economic development plays a critical role in achieving long-term economic and environmental goals; nevertheless, sustainable development only becomes realistic after the effective administration of natural resources as well as promoting social justice and realizing ecological significance [26].The incorporation of ESG practices and natural resource management are indispensable tools to attain sustainable growth, especially for SMEs.Therefore, after implementing ESG practices and efficient management of natural resources, SMEs can contribute to sustainable development.
The theoretical connection between the digital economy and sustainable development can be explained in the light of the current body of literature in the following two ways.Firstly, there is a direct connection between digitalization and sustainable development.Due to its inbuilt benefits and characteristics, digitalization introduces new sources of growth that may foster sustainable development [27].By making use of sophisticated information technology, digitalization develop an economic structure that integrates "economies of scale, economies of scope, and the long-tail effect".This unification boosts the balance between supply and demand in the market, resulting in high economic growth.Any development in sophisticated information technology is anticipated to enhance the mitigating efforts [28], which then help attain sustainable economic development.Secondly, there is a connection between digitalization and sustainable development via "industrial agglomerations", which is the process of clustering industries together in certain localitieis [29].The agglomeration helps to combine the resources from different industries, establishing robust industrial interdependencies and cooperative coalitions, resulting a rise in industrial benefits.This improves efficiency, nurtures innovation, fosters competitiveness, and encourages sustainable development.Digitalization employs data to determine user wants, facilitating the right balance between supply and demand, lowering transaction expenses for both sides and boosting demand, thereby fostering industrial agglomeration and sustainable development [30].Thus, we follow Prashar [8] and Nchofoung & Asongu [31] who relied upon the previous standard literature and begin with the following sustainable development model: where; SME, ICT, IQ, and RD represent small and medium-sized enterprises, information and communications technology, institutional quality, research and development, respectively.While λ 0 and ε t denote the intercept and the error term, respectively.λ 1 , λ 2 , λ 3 , and λ 4 are parameters that show the impact of SME, ICT, IQ, and RD, respectively.Digitalization and entrepreneurial SMEs have also favorable effects on sustainable development.Thus, we expect an estimate of λ 1 and λ 2 to be positive.Coefficient estimates of Eq. ( 2) reflect the long-run effects of SMEs, ICT, IQ, and RD on ANS.Previous Eq. ( 1) only offers long-run estimates.Eq. ( 2) has been converted into the error correction format for short-run estimates.
Specification ( 2) is made up of two different types of coefficients, signifying its strength of producing short and long-run estimates at once.First type of coefficients are the ones adjacent to "Δ" indicator, which represent the outcomes in the short-term, while the second type of coefficients are the ones that range from λ 2 − λ 5 normalized on λ 1 represent the outcomes in the long-run.There is a validity issue with the long-run results, which are considered spurious unless we prove cointegration between dependent and independent variables.The solution is provided by the Pesaran et al. [32] by developing two tests, namely the F test and ECM, to assess the validity of the findings.They also tabulated new critical values for these tests.Pre-unit testing is not a condition for this technique because it can deal with variables with diverse integrating characteristics.i.e., I(0) or I(1), which is its main strength and give it an edge over other cointegration techniques [33].Since macroeconomic variables are either I(0) or I(1), and the results of our KPSS unit root test also align with this statement, this provides the justification for selecting ARDL over other time series techniques.Lastly, the results of this technique are valid in the case of the brief sample.This research employs diagnostic testing to check the accuracy of our outcomes.The CUSUM and CUSUM-sq are the tests for parametric stability, while the Remsey RESET and LM tests are applied to check misspecification and serial correlation, respectively.In this study, we use the ARDL methodology as the main method.However, we also use the QARDL model to enhance the reliability of our results, especially when dealing with non-normal data.The QARDL model yields precise estimations in such circumstances.
In this study, the dependent variable sustainable development is proxied by adjusted net savings as % of GNI (ANS).Entrepreneurial SMEs and digitalization are the focused variables.Entrepreneurial SMEs is measured by number of SMEs in a million, and digitalization is measured via ICT (i.e.individuals using internet in total population).The role of institutional quality and research and I. Ozturk et al. development are also added in regression analysis as control variables.The economic freedom index measures institutional quality (IQ), while RD is measured through research and development expenditures as a percent of GDP.The details of the variable series are reported in the Appendix (Table A1).The required data for this study is acquired from the World Bank, Freedom House Report, and National Bureau of Statistics of China for the period from 1998 to 2020.Descriptive statistics of the variables are given in Table 1.The highest mean value is recorded for IQ with a maximum score of 4.086 and a minimum of 3.932, respectively.However, lowest mean score is noted for RD with maximum range 2.401 and minimum range 0.893.Highest S.D is observed for ICT and lowest is noted for IQ.
Empirical results
Before estimating the regression model, it is mandatory to confirm the unit root properties of the data series.For that purpose, we applied the KPSS unit root test.The obtained results are given in Table 2.According to KPSS results, there is a mixed order of integration among variables.For instance, SME, ICT, and RD are stationary at I(0), whereas ANS and IQ are stationary at I(1).Table 3 displays the results of F-test.The obtained value for F-stat is statistically significant, confirming that long-run cointegration association exists among variables.After confirming the unit root characteristics and Cointegration results, the next step is to regress the mode through the ARDL method.The obtained results for short-run parameters are given in Table 4.It is shown that SME report a significant and positive impact on ANS, describing that a 1% increase in SME enhances ANS by 1.141% in the short-run.It confirms the positive role of SME in enhancing sustainable development.The results show that ICT significantly and positively impacts ANS, revealing that a 1% upsurge in ICT enhances ANS by 0.156%.It proves the positive contribution of digitalization in bringing sustainable development to the Chinese economy.Conversely, the IQ impact on ANS is observed as insignificant in the short run, disclosing that IQ does not play any role in bringing sustainable development in the short-run.RD and ANS are associated with positivity in the short-run.It shows that a 1% upsurge in RD tends to enhance ANS by 0.465% in the short-run.
The output for long-run parameters is displayed in Table 5.It infers that SMEs significantly and positively influence ANS, revealing that SMEs tend to enhance sustainable development significantly in China.The results depict that a 1% upsurge in SME augments ANS by 0.613%.Hence, the long and short-run findings confirm that SME is a fundamental determinant of sustainable development.In terms of digitalization role, the results display that ICT also reports a significant and positive impact on ANS as found in the short-run.It confirms that digitalization tends to augment sustainable development in China.It is found that a 1% upsurge in ICT augments ANS by 0.433% in the long-run.The impact of IQ on ANS is found to be significantly positive in the long-run, confirming that a good quality institutional framework improves sustainable economic development.The findings imply that a 1% improvement in IQ enhances ANS by 0.205%.RD and ANS are positively associated in the long run, implying that RD significantly enhances sustainable development.It shows that a 1% upsurge in RD enhances ANS by 1.094% in the long-run.
Table 6 displays the results of diagnostic tests such as ECM, LM, BPG, and RESET.These tests are important to confirm the validity of ARDL estimates.The ECM term is significant and negative confirming that there is the possibility of achieving stability in the longrun.The ECM term is − 0.173 which shows that almost 17% stability will be achieved in the span of one year.The results of LM and BPG tests confirm that no issue of autocorrelation and heteroskedasticity is detected in the model.In the end, the RESET test result confirms that the model is correctly specified.The CUSUM tests also show stability in graphs (Fig. 1).Finally, an adjusted R2 of 0.547 shows a good fit.
The output from the QARDL model is shown in Table 7.It shows that the estimates of ECM are significant and negative overall quantiles, confirming the long-term association between ANS, SME, ICT, IQ, and RD.The long-run estimates of SME are positive and significant from the 50th to 95th quantiles, while in the short-run, they are significant at all quantiles.However, the estimates of ICT are positive and significant only in the long run at all quantiles.The long-run estimates of IQ are significant from the 70th to 95th quantiles, and the estimates of RD are significantly positive at all quantiles.In the short run, the estimates of IQ are significantly positive in the last two quantiles only, while the estimates of RD are significantly positive from the 60th quantiles onwards.These results suggest that the QARDL model provides more significant results in the long run, where SME, ICT, IQ, and RD all have a favorable impact on ANS at most intensities of ANS.
Results discussion
Our empirical results are backed by Prashar [8], who denoted that SMEs positively enhance sustainable development through increased economic growth, employment, and poverty reduction.Abisuga-Oyekunle et al. [6] jobs, stimulate entrepreneurship, and foster innovation.By providing employment opportunities, SMEs enhance social well-being and reduce poverty.The study of Smith et al. [34] supported our results and noted that SMEs contribute significantly to technology diffusion within communities.SMEs catalyze positive environmental changes by embracing digital technologies, implementing sustainable practices, and promoting eco-friendly innovations.This aligns with SDGs 9 (industry, innovation, and infrastructure), emphasizing the importance of fostering innovation for sustainable development.SMEs are considered as an instrument of change that can boost sustainability at the national and international levels.SMEs are flexible enough and capable of adopting sustainable practices in their operations, products, and services.These empirical inferences are also supported by Westman et al. [35], who observed that a positive connection exists between SMEs and sustainability.According to Liu et al. [36], if SMEs have been provided with venture capital, they can grow in a sustainable manner due to the provision of funds, supervision, and noncapital value-added services.In addition, Platonova and Maksakova [37] suggest that full-fledged assistance for SMEs (e.g.cooperation with large enterprises), can increase their ability to overcome several hurdles and support them to participate in international value chains, fostering sustainable development.Further, the role of SMEs can not be underestimated in fostering economic growth, enhancing employment opportunities, and offering innovative ideas for sustainable development.
The study of Nchofoung & Asongu [31] supports our findings by arguing that digitalization contributes to sustainable development in many ways, such as economic growth, financial stability, and environmental sustainability.Vyas-Doorgapersad [38].argued that ICT helps develop transportation infrastructure, smarter cities, industrial processes, electrical grids, and energy growth, thus contributing to sustainable development.Tjoa & Tjoa [39] highlight that digitalization improves the information flow and augments financial integration, thus enhancing sustainable development.Kendall & Dearden [40] denote that digitalization enhances sustainable development by improving society's social, environmental, and economic dimensions.The ICT findings also infer that ICT fosters economic growth by promoting innovation, entrepreneurship, and digital economies.E-commerce platforms, digital marketplaces, and online banking services enable businesses, especially SMEs, to expand their reach and access global markets.Digital innovation and automation enhance productivity and efficiency, driving sustainable development [15].Moreover, ICT promotes digital inclusion by providing internet access and digital literacy training to underserved communities.Bridging the digital divide ensures that marginalized populations have access to information, education, healthcare, and economic opportunities, thus promoting sustainable development [18].
The result of institutional quality is consistent with Azam et al. [41], who noted that institutional quality favours sustainable development via effective governance.This means that good institutional quality promotes sustained economic growth and development.Sound institutions provide a favorable environment for individuals, businesses, and communities, thereby contributing to long-term sustainable development.These empirical inferences support sustainable development [42].The findings are also backed by Niesten et al. [43], who reported the positive role of well-functioning institutions in shaping environmental sustainability practices, emphasizing that such institutions facilitate the enforcement and adoption of eco-friendly policies that lead to sustainable development.Strong institutions play a vital role in maintaining the rule of law, preserving human rights, and fighting against corruption.All these factors, according to Jahanger et al. [44], are helpful in achieving sustainable development.The results also revealed that institutional quality has a crucial role to play in achieving SDGs due to its contribution to the development of peaceful and inclusive societies, which have important characteristics of access to justice and effective, answerable, and transparent institutions.The study of Ren et al. [45] also confirmed that institutional quality is highly supportive in attracting foreign direct investment from abroad, which is crucial in bringing clean and green technology to the home nation and thus supporting sustainable development.
The result of RD is consistent with Aldieri et al. [46], who reported that the R&D role in technological advancements leads to more resource-efficient and eco-friendly practices, thus enhancing sustainable development.The study of Mo et al. [47] illustrated similar results and noted that R&D activities contribute to increased economic growth, job creation, and productivity, thus positively influencing sustainable development.These outcomes are also supported by green growth theory [48], which argues that R&D is a key pillar of sustainable development goals.According to Sánchez-Sellero & Bataineh [49], firms can achieve environmental sustainability with the help of R&D.By emphasizing R&D activities, organizations can help develop their production techniques in line with the principle of sustainability and produce products that keep pace with technological advancement, resulting in the achievement of the ecological aspect of sustainable marketing.Roper et al. [50] stated that the positive externalities that emerge as a result of R&D activities in the area of innovation diffusion have a significant role in creating new ideas by ensuring access to information, thus fostering economic growth and protecting the environment simultaneously.
Conclusion and implications
It has been shown that there is a significant correlation between global temperature variations and total emissions.Indeed, there is a strong likelihood that anthropogenic actions since the middle of the 20th century have produced GHGs, leading to an apparent rise in the world's temperature.Due to the increased burning of traditional energy sources, CO2 releases make up around 75% of the world's emissions.Over the recent 40 years, human activities have increased CO2 emissions, with non-renewable energy use accounting for up to 2/3 of the total world pollution level.In order to combat the problem of environmental degradation due to rising CO2 emissions levels, sustainable development is the most viable option for the world community.In this regard, the role of SMEs can be crucial because they are trying their best to transform their structure in the light of sustainable development.Moreover, the role of ICT is important in making economies more digitalized.Digitalization effectively converts the economy into a weightless economy, which is crucial in achieving sustainable economic development.Therefore, the analysis aims to investigate the impact of SMEs and ICT on sustainable development.
For empirical analysis, we have first conducted the KPSS unit root test that has confirmed that the series in the model is a mixture of I(0) and I(1); hence, we can apply the ARDL model, which can accommodate both I(0) and I(1) variables.The short and long-run estimates attached to SMEs are significant and positive, confirming that SMEs help to achieve sustainable development.Similarly, the estimates attached to ICT are positive and significant both in the short and long run, confirming the beneficial role of ICT in achieving sustainable development.The estimates attached to institutional quality and R&D control variables are positive and significant in the long run, but only RD estimates are significant in the short run.
We have utilized the findings of the studies to provide policy suggestions.The role of SMEs is crucial in achieving sustainable development; hence, the policymakers must facilitate the SMEs in transforming their structure to be more environmentally friendly.In this regard, SMEs must completely renovate their structures and align them with sustainable guidelines by introducing green practices.Moreover, the authorities in China must remove financial and institutional hurdles in the way of developing SMEs that pledge to perform their business activities without damaging the balance of the ecosystem, thus promoting sustainable development.Policymakers can use the findings of the study to formulate targeted policies that incentivize the digital transformation of SMEs.SMEs should align their strategies with sustainable development goals by incorporating eco-friendly practices.SMEs should make strategic decisions focusing on innovations and technology adoption that increase efficiency, reduce environmental impact, and contribute to sustainable development goals.ICT-based remedies to energy intensity, transportation, and resource usage may enhance environmental quality if used more effectively.Widespread application and acceptance of ICT in society would be an important strategy for the sustainable development of China because ICT relies more on information resources, leading to the foundation of a weightless, dematerialized, and digitalized economy.Hence, policymakers must try to increase the role of ICT in every sector of the economy that would significantly contribute to sustainable development.Implement nationwide digital literacy programs targeting SMEs owners and employees.These programs should focus on imparting essential digital skills, fostering a culture of innovation, and ensuring that SMEs can harness digital technologies effectively for sustainable development initiatives.Provide financial support, subsidies, and tax incentives to SMEs that invest in digitalization efforts aligned with sustainable practices.Establish dedicated funds to assist SMEs in adopting eco-friendly technologies, implementing energy-efficient processes, and enhancing overall digital infrastructure.Facilitate partnerships between SMEs, government agencies, and private technology firms.These partnerships can provide technical expertise, training, and access to green technologies.By implementing these policy suggestions, China can create an enabling environment for SMEs to embrace digitalization while advancing sustainable development goals.These initiatives can enhance SMEs' competitiveness, promote innovation, and contribute to a greener, more inclusive green economy.
The study has certain shortcomings which need to be highlighted.Since most macroeconomic variables move asymmetrically, our analysis does not estimate the asymmetric impact of SMEs and digitalization on sustainable development.Therefore, future studies must emphasize capturing the asymmetric relationship between SMEs, digitalization, and sustainable development.Another critical shortcoming of the study is its dependence on time series data, which only estimates the relationship in one country.The scope of the study in the context of policy implications remains limited.The study is also limited to using time-series data from 1998 to 2020.In the future, economists should try to gather data for advanced and emerging economies that would increase the effectiveness of the study's results in terms of policy implications.
Table 1
support our findings by arguing that SMEs play a fundamental role in economic structure and generate economic and social benefits, thus augmenting sustainable development.These empirical inferences indicate that SMEs are crucial contributors to sustainable development because they create Descriptive statistics of the variables.
Table 3
F bounds test.
Table 7
Long and short-run estimates-QARDL.
I.Ozturk et al. | 6,448.4 | 2024-03-01T00:00:00.000 | [
"Environmental Science",
"Business",
"Economics"
] |
Profiling of Metabolic Differences between Hematopoietic Stem Cells and Acute/Chronic Myeloid Leukemia
Although many studies have been conducted on leukemia, only a few have analyzed the metabolomic profiles of various leukemic cells. In this study, the metabolomes of THP-1, U937, KG-1 (acute myelogenous leukemia, AML), K562 (chronic myelogenous leukemia, CML), and cord blood-derived CD34-positive hematopoietic stem cells (HSC) were analyzed using gas chromatography-mass spectrometry, and specific metabolic alterations were found using multivariate statistical analysis. Compared to HSCs, leukemia cell metabolomes were found to have significant alterations, among which three were related to amino acids, three to sugars, and five to fatty acids. Compared to CML, four metabolomes were observed specifically in AML. Given that overall more metabolites are present in leukemia cells than in HSCs, we observed that the activation of glycolysis and oxidative phosphorylation (OXPHOS) metabolism facilitated the incidence of leukemia and the proliferation of leukemic cells. Analysis of metabolome profiles specifically present in HSCs and leukemia cells greatly increases our basic understanding of cellular metabolic characteristics, which is valuable fundamental knowledge for developing novel anticancer drugs targeting leukemia metabolism.
Introduction
Leukemia, a type of hematologic malignancy, occurs when immature white blood cells grow abnormally. Leukemia is known to be related to carcinogenic genes, chromosomal abnormalities, or bone marrow damage caused by viruses, radiation, or chemicals. It can be acute or chronic, depending on 2 of 12 its progress pattern. Additionally, it can be myeloid or lymphocytic in nature, depending on the type of white blood cells affected. Generally, acute leukemia occurs when immature hematopoietic stem cells (HSC) develop into malignant tumor cells, whereas chronic leukemia occurs when partially matured hematopoietic cells are transformed [1][2][3]. Similar to other cancers, leukemia cells show obvious genetic variation and reprogram nutrition acquisition and metabolic pathways to meet the demands for bioenergy, biosynthesis, and oxidation-reduction [4]. Generally, to meet the increased nutritional demand, cancer cells undergo metabolic reprogramming of ATP via conversion of pyruvate to lactate rather than channeling it to the tricarboxylic acid (TCA) cycle and oxidative phosphorylation (OXPHOS) in mitochondria [5,6]. However, recently, aerobic glycolysis and OXPHOS metabolism have been found to be actively involved in cancer cell growth and division [7]. Hence, each cell has a unique metabolic mechanism depending on cell fate, and thus, has a different type of metabolome. Therefore, metabolic profiling research has drawn much attention as an approach for immediate detection of dynamic cellular alteration and status, such as oncogenesis.
The metabolome is a set of metabolites that can be used to quantify phenotypes in cells, tissues, and diseases [8]. Through metabolome profiling, it is possible to provide basic physiological information on phenotype expression independently or in combination with gene expression data. It is also possible to identify, quantify, and systematically determine the shift of metabolomes in cells or tissues, which helps in providing a better understanding and re-analysis of metabolome networks in association with the physiologic and pathologic states of the metabolome group. It further allows for the elucidatation of disease-specific metabolome alterations in the network model. By detecting and defining the main metabolic changes in a disease state and comparing them with the metabolomic profile in the normal state, it is possible to identify the cause of disease [9,10]. In particular, the detection of alterations in a few metabolomes allows early diagnosis of disease. Further, metabolome profiling-based classification makes it easier to identify diagnostic and other biomarkers through a clustering pattern analysis. With metabolome-directed disease detection, especially the detection of a new metabolic mechanism, which may be the direct cause of a disease, the challenges related to the medicinal efficacy and adverse effects of existing drugs can be overcome, and new drugs for intractable diseases can be developed.
Unlike normal cells, cancer cells metabolize glucose by glycolysis rather than by producing ATP via further oxidative phosphorylation. Even in the presence of oxygen, many cancer cells produce ATP by abnormally depending on glycolysis. This is known as the Warburg effect (a process called aerobic glycolysis), the main characteristic of cancer cell metabolism [11]. This metabolic alteration resulting from DNA mutation does not mean that the cancer cell lacks respiratory capacity. Via aerobic glycolysis, intermediates in the process are converted to biosynthetic pathways, thereby generating nucleotides, lipids, and amino acids required by the fast proliferating cells. Therefore, metabolic alteration is considered to be necessary for cell growth and division. It is known that metabolic alterations in cancer cells inhibit immune responses against them and help activate oncogenes [12]. Since the Warburg effect is a critical change during tumorigenesis, it is important to accurately determine the metabolic mechanism of cancer cells to develop anticancer drugs. In addtion the oxidative phosphorylation in some cancer cells, including leukemias, lymphomas, pancreatic ductal adenocarcinomas, high OXPHOS subtype melanomas, and endometrial carcinomas, fails to be suppressed and cancer growth continues unabated [7].
Metabolomic profiling of tumor cells helps predict a patient's present condition and changes that may occur in the future. Therefore, metabolomic reprogramming can be applied for oncotherapy [13]. In this study, gas chromatography was used to determine the metabolome expression in cell lines derived from acute myelogenous leukemia (AML), chronic myelogenous leukemia (CML), and cord blood (V-derived CD34 positive hematopoietic stem cells (HSCs) and to select a common metabolome between AML and CML for the identification of novel putative diagnostic biomarkers for leukemia.
Metabolic Differences between HSCs and Leukemia Cell Lines
To analyze the specific metabolites of leukemia cells, three AML cell lines and one CML cell line were purchased from the American Type Culture Collection (ATCC). These cells, alongside normal blood cells and cord blood-derived HSCs, were cultured individually. Samples analyzed using GC-TOF-MS were used for further multivariate analysis of each feature. After that, by comparing the integrated metabolites, the relative abundance of metabolites for each cell population was quantified. We performed principal component analysis (PCA) and partial least squares-discriminant analysis (PLS-DA) to develop a visual plot for evaluating differences and consistencies in the metabolite profiles of four leukemia cell lines and HSC. The principal component (PC) scores used for PCA plotting increased for different cell types. Our PCA plot indicates that the normal control HSCs were clearly clustered from the leukemia cell line groups (THP-1, U-937, KG-1, and K562) along with PC1 (32.14%). Along with PC2 (15.37%), the normal control HSC and acute leukemia cell lines were clearly clustered from the chronic leukemia cell line groups (K-562) ( Figure 1A). PLS-DA with model values of R 2 X (cum) = 0.580, R 2 Y (cum) = 0.930, and Q 2 (cum) = 0.930 indicated that the fitness and prediction accuracy of the model were similar to the PCA results ( Figure 1B). The quality of the model was evaluated by cross-validation analysis (p = 0.012858). PCA and PLS-DA showed obvious differences in the metabolite profiles of these cell types. Similar metabolite profiles between the cell types indicate that they are closely related in their metabolic properties, and hence, cell fate.
Metabolites 2020, 10, x FOR PEER REVIEW 3 of 12 select a common metabolome between AML and CML for the identification of novel putative diagnostic biomarkers for leukemia.
Metabolic Differences between HSCs and Leukemia Cell Lines
To analyze the specific metabolites of leukemia cells, three AML cell lines and one CML cell line were purchased from the American Type Culture Collection (ATCC). These cells, alongside normal blood cells and cord blood-derived HSCs, were cultured individually. Samples analyzed using GC-TOF-MS were used for further multivariate analysis of each feature. After that, by comparing the integrated metabolites, the relative abundance of metabolites for each cell population was quantified. We performed principal component analysis (PCA) and partial least squares-discriminant analysis (PLS-DA) to develop a visual plot for evaluating differences and consistencies in the metabolite profiles of four leukemia cell lines and HSC. The principal component (PC) scores used for PCA plotting increased for different cell types. Our PCA plot indicates that the normal control HSCs were clearly clustered from the leukemia cell line groups (THP-1, U-937, KG-1, and K562) along with PC1 (32.14%). Along with PC2 (15.37%), the normal control HSC and acute leukemia cell lines were clearly clustered from the chronic leukemia cell line groups (K-562) ( Figure 1A). PLS-DA with model values of R 2 X(cum) = 0.580, R 2 Y(cum) = 0.930, and Q 2 (cum) = 0.930 indicated that the fitness and prediction accuracy of the model were similar to the PCA results ( Figure 1B). The quality of the model was evaluated by cross-validation analysis (p = 0.012858). PCA and PLS-DA showed obvious differences in the metabolite profiles of these cell types. Similar metabolite profiles between the cell types indicate that they are closely related in their metabolic properties, and hence, cell fate.
Hierarchical Clustering between HSCs and Leukemia Cell Lines
To select the metabolites responsible for the differences observed in Section 2.1, variable importance to projection (VIP) values > 0.7 of PLS-DAs were used. The VIP value is an important parameter for detecting potential biomarker candidates and possible pathways, including those involved in diseases that reflect the correlation of the metabolites with different biological states. For evaluating statistical significance, p < 0.05 derived from the one-way ANOVA was applied [14,15]. Selected metabolites were identified by comparing MS fragment patterns with commercial standard compounds and various databases, including the National Institutes of Standards and Technology (NIST) library, the Human Metabolome Database (HMDB, http://www.hmdb.ca/), and Wiley 9 [14,15]. Detailed information regarding these metabolites is presented in Table 1. A total of 43 metabolites, including five organic acids, eight amino acids, five sugars/sugar alcohols, eight fatty acids/lipid, three electron transport chains, and 14 unknown metabolites, were identified that differed significantly among the experimental groups.
Hierarchical Clustering between HSCs and Leukemia Cell Lines
To select the metabolites responsible for the differences observed in Section 2.1, variable importance to projection (VIP) values > 0.7 of PLS-DAs were used. The VIP value is an important parameter for detecting potential biomarker candidates and possible pathways, including those involved in diseases that reflect the correlation of the metabolites with different biological states. For evaluating statistical significance, p < 0.05 derived from the one-way ANOVA was applied [14,15]. Selected metabolites were identified by comparing MS fragment patterns with commercial standard compounds and various databases, including the National Institutes of Standards and Technology (NIST) library, the Human Metabolome Database (HMDB, http://www.hmdb.ca/), and Wiley 9 [14,15]. Detailed information regarding these metabolites is presented in Table 1. A total of 43 metabolites, including five organic acids, eight amino acids, five sugars/sugar alcohols, eight fatty acids/lipid, three electron transport chains, and 14 unknown metabolites, were identified that differed significantly among the experimental groups. Our findings demonstrate the major differences in the metabolomic profiles of leukemia cells and normal HSC. As metabolite differences between these cells may have significant phenotypic consequences and include biomarkers for leukemia, we identified metabolites that differed between these different cell types. To obtain comprehensive metabolite accumulation patterns in our experimental cell groups, metabolites were organized by hierarchical clustering analysis (HCA; Figure 2), which revealed six clusters. The six clusters were based on the metabolites that were distinctively expressed in each cell type. Cluster 1 contained metabolites, such as threonine, cortisol, and salicylic acid, with relatively higher accumulation in HSCs, KG-1, and K562 cells. Cluster 2 was specifically expressed in HSCs and included fructose, lysine, phosphoric acid, succinic acid, myristic acid, glucose, saccharide, serine, and palmitic acid. Cluster 3 included metabolites such as pyruvic acid, linoleic acid, hydroxylamine, ornithine, and oleamide, which were specifically expressed in leukemia cell lines. Metabolites such as saccharide, phosphorylethanolamine, and alpha-palmitin from Cluster 4 were expressed in THP-1 and U937 cells. The metabolites belonging to Clusters 3 and 4 were relatively highly expressed compared to HSC, and Cluster 4 is a metabolite that was relatively highly expressed in THP-1 and U937 cells. Cluster 5 was specifically expressed in K562 cells as an AML and included glycine, aspartic acid, malic acid, 5-oxo-proline, beta-alanine, citric acid, and myo-inositol. Metabolites, such as lactic acid, oleic acid, and cholesterol from Cluster 6 were expressed in U937 and K562 cells. The HCA also grouped these samples separately according to the metabolic status, which suggests that differences in cell metabolite characteristics between leukemias and normal HSCs may reflect the reprogramming of metabolic systems during disease development.
Metabolites 2020, 10, x FOR PEER REVIEW 6 of 12 Our findings demonstrate the major differences in the metabolomic profiles of leukemia cells and normal HSC. As metabolite differences between these cells may have significant phenotypic consequences and include biomarkers for leukemia, we identified metabolites that differed between these different cell types. To obtain comprehensive metabolite accumulation patterns in our experimental cell groups, metabolites were organized by hierarchical clustering analysis (HCA; Figure 2), which revealed six clusters. The six clusters were based on the metabolites that were distinctively expressed in each cell type. Cluster 1 contained metabolites, such as threonine, cortisol, and salicylic acid, with relatively higher accumulation in HSCs, KG-1, and K562 cells. Cluster 2 was specifically expressed in HSCs and included fructose, lysine, phosphoric acid, succinic acid, myristic acid, glucose, saccharide, serine, and palmitic acid. Cluster 3 included metabolites such as pyruvic acid, linoleic acid, hydroxylamine, ornithine, and oleamide, which were specifically expressed in leukemia cell lines. Metabolites such as saccharide, phosphorylethanolamine, and alpha-palmitin from Cluster 4 were expressed in THP-1 and U937 cells. The metabolites belonging to Clusters 3 and 4 were relatively highly expressed compared to HSC, and Cluster 4 is a metabolite that was relatively highly expressed in THP-1 and U937 cells. Cluster 5 was specifically expressed in K562 cells as an AML and included glycine, aspartic acid, malic acid, 5-oxo-proline, beta-alanine, citric acid, and myo-inositol. Metabolites, such as lactic acid, oleic acid, and cholesterol from Cluster 6 were expressed in U937 and K562 cells. The HCA also grouped these samples separately according to the metabolic status, which suggests that differences in cell metabolite characteristics between leukemias and normal HSCs may reflect the reprogramming of metabolic systems during disease development.
Metabolic Differences Observed between HSCs and Leukemia Cell Lines Suggest Novel Putative Metabolic Biomarkers
Following the metabolomic analysis of HSC control and leukemia cell lines, various metabolites were selected as candidate biomarkers by multivariate analysis, and we generated a metabolic pathway to show the distribution and the relationships among these metabolites (Figure 3). These metabolites belong to pathways relating to amino acids, carbohydrates, and fatty acid biosynthesis. The relative levels of the metabolites were dramatically different between normal HSC control and leukemia cell lines. Carbohydrate metabolism linked to glucose and saccharide appeared to be upregulated in HSCs but downregulated in leukemia cell lines. In contrast, the metabolic pathways related to amino acid biosynthesis (glycine, aspartic acid, ornithine, lysine, 5-oxo-proline, and beta-alanine) were upregulated in leukemia compared to HSC. However, unlike other amino acid metabolites, serine was relatively downregulated in leukemia cell lines. Significant induction of these compounds (pyruvate, lactic acid, citric acid, and malic acid) coupled with intermediate glucose metabolism contents in leukemia cell lines suggest their collective contribution to leukemia development. However, normal HSCs showed higher levels of glucose in cellular metabolites than leukemia cell lines. Therefore, from these data, we suspected that glucose consumption might enhance leukemia cell metabolism to maintain the cancerous phenotype by increasing the levels of glycolysis and TCA intermediate metabolites to meet the heightened energy demands.
Metabolic Differences Observed between HSCs and Leukemia Cell Lines Suggest Novel Putative Metabolic Biomarkers
Following the metabolomic analysis of HSC control and leukemia cell lines, various metabolites were selected as candidate biomarkers by multivariate analysis, and we generated a metabolic pathway to show the distribution and the relationships among these metabolites (Figure 3). These metabolites belong to pathways relating to amino acids, carbohydrates, and fatty acid biosynthesis. The relative levels of the metabolites were dramatically different between normal HSC control and leukemia cell lines. Carbohydrate metabolism linked to glucose and saccharide appeared to be upregulated in HSCs but downregulated in leukemia cell lines. In contrast, the metabolic pathways related to amino acid biosynthesis (glycine, aspartic acid, ornithine, lysine, 5-oxo-proline, and beta-alanine) were upregulated in leukemia compared to HSC. However, unlike other amino acid metabolites, serine was relatively downregulated in leukemia cell lines. Significant induction of these compounds (pyruvate, lactic acid, citric acid, and malic acid) coupled with intermediate glucose metabolism contents in leukemia cell lines suggest their collective contribution to leukemia development. However, normal HSCs showed higher levels of glucose in cellular metabolites than leukemia cell lines. Therefore, from these data, we suspected that glucose consumption might enhance leukemia cell metabolism to maintain the cancerous phenotype by increasing the levels of glycolysis and TCA intermediate metabolites to meet the heightened energy demands.
Discussions
The metabolome refers to the collection of all low molecular weight (10-1000 Da) metabolites in a biological cell, tissue, organ, or biological fluid. Metabolomes are produced as the final stage of biological processes and help to maintain cellular homeostasis. They are also useful for monitoring systemic changes in a living organism that cannot be understood via gene expression and proteome alteration studies alone. Metabolomic profiles provide actual snapshots of physiological conditions within biological systems by establishing a network of low molecular metabolites influenced by various genetic, physiological, pathological, or environmental factors. Thus, a comprehensive analysis of metabolomes can highlight the variations observed with physiological and disease states and may help to elucidate the basis for the observed differences. This offers valuable information for investigating the biological mechanisms influencing disease phenotypes. Accordingly, metabolome-based biomarkers can help identify specific phenotypes and serve as primary markers for determining the mechanism and basis for vital phenomena [16,17]. Here, we profiled the metabolomes of three types of AML-derived cell lines (TH-1, KG-1, and U937 cells) and one CML-derived cell line (K562), and compared our results with those obtained from normal HSCs. We defined the specifically expressed metabolomes in each cell line, verified the characteristics of each leukemia cell line, and proposed potential biomarkers. Following the metabolomic analysis of leukemia cell lines and normal HSCs, various metabolites and metabolic pathways were evaluated via multivariate analysis to identify candidate biomarkers (Figures 1 and 2). Further, we linked various pathways related to amino acids, carbohydrates, and fatty acid metabolism to highlight the relationships among these metabolites (Figure 3).
The THP-1 cell line used in this study is a human leukemia monocytic cell line derived from the peripheral blood of a one-year-old patient with acute monocytic leukemia [18,19]. This cell line expresses a high level of citric acid (organic acid), myo-inositol (sugars and sugar alcohols), oleamide, alpha-palmitin, and cholesterol (fatty acids and lipids), but lower levels of saccharide, phosphoric acid, succinic acid, and myristic acid than do HSCs ( Figure S1). The human monoblastic leukemia cell line U937, which is a valuable model for analyzing monocyte-macrophage differentiation, was isolated from the histiocytic lymphoma of a 37-year-old male patient and harbors the t(10;11)(p13;q14) translocation [20,21]. This cell line expresses higher levels of citric acid (organic acid), myo-inositol (sugars and sugar alcohols), oleamide, alpha-palmitin, and cholesterol (fatty acids and lipids), but lower levels of glucose, saccharide, cortisol, myristic acid, succinic acid, phosphoric acid, pyruvic acid, and lysine than do HSCs ( Figure S2). It was possible to differentiate THP-1 and U937 monocytic circulatory leukemic cells, based on having similar abnormalities in the 11q23 translocation, into various types of macrophages or dendritic cells in vitro [22,23]. The basic difference between the two cell types is their origin and maturity. Since they can differentiate into tissues, they are more mature, whereas THP-1 cells are less mature as they originate from leukemic cells [19]. THP-1 and U937 as monocytic leukemia cells specifically expressed alpha-palmitin, and saccharides were relatively overexpressed in both cell lines compared to that of other leukemia cell lines. When THP-1 and U937 were compared to each other, THP-1 expressed more citric acid, hydroxylamine, oleamide, lysine, and oleic acid.
The KG-1 cell line was established from bone marrow cells of a patient with erythroleukemia evolving to AML with considerable pleomorphism with a predominance of myeloblasts and promyelocytes, and it harbors a partial hexasomy of the long arm of chromosome 8 [24]. This cell line expresses high levels of citric acid (organic acid), myo-inositol (sugars and sugar alcohols), oleamide, alpha-palmitin, cholesterol (fatty acids and lipids), and 5-oxo-proline (amino acids) compared to the levels produced by HSCs ( Figure S3).
The human chronic myeloid leukemia K562 cell line is the first human immortalized erythroleukemia cell line established from a 53-year-old female CML patient [25,26]. Unlike CML, AML cell lines showed abnormal growth of undifferentiated and nonfunctional hemocytoblasts (leukemia blasts). However, in CML, cells carrying the Philadelphia chromosome express the Bcr-Abl fusion protein, are relatively mature, and have excessively accumulated abnormal white blood cells [27]. K562 highly expressed citric acid and malic acid, myo-inositol (sugars and sugar alcohols), oleamide, alpha-palmitin, cholesterol (fatty acids and lipids), 5-oxo-proline, beta-alanine, glycine, and aspartic acid (amino acids) compared to the levels produced by HSCs ( Figure S4). Furthermore, they expressed at relatively higher levels myo-inositol, fructose, malic acid, glucose, cholesterol, 5-oxo-proline, beta-alanine, and citric acid metabolites compared to those produced by AML cell lines (THP-1, U937, and KG1). Especially, K562 was confirmed to have increased amino acid metabolites expression compared to that of AML.
To analyze the specific metabolomes of leukemia cells, this study used CD34+ cells extracted from human cord blood as normal control. CD34+ HSCs are precursors for producing all blood cell types and feature self-renewal and differentiation. One of the many proposed causes of leukemia is that HSCs can accumulate multiple mutations within a short period, and the existing ability for asymmetric differentiation and self-renewal can result in carcinogenic mutation [28,29]. Since normal HSCs and leukemic cells share self-renewal and diverse developmental pathways, HSCs with accumulated genetic variation are highly likely to be the origin of leukemia [30]. Hence, comparing and analyzing metabolism in HSCs and leukemia cells can help identify metabolic processes unique to each cell type and reveal the different mechanisms behind their differentiation and self-renewal. This, in turn, would provide important information for the development of drugs targeting leukemia metabolism. From our data, we infer that HSCs produce higher levels of succinic acid/serine/glucose/saccharide/palmitic acid/oleic acid/stearic acid than do leukemia cell lines. In contrast to a previous study in which fatty acid oxidation was critical for the growth of acute leukemia cells, the findings of our study reveal that fatty acid biosynthesis is downregulated in leukemia cell lines compared to that in HSCs [31,32].
Similar to a previous report, our metabolite profiling study also revealed that leukemia cell lines produce an overall higher number of metabolites compared to that of HSCs, possibly owing to a high rate of aerobic glycolysis associated with cancer cells [33,34]. Both glycolysis and OXPHOS are activated in leukemia cells owing to the enhanced need for energy metabolism and synthesis of intermediates to support cancer occurrence and development. Although these study results have helped to improve the understanding of leukemia cell metabolism, no new metabolic program for controlling the start and progress of leukemia could be suggested. Therefore, further studies focusing on multiple metabolic pathways using various systems and approaches are warranted to understand the alterations in metabolism and propose reliable biomarkers.
Sample Collection and Preparation for Metabolite Analysis
Metabolites were extracted from leukemia cell lines as described by He et al. [14] with some modifications. Briefly, cell samples were extracted with 100% methanol (1 mL) and 10 µL internal standard solution (2-chlorophenylalanine, 1 mg/mL in water) using an MM400 mixer mill (Retsch ® , Haan, Germany) at a frequency of 30 s −1 for 10 min, followed by 10 min of sonication. Subsequently, the extracted samples were centrifuged at 10,000 rpm for 10 min at 4 • C, and the supernatants were filtered using 0.2-µm polytetrafluorethylene (PTFE) filters (Chromdisc, Daegu, Korea). The filtered supernatants were completely dried using a speed vacuum concentrator (Biotron, Seoul, Korea). The final concentration of the analyzed sample was 10 mg/mL.
Gas Chromatography-Time-of-Flight Mass Spectrometry Analysis
Gas chromatography-time-of-flight mass spectrometry (GC-TOF-MS) analysis was performed using an Agilent 7890A gas chromatograph system coupled with an Agilent 7693 autosampler (Agilent, Atlanta, GA, USA) as previously described [15]. For analysis, all dried samples were oximated with 50 µL of methoxyamine hydrochloride (20 mg/mL in pyridine) for 90 min at 30 • C and silylated with 50 µL of MSTFA for 30 min at 37 • C. The derivatized sample (1 µL) was injected into the GC-TOF-MS instrument in the split-less mode. The temperatures of the injector and ion source were maintained at 250 • C and 230 • C, respectively. The column temperature was sustained at 75 • C for 2 min and then raised to 300 • C at 15 • C/min and subsequently maintained for 3 min. The acquisitions were recorded at the rate of 10 scans/s with a mass scan range of 50-1000 m/z. The GC-TOF-MS analysis was performed with three repetitive chromatographic runs for each sample extracts. Discriminant metabolites were identified by comparing the retention times and mass fragment patterns with those of standard compounds, the NIST database (version 2.0, 2011, FairCom, Gaithersburg, MD, USA), and an in-house library.
Data and Statistical Analysis
MS data processing and multivariate statistical analysis were conducted as previously described [15]. Significantly different metabolites derived from GC-TOF-MS data were tentatively identified using standard compound retention time and MS fragments. Moreover, we confirmed the MS spectrum data for selected metabolites with in-house libraries and available web databases, including Wiley 9, the NIST database (Version 2.0, 2011 FairCom; Gaithersburg, MD, USA), and the Human Metabolome Database (HMDB; http://www.hmdb.ca/). Statistical analysis was performed using PASW Statistics (IBM SPSS Inc., Chicago, IL, USA). The significantly discriminant metabolites from the analytical datasets were selected based on the variable importance in projection, VIP > 0.7 at p < 0.05. Further, the significant differences (p value < 0.05) among the selected metabolites were evaluated through one-way ANOVA using STATISTICA 7 (Stat Soft Inc., Tulsa, OK, USA). Results with p < 0.05 were considered statistically significant.
Conclusions
In conclusion, based on our results, we confirmed that the AML and CML cell lines analyzed in this study have higher overall metabolic activity than do HSCs, which may be attributed to the accumulation of chromosomal abnormalities. Compared to HSCs, we confirmed specifically increased expression of the citric acid, myo-inositol, oleamide, alpha-palmitin, and cholesterol metabolites in leukemia cell lines. These results provide information that may help identify leukemia cell-specific metabolites and related mechanisms in future studies. | 6,154.4 | 2020-10-26T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Phase I study of the anti-FcRH5 antibody-drug conjugate DFRF4539A in relapsed or refractory multiple myeloma
FcRH5 is a cell surface marker enriched on malignant plasma cells when compared to other hematologic malignancies and normal tissues. DFRF4539A is an anti-FcRH5 antibody-drug conjugated to monomethyl auristatin E (MMAE), a potent anti-mitotic agent. This phase I study assessed safety, tolerability, maximum tolerated dose (MTD), anti-tumor activity, and pharmacokinetics of DFRF4539A in patients with relapsed/refractory multiple myeloma. DFRF4539A was administered at 0.3–2.4 mg/kg every 3 weeks or 0.8–1.1 mg/kg weekly as a single-agent by intravenous infusion to 39 patients. Exposure of total antibody and antibody-conjugate-MMAE analytes was linear across the doses tested. There were 37 (95%) adverse events (AEs), 8 (21%) serious AEs, and 15 (39%) AEs ≥ grade 3. Anemia (n = 10, 26%) was the most common AE considered related to DFRF4539A. Two cases of grade 3 acute renal failure were attributed to DFRF4539A. There were no deaths; the MTD was not reached. DFRF4539A demonstrated limited activity in patients at the doses tested with 2 (5%) partial response, 1 (3%) minimal response, 18 (46%) stable disease, and 16 (41%) progressive disease. FcRH5 was confirmed to be expressed and occupied by antibody post-treatment and thus remains a valid myeloma target. Nevertheless, this MMAE-based antibody-drug-conjugate targeting FcRH5 was unsuccessful for myeloma.
Introduction
Several classes of drugs including immunomodulatory agents 1 , monoclonal antibodies 2 , and proteasome inhibitors 3 have shifted the paradigm of treatment choices and outcomes for multiple myeloma patients. Newer agents such as daratumumab, bortezomib, carfilzomib, lenalidomide, and pomalidomide have contributed towards better survival outcomes 4 . However, even with improved treatments, the majority of multiple myeloma patients continue to experience relapse. There is thus a continued need for treatments that may significantly extend diseasefree and overall survival, with desirable safety profiles. A recently identified gene family that encodes cell surface receptors on B cells has provided a potential target for new drug development. Fc receptor-homolog 5 (FcRH5; also known as FcRL5, IFGP5, BXMAS1, CD307, and IRTA2) 5,6 belongs to a family of six genes of the immunoglobulin superfamily (IgSF) 7 . FcRH5 is a cell surface antigen of unknown function whose expression is restricted to mature B cells, and expression is maintained on plasma cells (PCs). Notably, as compared to normal human PCs, FcRH5 is expressed at higher levels in multiple myeloma cells [7][8][9] .
DFRF4539A is an antibody-drug conjugate (ADC) that contains a humanized immunoglobulin-G1 (IgG1) anti-human FcRH5 monoclonal antibody (MFRF3266A) and a potent anti-mitotic agent, monomethyl auristatin E (MMAE), linked through a protease-labile linker, maleimidocaproyl-valine-citrulline-p-aminobenzyloxycarbonyl (MC-VC-PABC) 8 . In preclinical models, antibodies bound to FcRH5 were internalized, suggesting that FcRH5 may be suited for targeted delivery of cytotoxic agents 8,10 . MMAE has a mode of action similar to vincristine, and ADCs containing MMAE have induced durable responses in hematologic malignancies including Hodgkin lymphoma 11,12 . Following internalization, the conjugate is cleaved by lysosomal enzymes to release MMAE, which binds to tubulin and disrupts the microtubule network, thereby resulting in inhibition of cell division and cell growth [13][14][15] . DFRF4539A has demonstrated efficacy in nonclinical xenograft models of human FcRH5-positive multiple myeloma 8 , and based on this data and an acceptable nonclinical safety profile, we tested this agent in patients with relapsed/refractory multiple myeloma in a phase I clinical trial.
Study design
This phase I open-label study (ClinicalTrials.gov number NCT01432353) was designed to investigate the safety, tolerability, pharmacokinetics (PK), and biologic activity of DFRF4539A (supplied by Genentech, Inc.) in patients with relapsed/refractory multiple myeloma, and to determine a recommended phase II dose (RP2D). DFRF4539A was administered at doses of 0.3-2.4 mg/kg every 3 weeks or 0.8-1.1 mg/kg weekly as a single agent by intravenous (IV) infusion. The study consisted of a dose-escalation stage using a 3 + 3 design to determine the maximum tolerated dose (MTD) of an every 3 week (Q3W) dosing schedule, followed by a cohort expansion at the Q3W RP2D to further characterize the safety and activity of DFRF4539A. Additionally, to test whether more frequent dosing would be better tolerated, a weekly (Q1W) dosing schedule was implemented to determine the MTD of weekly dosing.
Patients
Eligible patients age ≥ 18 years had relapsed or refractory multiple myeloma for which no effective standard therapy exists. Patients were required to have been previously treated with a proteasome inhibitor or immunomodulatory drug. Eastern Cooperative Oncology Group (ECOG) performance status of 0-2, measurable disease as per the International Myeloma Working Group definitions 16 by the presence of plasma or urine monoclonal protein, and serum immunoglobulin free light chain (FLC) and abnormal serum immunoglobulin kappa (FLC to lambda FLC ratio) were also required. Patients receiving monoclonal antibody within 4 weeks of planned cycle 1, day 1 (C1D1), radio/chemotherapy with 2 weeks of C1D1, autologous stem cell transplant within 100 days prior to C1D1, prior allogenic stem cell transplant, or diagnosed with confounding malignancy were excluded.
The protocol was approved by Institutional Review Boards prior to patient recruitment and was conducted in accordance with International Conference on Harmonization E6 Guidelines for Good Clinical Practice. Written informed consent was obtained for all patients prior to performing study-related procedures in accordance with federal and institutional guidelines.
Safety assessment
The primary objective of the study was to assess safety and tolerability of DFRF4539A. Safety was evaluated according to NCI CTCAE v4.0. Dose limiting toxicities (DLT) were defined as grade 3-4 non-hematologic toxicity, except for reversible grade 3 allergic and non-allergic infusion toxicities, grade 3 or 4 hypercalcemia if due to underlying disease, grade 3 or 4 hyperuricemia, hyperphosphatemia, or hypocalcemia or grade 3 hyperkalemia, if transient (i.e., lasting <48 h) and without manifestations of clinical tumor lysis syndrome (i.e., creatinine ≥ 1.5 × the upper limit of normal [ULN], cardiac arrhythmias, sudden death, or seizures). The following hematologic toxicities also qualified as DLTs unless they were related to underlying disease: grade 4 anemia, grade 3 or 4 thrombocytopenia, and grade 3 or 4 neutropenia that did not recover to grade ≤2 within 72 h without growth factor support or was accompanied by temperature elevation (oral or tympanic temperature of ≤38°C). The MTD was defined as the highest dose at which ≤17% of patients at an assigned dose experienced a protocol-defined DLT.
Pharmacokinetics and immunogenicity assessments
Serum concentrations of total antibody (a measure of three key antibody analytes: conjugated, partially deconjugated, and fully de-conjugated antibody) was determined using a validated enzyme-linked immunosorbent assay (ELISA) 17,18 . DFRF4539A conjugate (as antibodyconjugated MMAE [ac-MMAE]) concentrations were measured in plasma samples by protein A affinity capture followed by enzyme-mediated release of MMAE and analysis using liquid chromatography-tandem mass spectrometry (LC-MS/MS 17,18 . PK parameters for the total antibody, ac-MMAE, and unconjugated MMAE following the first dose of DFRF4539A in cycle 1 (Q3W and weekly schedules) were estimated using non-compartmental analysis using Win-Nonlin 5.2.1 software (Pharsight, Sunnyvale, CA). Baseline and pre-dose post-baseline serum anti-drug antibody (ADA) samples were collected from all treated patients, and analyzed using a validated bridging antibody ELISA to screen, confirm and characterize ADA responses 19,20 .
Confirmed positive ADA responses were further characterized by competitive binding to determine if the response was primarily directed against the antibody or the linker-drug portion of the ADC and the relative ADA levels determined by titration.
Preliminary assessment of anti-tumor activity
Objective response, defined as a stringent complete, complete, very good partial, partial response, or minimal response, confirmed ≥4 weeks after initial documentation was determined using International Myeloma Working Group (IMWG) Uniform Response Criteria and/or European Bone Marrow Transplant (EBMT) Criteria 21,22 . Duration of objective response was defined as the time from first occurrence of a documented, objective response until the time of relapse or death from any cause. Progression-free survival (PFS) was defined as the time elapsed between treatment initiation and tumor progression or death from any cause.
Biomarker assessment
FcRH5 (CD307) expression and occupancy were assessed using a validated flow cytometry method (Labcorp, Burlington, North Carolina, USA) as described previously 8,10 . Cells were stained with appropriate antibody combinations and data was acquired on FACSCanto II (BD BioSciences, San Jose, CA). Briefly, 100 µL of sodium heparin anticoagulated whole blood or bone marrow from each patient per available time point, shipped at 3-8°C for receipt within 54 h of collection, was pipetted into test tubes. Five µL of human serum (Sigma, St. Louis, MO) and 5 µL of mouse serum (Rockland Immunochemicals, Limerick, PA) were added to the cells and incubated for 10 min at room temperature. The cells were stained with the appropriate fluorescent-conjugated antibody combinations (Ms IgG 1 , CD27, humanized anti-gD, Her2, FcRH5 [10A8], FcRH5 [7D11], CD19, CD138, CD3, CD38, CD45, and CD56) (BD Biosciences, San Jose, CA; Southern Biotech, Birmingham, AL; Invitrogen/Thermo Fisher Scientific, Waltham, MA) and incubated on ice for 30 min in the dark. All tubes were lysed with 4 mL of a cold (2-8°C) ammonium chloride lysing solution (BD Biosciences) and washed with 2 mL phosphate buffered saline (PBS) (BD Biosciences) with 1% bovine serum albumin (BSA) (Hyclone/GE Healthcare Life Sciences, Logan, UT). All cells were then stained with the appropriate amount of Streptavidin-Qdot605 (Invitrogen) on ice for 20 min in the dark. The cells were washed again with PBS with 1% BSA, resuspended in 500 µL of 1% paraformaldehyde solution (BD Biosciences) and stored at 2-8°C until they were acquired on the FACSCantoII. Fluorescent quantitation beads (BD Biosciences) were acquired daily for quality control of the instruments. PCs were defined by strong CD138 and CD38 expression, CD45 Lo, and with light scatter characteristics of large mononuclear cells. Gated PCs were used to calculate FcRH5 expression and drug occupancy; anti-Her2 was used as a negative control. Fluorescence intensity was quantified using standard units-molecule of equivalent soluble fluorophores (MESF).
Statistical analysis
Design considerations were not made with regard to explicit power and type I error, but to obtain preliminary safety, PK, and PD information. All patients who received any amount of DFRF4539A were included in the safetyevaluable population. For activity analyses, all patients who completed at least one on-treatment disease assessment were included.
Baseline patient demographics and treatment
Thirty-nine patients were enrolled at 8 sites between 17 September 2011, and 7 April 2014. The cutoff date for analysis was 2 September 2014, resulting in a median follow-up time of 43 days (range 16-241 days) for 39 patients. Patients demonstrated uniform baseline and disease characteristics ( Table 1). All patients had undergone prior systemic therapy (median six prior therapies, range 2-13), and all had previously received proteasome and corticosteroid therapy. The majority of patients had previously undergone immunomodulatory therapy (97%) as well. The patient population thus represented a multiple treatment relapse population with significant unmet need.
The study initially enrolled patients on the Q3W doseescalation schedule (Supplementary Figure S1). During escalation, the first DLT occurred among the first three patients enrolled in the 1.8 mg/kg cohort. Consequently, an additional four patients were enrolled at 1.8 mg/kg. No further DLTs were observed at this dose level; therefore, the escalation continued to 2.4 mg/kg. At this dose and schedule, a DLT was observed in one of the first three patients, and an additional three patients were enrolled. No further DLTs were observed at the 2.4 mg/kg dose level. However, based on the totality of the safety data, this dose was determined to be the RP2D and cohort expansion occurred for this dose and schedule, enrolling 11 additional patients. Data for this dose and schedule were combined from both the dose-escalation and expansion patients (n = 17).
Once the Q3W RP2D was declared (2.4 mg/kg), a Q1W dose-escalation cohort was opened, starting at a dose of 0.8 mg/kg and escalating to a dose of 1.1 mg/kg Q1W with three patients per cohort. No DLTs were observed in either cohort. However, following a review of the safety, tolerability, PK, and activity, no further enrollment on the Q1W schedule was pursued.
The MTD was not reached in this study. Overall, the median duration of exposure to DFRF4539A among patients was 22 days (range 1−219) ( Supplementary Figure S2). The number of treatment cycles received ranged from 1 to 11 (median 2). All 39 enrolled patients discontinued the study. The majority of patients were withdrawn due to disease progression (29 patients [74%]).
Seven patients (18%) were withdrawn because of AEs, and three patients (8%) were withdrawn at the investigator's discretion.
Safety
Adverse events (AEs) related to DFRF4539A are shown in Supplementary Table S1, the most common of which Musculo-skeletal and connective tissue disorder Table 2). One patient experienced a grade 2 hypercalcemia, seven patients experienced grade 3 SAEs; grade 3 SAEs included acute renal failure, back pain, pathological fracture, and pneumonia. Two patients (5%) receiving DFRF4539A on the 2.4 mg/kg Q3W dosing schedule experienced acute renal failure (ARF). These two SAEs were deemed related to the study drug. The remaining grade 3 SAEs occurred in one patient (3%) each. There were no deaths on the study.
One DLT of grade 3 transaminitis was observed at 1.8 mg/kg Q3W. At 2.4 mg/kg Q3W, one DLT was observed that consisted of grade 3 hyponatremia accompanied by altered mental status (metabolic encephalopathy) requiring ICU admission, ARF, thrombocytopenia, and neutropenia.
Peripheral neuropathy is a known side effect of MMAElinked ADCs 12 , and peripheral neuropathy was observed in eight patients (21%) treated with DFRF4539A. The median time to onset of peripheral neuropathy at the 2.4 mg/kg Q3W dosing schedule was 105 days (95% CI, 71-NE) (Supplementary Figure S3).
Per protocol, pre-infusion prophylactic medications including corticosteroids were not allowed prior to the first DFRF4539A infusion. No episodes of hypersensitivity to DFRF4539A were reported, and consequently, corticosteroids were not administered in subsequent doses.
Pharmacokinetics
DFRF4539A total antibody and ac-MMAE demonstrated linear PK across the tested doses of 0.8-2.4 mg/kg doses at both the Q3W and the Q1W schedules. The average C max and AUC inf values of total antibody were higher, t 1/2 values were longer, and CL values were lower than those of ac-MMAE compared within the same dose group in both the Q3W and Q1W schedules. The V ss values for the ac-MMAE and total antibody analytes approximated the physiological plasma volume and were generally independent of dose, suggesting that the ac-MMAE distribution was dominated by its antibody component. The systemic unconjugated MMAE exposure was consistently low (>100-fold less than exposure to ac-MMAE), suggesting that majority of MMAE remained conjugated to the ADC in circulation. The T max of unconjugated MMAE was delayed as compared to ac-MMAE; t 1/2 of unconjugated MMAE was relatively long for a small molecule drug and was approximate towards that of ac-MMAE. These results suggested that the slow and sustained release of unconjugated MMAE and its elimination rate was limited by its formation rate. Minimal accumulation was observed for all the three analytes upon repeated dosing for the Q3W and Q1W schedules, suggesting steady state was reached within cycle 1.
The PK parameters for all the three analytes at the RP2D dose level of 2.4 mg/kg at the Q3W schedule are summarized in Table 3. The cumulative exposure of acMMAE and total antibody in cycle 1 after the weekly dose of 0.8 mg/kg was roughly similar to the exposure observed at Q3W at 2.4 mg/kg in cycle 1.
Immunogenicity
The prevalence of ADA at baseline was 5.3% (two out of 38 evaluable patients). Post-treatment with DFRF4539A ADAs were detected in nine of 31 patients for which postbaseline data was available. These included the two patients with baseline positive signals that were not enhanced by the treatment. Therefore the overall treatment-emergent ADA incidence was 22.6% (seven out of 31). The presence of ADA appeared to have minimal impact on the ADC exposure in this study. In patients that were ADA positive, no apparent impact on safety was observed.
Clinical activity
Thirty-seven patients (95%) were evaluated for tumor response (Fig. 1). Two patients (5%) had a partial response, one patient (3%) had minimal response, 18 patients (46%) had stable disease, and 16 patients (41%) had progressive disease ( Table 4). The two patients with a partial response were treated at the highest dose tested, 2.4 mg/kg Q3W DFRF4539A. The duration of objective response in the two patients with PR were 22 and 66 days. Figure 1 depicts the best percent change in either serum M-protein or serum FLC levels (in patients without detectable M-protein) relative to baseline for all efficacyevaluable patients.
Biomarker analysis target occupancy
Two phycoerythrin-conjugated anti-FcRH5 antibody clones (anti-CD307) were used separately to stain patient samples at baseline and after dosing. Clone 10A8, which consisted of the antibody in DFRF-4539A without the drug conjugate, was used to determine the occupancy of the FcRH5 receptor before and after dosing and was a competing and blocking antibody, whereas clone 7D11 was a non-competing and non-blocking antibody with respect to DFRF4539A for binding to FcRH5. The resulting fluorescence intensity units (MESF) for each antibody was plotted against each other for each patient sample at screening and found to be highly correlated (Pearson correlation coefficient = 0.8), demonstrating comparable binding of their respective targets (data not (Fig. 2). When patient samples at baseline and post-dosing were analyzed using the competing antibody clone 10A8, the median MESF value at baseline (8483.5) was comparable to that of clone 7D11 as expected. However, the median post-dosing MESF value of clone 10A8 (1515.5) was significantly lower in comparison to its baseline value, thereby quantitatively demonstrating receptor occupancy in post-dosing patient samples. Receptor occupancy was estimated to be 62.57% (n = 8) (Fig. 2). Anti-FcRH5 expression levels on gated PCs in patient samples varied from 19 to 100%. Representative flow cytometry data plots that demonstrate FcRH5 receptor occupancy and expression on PCs after 1 cycle of anti-FcRH5 therapy are shown in Fig. 3. At screening, positive staining relative to isotype control was observed on PC using anti-FcRH5 antibody clone 10A8, which competes with DFRF4539A for binding to FcRH5. On cycle 1, day 15, FcRH5 receptor occupancy by DFRF4539A was demonstrated by a downshift of staining by antibody clone 10A8 relative to isotype control on PCs (Fig. 3a). In contrast, there was no observed loss of staining between screening and cycle 1, day 15, by the anti-FcRH5 antibody, clone 7D11, which is non-competing and non-blocking with respect to DFRF4539A (Fig. 3b). This demonstrated that expression of FcRH5 receptors was maintained on PCs after DFRF4539A treatment and that DFRF4539A remained bound to FcRH5 at the cell surface.
PCs were not consistently depleted after anti-FcRH5 treatment (Fig. 4). In comparing baseline (screening samples) to post-dosing (cycle 1, day 15 samples), some patients showed depletion of PC (representative patient data, Fig. 4b) while other patients did not show depletion of PC (representative patient data, Fig. 4c).
Discussion
Administration of DFRF4539A in patients with previously treated relapsed or refractory multiple myeloma was found to have acceptable tolerability, but demonstrated limited activity at the dose and schedule tested with this formulation. Target study drug exposures were achieved. There were no significant safety events considered related to DRF4539A, and there were no grade 5 AEs. The SAE reported with highest incidence overall was grade 3 acute renal failure (n = 2; 5.1%) at the 2.4 mg/kg Q3W dose level, and this was the only SAE found to be related to the study drug. All patients discontinued from the study largely because of disease progression, AEs, or discretion of the investigator. Overall, the rate of discontinuations due to AE's at the 2.4 mg/kg Q3W dose level was 29%, considered high in comparison to other ADC programmes at 5-10%.
The exposure of the total antibody and the ac-MMAE analytes was linear across the tested dose range of 0.8-2.4 m/kg for both the Q3 and the Q1 schedules. Systemic exposure to unconjugated MMAE was consistently low, suggesting that majority of MMAE remained conjugated to the ADC in circulation. The T max of unconjugated MMAE was delayed as compared to ac-MMAE, suggesting formation-rate limited kinetics, which was consistent with the mechanism of action for an ADC. Minimal accumulation was observed for the ac-MMAE, total antibody and unconjugated MMAE analytes upon repeated dosing for the Q3 and Q1 schedules, suggesting steady state was reached within cycle 1.
The primary clinical toxicities observed with ADC's that contain microtubule inhibitors include bone marrow toxicity and peripheral neuropathy 23 . Bone marrow toxicity is expected due to the effect on rapidly proliferating cells in that compartment. As such, neutropenia is a commonly reported AE seen with MMAE, and neutropenia rates observed in this study are consistent with rates observed in studies of other MMAE-conjugated ADCs 24,25 . In the current study, anemia was the most common AE, and thrombocytopenia was also observed. Microtubule inhibitors also have an effect on peripheral nerves due to the long projections of axons and the critical role of the microtubule network in the nerve cell for axonal transport 26 . Peripheral neuropathy is recognized as a class-effect of microtubule inhibitors and can be one of the most frequent treatmentrelated AEs, ranging from 20% to 56% with the use of conventional MMAE ADCs 27 . Peripheral neuropathy (n = 4; 10%) and peripheral sensory neuropathy (n = 4; 10%) were reported in the current study. FcRH5 during disease progression has been demonstrated by others to be consistently expressed on malignant PCs from patients with multiple myeloma 9,10 . In the current study, we used flow cytometry on pre-dose vs. post-dose patient peripheral blood samples and demonstrated target engagement of FcRH5 by DFRF4539A, and maintenance of FcRH5 expression in patient samples post-dosing. Others have demonstrated that 49% of multiple myeloma patients present with high levels of soluble FcRH5 6 . While high soluble antigen levels are a plausible barrier to therapy, we found that this did not impact PK in this patient population.
Despite achieving target drug exposures in patients, response rates in this patient population were generally low, with 5% PR, 46% SD, and 41% PD. The low activity of DFRF4539A observed in this study may be due to several factors. While the expression of FcRH5 on malignant PCs is increased in multiple myeloma patients in comparison to control PCs from normal controls 8 , the threshold required for ADC activity in the patient population is unknown. It is possible that DFRF4539A cannot kill multiple myeloma cells expressing endogenous levels of FcRH5. Additionally, levels of soluble FcRH5 are known to be elevated in the blood of multiple myeloma patients 6 , and this shed form of FcRH5 may have resulted in decreased binding of DFRF4539A to membrane-bound FcRH5. Finally, the degree of internalization of DFRF4539A by multiple myeloma cells was not directly assessed in this study. Therefore, it is possible that sufficient MMAE was delivered to the cell surface of multiple myeloma cells, but intracellular MMAE concentrations were insufficient to kill these cells.
While historical response rates to single agent MMAE is 10%, multiple myeloma cells typically have a low proliferative index (Ki67 median 4.4%) 28 , and therefore cellcycle dependent drugs such as MMAE conjugates may be less effective for this cell population. Microtubule inhibitors, including vinca-alkaloids, have been shown to have limited activity in multiple myeloma 29,30 . However, an ADC carrying a microtubule inhibitor payload and targeting the myeloma-associated antigen BCMA has recently shown promise in heavily-pretreated multiple myeloma patients 31 , and thus the role of microtubule inhibitors in future of myeloma therapy is uncertain. Given the small sample size, data from this study has limited statistical power. Further investigation of DFRF4539A has been stopped due to the limited activity observed in this study. However, it should be noted that approximately 50% of patients on study appeared to derive some clinical benefit (achieving either SD or a PR). Hence, FcRH5 may be a valid myeloma target, although using an MMAE-based ADC may not be an optimal strategy to target FcRH5. Drugs with other mechanisms of action, including T-cell directing, bi-specific antibodies, or chimeric antigen receptor-modified T cells, may prove beneficial to multiple myeloma patients in the future, when directed against FcRH5. | 5,586 | 2019-02-01T00:00:00.000 | [
"Biology",
"Medicine"
] |
A readout system based on SiPM for the dRICH detector at the EIC
The ePIC experiment at the future Electron-Ion Collider (EIC) aims to use silicon photomultipliers (SiPMs) as the photodetector technology for the dual-radiator ring-imaging Cherenkov detector (dRICH). Despite their advantages for this low light application and insensitivity to high magnetic fields, SiPMs are sensitive to radiation and require rigorous testing to ensure that their single-photon counting capabilities and dark count rate are kept under control over the years of operation. The presented results show the successful use of a complete prototype readout chain based on the ALCOR chip for SiPM characterization measurements and assembled in an optical plane for test-beam measurements using the dRICH prototype.
Introduction
The Electron Ion Collider is a future accelerator to be built at the Brookhaven National Laboratory in the early 2030s [1,2].The EIC will be the first collider designed for polarized electrons, polarized protons, and light nuclei.With its high center-of-mass energy (20 to 141 GeV) and large luminosity (10 34 cm −2 s −1 for electron-proton scattering), it will enable scientists to explore the quark and gluon structure of protons and nuclei, helping to understand the origin of nuclear spin and mass.ePIC is the main detector, it is placed at the interaction point 6 and it will be built around a superconductive solenoid magnet with a magnetic field up to 1.7 T. Around that, a serie of subsystem is built for tracking, calorimetry and Particle IDentification (PID).PID is a significant challenge and the proposed solution for the forward region is a dual radiator Ring Imaging Cherenkov (dRICH) detector [3].This dRICH is considered a compact and cost-effective choice to cover a wide range of particle momenta, from a few GeV/c up to 50 GeV/c, typical of the forward rapidity region, achieving 3 K/ separation.As the name suggests, the detector exploits two Cherenkov radiators: aerogel and gas (C 2 F 6 ) with refractive indices of 1.02 and 1.0008 respectively.The Cherenkov rings are reflected by an array of 6 spherical mirrors onto 6 optical readout sectors for a total surface of 3 square meters.The optical readout is required to have a spatial resolution of 3 × 3 mm 2 (that defines the photosensor pixel dimension) for a total of about 300,000 channels.The photosensors must be capable of efficiently detecting single photons within a high magnetic field of around 1 Tesla, while withstand mild radiation levels that are on the order of 10 11 1-MeV neq/cm 2 for the entire life of the experiment.Interestingly, the photosensors are placed outside of the detector's acceptance region, offering the opportunity for exploring the use of silicon photomultiplier sensors (SiPMs).The SiPMs are highly sensitive to photon detection, have excellent time resolution [4] and represent a cost-effective solution.Importantly, SiPMs, being solid state devices, are not affected by high magnetic fields.However, it's worth noting that SiPMs have their drawbacks, having intrinsic high dark count rates (DCR) at room temperature and being susceptible to radiation damage [4].The radiation damage can lead to a significant increase in dark currents thus DCR levels, reducing the sensor life-span.However, the effect on the DCR can be mitigated with annealing techniques [5].
In order to study the radiation damage (and the recovery by different annealing techniques) to SiPMs and evaluate their detection capability after irradiation, we have developed a prototype of the readout system for future implementation into the dRICH detector.We tested several SiPMs from different vendors arranged in a 4 × 6/8 matrix mounted on a custom carrier PCB with fluences up to 10 11 1-MeV neq/cm 2 .In order to keep the DCR low, the SiPMs are cooled down to −30 • C by -1 -means of peltier cells.To maintain flexibility, bias voltages are independently supplied to each SiPM through an adapter board.The signals from the SiPMs are routed to the front-end board, where an ALCOR ASIC [6] amplifies and timestamps them, generating a digital stream sent to an FPGA.In the following sections, we provide a description of the individual components of the readout system, along with results from the irradiation campaigns and the initial use in a prototype dRICH detector.
Material and methods
Carrier board and SiPMs.We designed four kinds of carrier boards specially engineered to accommodate different 3 × 3 mm 2 SiPM devices that underwent several irradiation and annealing phases.The primary specifications for this carrier board are to withstand high-temperature oven annealing processes (up to 175 • C), to facilitate precise temperature control for the SiPM devices (-30 • C), and to enable high-current operations during annealing techniques involving high current delivered to the SiPMs.Furthermore, these carrier boards were also designed with the capability to perform imaging in a dRICH prototype.The high-temperature endurance was achieved by using a high Tg PCB material and employing high-temperature reflowing paste during the soldering process.Additionally, the connection between the carrier board and the adapter board was established using an edge connector, effectively eliminating the use of plastic components in this critical interface.This design choice ensures that the carrier board, once dismounted from the prototype, can withstand temperatures of up to 175 • C for annealing and remains resilient and functional afterward.To maximize thermal conduction with the peltier cell during −30 • C operations, the back side of the 8-layer PCB features full metalization exposure with no solder resist.Precise temperature control is achieved through the use of an LM73 temperature sensor, allowing for accurate setting and monitoring of the operative temperature.An essential characteristic of the carrier board is the absence of resistors in the bias voltage path.This design choice facilitates the passage of high currents through the SiPM sensors for the current annealing technique.Instead of resistors, a ferrite bead (1 kΩ at 100 MHz) is used in conjunction with 100 nF capacitor to cut high frequency noise on the bias line.As for the SiPM sensors, one board is outfitted with 16 Hamamatsu S13360-3050VS (50 μm cell pitch) sensors and 16 Hamamatsu S13360-3025VS (25 μm cell pitch) sensors, one board is equipped with 16 Hamamatsu S14160-3050HS (50 μm cell pitch) sensors and 16 Hamamatsu S14160-3015PS (15 μm cell pitch) sensors.Of the remaining two boards, one houses 12 NUV-HD-CHK sensors (40 μm cell pitch) and 12 NUV-HD-RH prototype sensors (15 μm cell pitch) provided by Fondazione Bruno Kessler (FBK) while the other 16 SENSL MICROFJ 30035 (35 μm cell pitch) and 16 SENSL MICROFJ 30020 (20 μm cell pitch).These diverse sensor configurations enable comprehensive experimentation and performance assessment across varying cell pitch sizes, breakdown voltages and vendors.
Adapter board.The carrier with the SiPMs is connected to an adapter board thanks to a robust Samtec mini edge card connector.This board is engineered to fulfill three primary functions.Firstly, it regulates the voltage bias (Vbias) of SiPMs across eight distinct bias lanes.Secondly, it provides precise polarization bias to each SiPM sensor, using digital-to-analog converters (specifically, the LTC1665) to fine tune the voltage at the anode from 0 to 5 V. Thirdly, it hosts 32 1 nF capacitors for AC coupling with the subsequent front-end board.The control is ensured via a I2C communication with an external board connected to a computer via a RS-232 to USB.The adapter board allows to efficiently supply the Vbias to SiPMs with different overvoltages on the same carrier board, and to individually switch-off noisy channels.
-2 -Front-end board and ALCOR.The front-end board is connected to the adapter through a micro low-profile Samtec connector.Beyond the connector and voltage regulators, the board is equipped with the ALCOR ASIC (developed by INFN Torino), originally designed for SiPMs in cryogenic environments.ALCOR is wire bonded on the board and has a 32-pixel matrix mixed-signal architecture, which integrates amplification, signal conditioning, and event digitization with fully digital input and output capabilities.Each pixel on the chip consists of a regulated common gate amplifier with a 10 Ω/5 nF input impedance, a post-amplifier TIA configurable for four different gain settings, two independent leading-edge discriminators with customizable threshold settings, and four time-to-digital converters (TDCs) featuring 50 ps least significant bit (LSB) resolution at a 320 MHz sampling rate.A schematic representation of the internal architecture is shown in figure 1 (left).ALCOR operates in three triggerless modes: LET for leading-edge threshold measurement with a maximum time stamp rate up to 5 MHz, ToT for Time-over-Threshold measurements, and slew rate measurements for signal characterization.The ASIC provides a fully digital output via four LVDS TX data links, employs SPI-based chip configuration, and generates 64-bit event and status data word.A dedicated Xilinx Kintex-7 FPGA KC705 evaluation board is used to provide the clock to up to 6 ALCORs, program them and receive the LVDS data trough Samtec FireFly high speed cables.The system is controlled by a Linux PC.The fully assembled board is shown in figure 1 (right).Optical plane prototype.The readout system is assembled as depicted in figure 2. The carrier board connects to the adapter, which is positioned above the front-end board.This configuration reduces the system's form factor and, by mounting the adapter on top of the front-end, the wire-bonded ASIC is kept protected.The optical plane prototype is assembled with four readout systems that have distinct SiPM matrixes (one for each vendor) each previously irradiated with a dose of 10 10 1-MeV neq/cm 2 and subjected to a 150 hours annealing phase at 150 • C. To lower the DCR by a factor ≈ 100, SiPMs are operated at −30 • C.This is done by using two peltier cells stacked in series connected to each matrix pair.The current delivered to the stack is controlled by a software-implemented PID process, using the LM73 sensor's temperature measurements as feedback.The peltier cell's hot side is connected to a liquid cooled heat pipe (15 • C) using a thermal pad.The setup has 2 L P M of nitrogen gas circulation to prevent moisture and frost, while neoprene is employed to isolate from light the junction between the dRICH and the detector box. Figure 3 (left) shows the system assembled in the -3 -detector box with the carrier boards facing upwards and the adapter boards attached to them.The front end boards are located below the adapter boards.Water pipes and cables are on the back as in figure 3 (right), where the prototype is connected to the dRICH described in [7].
Results
The readout prototype was used in a climatic chamber kept at −30 • C for the studies on the radiation damage on more than 200 SiPMs.The DCR exhibits a linear increase with rising fluence, and it subsequently decreases following high-temperature annealing.The reduction is approximately a factor of ≈10 after annealing at 125 • C and about a factor of ≈100 after annealing at 150 • C. Both the annealings were performed for 150 hours.All the sensors display a similar trend but Hamamatsu S13360-3050VS consistently demonstrates the lowest DCR across all stages, starting at ≈1.5 kHz as brand new and increasing to ≈500 kHz for sensors exposed to 10 9 1-MeV neq/cm 2 before annealing.After the annealing the DCR is 15 kHz.The sensors exposed to 10 10 1-MeV neq/cm 2 and 10 11 1-MeV neq/cm 2 resulted after annealing in a DCR of ≈ 1.5 MHz and ≈ 150 kHz.In alternative, on-board -4 -annealing was induced by using direct current to heat up the SiPMs up to 175 • C (10 V and 100 mA per sensor) for 2.5 hours.The temperature feedback is achieved by using a thermal camera and we measured a reduction in DCR of a factor 10 was measured.This is less than what was obtained with the oven at 150 • C but in 1/10 of the time.The photo response of the Hamamatsu S13360-3050VS sensors was measured before and after irradiation and annealing observing no degradation in performance within a 5% margin (further details in [8]).Four sensor matrices irradiated up to 10 10 neq/cm 2 that underwent the oven annealing (150 • C for 150 hours) were integrated in the dRICH optical readout prototype and tested at the CERN Proton Synchrotron.The optical readout prototype is able to detect Cherenkov rings (figure 4 (left)) using a 10 ns time window centered on a trigger signal provided by the same readout connected to plastic scintillators.By looking at the time coincidences (figure 4 (right)) one can see the 15 kHz of DCR in the off-trigger region while a gain in signal of a factor 1000 is detected in coincidence with the trigger.The time resolution for the Hamamatsu S13360-3050VS peaks at 350 ps.After pulses are present and are within the expectation (1/100 probability).
Conclusion
In this paper, we have provided a comprehensive overview of the individual components comprising a SiPM-based readout system designed for the dRICH at the ePIC experiment at the EIC.Using this system, we successfully characterized SiPMs that had undergone irradiation and annealing through both indirect heating methods, such as oven annealing, and direct current-induced heating.The latter method serves as a proof of concept, demonstrating the feasibility of achieving in-situ annealing during EIC operation.In-situ annealing, aimed at reducing the dark count rate induced by radiation damage, has the potential to significantly extend the photodetection system's lifespan, by a factor of at least ten.Furthermore, we achieved the measurement of Cherenkov rings generated by the interaction of the beam with the dRICH prototype, showcasing the system's ability to do imaging with 350 ps time resolution with irradiated and annealed SiPMs.
Figure 2 .
Figure 2. Schematic representation of the readout system.The carrier board hosting the SiPM matrix is connected to the adapter board by using an edge connector.The front-end board is placed below the adapter reducing the form factor and protecting the wire-bonded ASIC.The connection to the power supply and FPGA are also shown.
Figure 3 .
Figure 3. Optical plane prototype (left).Optical plane connected to the dRICH prototype at the T10 beam line of the CERN Proton Synchrotron (right).
Figure 4 .
Figure 4. Cherenkov ring obtained in the dRICH prototype by the aerogel with negative 8 GeV/c beam (left).Time coincidence plot for the Hamamatsu S13360-3050VS (right). | 3,232.6 | 2024-02-01T00:00:00.000 | [
"Physics",
"Engineering"
] |
Folate Targeted Galactomannan Coated Iron Oxide Nanoparticles as a Nanocarrier for Targeted Drug Delivery of Capecitabine
Iron oxide nanoparticle is the most promising nanoparticles (NPs) capable in Drug Delivery and targeting. Iron oxide nanoparticles were synthesized by green synthesis. Galactomannan, when attached to the surface of the nanoparticles, increases the biocompatibility of the nanoparticles. Folic acid (FA) is used as the ligand to target folate receptors, which are found abundant in cancer cells. FeNPs-GM-FA could target cancer cells when used as drug carriers. The synthesized iron oxide nanoparticles using Mimosa pudica root extract was synthesized for targeted delivery of the anticancer drug, Capecitabine, by grafting folic acid (FA) onto the iron oxide nanoparticles coated with galactomannan (GM), a polysaccharide present in fenugreek gum. The cytotoxicity profile of the nanoparticles on human epithelial type 2 (HEp-2) cells as measured by standard 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay showed that the particles were nontoxic and may be useful for various in vivo and in vitro biomedical applications. The surface modification by galactomannan and folic acid grafting was confirmed by UV-visible spectroscopy and fourier transforms infrared (FTIR) spectroscopy. The in vitro release profile of capecitabine from FeNPs-GM-FA was characterized by an initial fast release followed by a sustained release phase. The histological investigation evidences the formation of improved liver cell architecture indicating the therapeutic nature of functionalized iron nanoparticles with Capecitabine, confirming a potential option for drug delivery and targeting tumor tissues.
pharmacological activity is required.It expands the therapeutic window of the drug by delivering the drug to the therapeutic site and by reducing delivery to the unwanted site.This decreases the minimum effective dosage of the drug compared to the usual route and thus reduces the toxic side effects of the drug [1].
Magnetic nanoparticles (MNPs) possess unique properties that are the ability to function at the cellular and molecular level of biological interactions making them an attractive platform as contrast agents for magnetic resonance imaging (MRI) and as carriers for drug delivery [2].Nanoparticles are used for drug targeting because the diameter of the smallest blood capillary is approximately 5 μm.It can be penetrable into the smallest blood capillaries.The nanoparticles (NPs) used should be specific, efficient and rapidly internalized into specific target cells.Coating the nanoparticles with biocompatible polymers and targeting agents can improve the dispersive and biocompatibility of nanoparticles [3].
The therapeutic agents are attached or encapsulated within a magnetic nanoparticle.These particles may consist of porous polymers that contain magnetic nanoparticles precipitated within the pores or may have magnetic cores with a polymer or metal coating which can be functionalized.By functionalizing with the polymer or metal coating, it is possible to attach a drug to cure a disease.Once attached, the particle/drug complex is injected into the bloodstream.Magnetic fields generally from high-field, high gradient, rare earth magnets are focused over the target site and the forces
Introduction
Targeted drug delivery is the process of delivering drug specifically to a cell, tissue and organ where a on the particles as they enter the field allow them to be captured and extravagated at the target [4].
The green synthesis of nanoparticles is a novel approach in nanotechnology.Plants have been reportedly used for synthesis of metal nanoparticles like gold, silver, iron, copper and alloy.Iron oxide nanoparticles (FeNPs) is a unique micro configuration and super-para magnetism.Super-para-magnetic iron oxide nanoparticles with tailored surface chemistry have been widely used in numerous applications such as magnetic resonance imaging (MRI) contrast enhancement, tissue repair, immunoassay, detoxification of biological fluids, hyperthermia, drug delivery, cell separation, etc.All these biomedical and bioengineering applications require that nanoparticles have high magnetization values and size smaller than 100 nm with overall narrow particle size distribution, so that the particles have uniform physical and chemical properties.In addition, these applications need special surface coating of the magnetic particles, which must be not only nontoxic and biocompatible but also allow a targetable delivery with particle localization in a specific area [5].
Polymers are coated on the nanoparticle surface to disperse it and make them more biocompatible.Polymer prevents the nanoparticles from agglomeration and particle surface from oxidation.Galactomannans, an important group of polysaccharide hydrocolloids, are produced in certain plants as cell wall and storage polysaccharides.Galactomannans generally consist of β, 1-4-linked linear mannose backbone, to which single galactose grafts are randomly linked by α, 1-6 glycoside bond.The structure of galactomannan is shown in Figure 1.Galactomannans from different legume seeds differ in mannose to galactose ratio, molecular weight and mode of placement of the galactose grafts.Galactomannan derived from the seeds of Trigonellafoenum-graecum (Comman name: Fenugreek) has mannose: galactose ratio of 1:1.Thus Fenugreek gum has the highest galactose (~48%) in its molecule and its linear mannan backbone has α, 16 linked single galactose grafts on nearly all the mannose groups of the main chain.A gum with higher percentage of galactose has good coldwater dispersability and high viscosity [6].
Folate receptor (FR) is an affinity membrane folatebinding protein.It is a glycosyl phosphatidylinositol (GPI)-linked membrane glycoprotein with an apparent molecular weight of 38-40 KDa.Its expression is negligible in healthy cells and is present in large numbers in cancer cells.Highly undifferentiated metastatic cancer sites express more FR.Over expression of FR on cancer cell makes it as a potential target for a ligand.Folic acid (FA), a low molecular weight targeting agent can be coated on nanoparticles as a ligand as it can couple to the folate receptor.FA is grafted on the polymer to target cancer cells [7].The structure of folic acid is shown in Figure 2.
This paper discusses the green synthesis of Iron nanoparticles and its conjugations with anti-tumor drug and the in-vitro drug release response of galactomannan functionalized iron oxide nanoparticles attached to folic acid and conjugated with the anti-cancer drug capecitabine as a model drug.The FeNPs incorporated with FA, galactomannan and drug was characterized using Scanning electron microscopy (SEM), particle size analyzer and UV-Visible and FT-IR spectroscopy.The pharmacological potential of functionalized FeNPs was investigated by cell culture and histological studies.
Materials and Methods
The green synthesized FeNPs prepared in our laboratory was used in this study.All chemicals used for the synthesis of FeNPs were purchased from Sigma-Aldrich, India.Double distilled water was used throughout the experiment.All glassware was washed well and dried using hot air oven (Figure 3).
Extraction of galactomannan
Fresh fenugreek seeds were washed thoroughly with distilled water and were dried completely.The dried seeds were crushed into powder.5 g of powder was soaked in 50 ml of distilled water and was stirred continuously for 4 hours.It was then centrifuged at 6000 rpm for 15 mins.The supernatant, which is the fenugreek gum, was collected and stored for further process.
UV-visible spectroscopy
The green synthesized Iron nanoparticles (FeNPs) is characterized by UV-Visible spectroscopy.The reduction of pure Iron nanoparticles was primarily monitored by measuring the UV-visible spectrum of the reaction medium after diluting the solution with the range between 100-900 nm in UV-visible spectrophotometervis absorption spectrum measures the wavelength of the light that the nanoparticles absorb.UV-spectrum is shown in the Figure 4.It shows a broad peak of Iron nanoparticles to detect the presence of Iron nanoparticles in the solution.Green synthesis of Iron nanoparticle was achieved using the plant as the color change was observed after the addition of ferrous sulphate solution due to the excitation of Surface Plasmon Resonance (SPR).In UV-visible spectrometer, the absorbance spectrum was measured.
SEM investigation
The surface appearance and morphology of the green synthesized iron particles are evaluated by Scanning electron microscopy.It was performed by SEM built up by utilizing Supra Zeiss with 1 nm determination at 30 kV with 20 mm Oxford EDS finder.
Fabrication of galactomannan-functionalized iron oxide nanoparticles (FeNPS-GM)
To synthesize Polymer-functionalized iron oxide nanoparticles, the iron oxide nanoparticles were mixed with the fenugreek gum, which was extracted earlier in the mass ratio of 1:1 and stirred overnight.The polymer-coated nanoparticles were then centrifuged at 6000 rpm for 15 mins.The polymer coated iron oxide nanoparticles were collected, washed with distilled water and dried.
Preparation of folic acid modified galactomannanfunctionalized iron oxide nanoparticles (FeNPs-GM-FA)
Folic acid is generally difficult to conjugate to the surface of the polymer because of the weak chemical reactivity.The carboxylic group of folic acid was first activated with dicyclohexylcarbodiimide (DCC).DCC activates the folic acid and iso-urea is formed.10 mg of Folic acid was dissolved in 10 ml of dimethyl sulfoxide (DMSO) solution.DCC was added to the solution corresponding to a ratio of folic acid to DCC 1:1.Galactomannan-functionalized iron oxide nanoparticles were added in the folic acid solution in the mass ratio of 1:1.It could soak for 1 hour.The nanoparticles were then separated by centrifugation, washed with distilled water and dried (5.7).
Conjugation of capecitabine to functionalized iron oxide nanoparticles (FeNPs-GM-FA-Cap)
The anticancer drug Capecitabine was dissolved in DMSO.Folic acid modified Polymer functionalized nanoparticles was added to drug solution (drug concentration = 1 mg/ml) in a mass ratio of 1:1 and stirred at room temperature for 4 hours.The suspension was then centrifuged (6000 rpm, 15 min) and the precipitate were separated and dried.The schematic representation of FeNPs-GM-FA-Cap is given in Figure 4.
Drug release -in vitro study
For in-vitro drug release study, Dialysis Membrane-110, LA395 (Membrane specifications: flat width -31.13 mm, Av. diameter -21.5 mm, capacity approx -3.63 ml/cm) was used.100 mg of FeNPs-GM-FA was taken along with 10 mg of Capecitabine.Then the sample (FeNPs-GM-FA-Cap) was packed in the dialysis membrane and immersed in phosphate buffer saline (PBS) solution (150 ml) with mild stirring at 37 °C throughout the process. 2 ml samples were withdrawn by a pipette at 30, 60, 80, 120, 150, 180, 240, 300, 360, 1440 and 4320 minutes and replaced immediately with 2 ml of fresh PBS medium, which was accounted for when calculating the amount released.Capecitabine concentration in the collected samples was measured using UV-Vis spectrophotometer at a wavelength of 307 nm.The percentage of drug released is given by, 100 (1 )
Percentage of drug releas d B A e A − × =
Where, A is the amount of initial capecitabine that was incorporated into the folic acid modified GMfunctionalized iron oxide nanoparticles and B is the amount of drug released at a time, t.The data are collected and statistically analyzed from the triplicate if the experiments.The standard deviation of the analysis is expressed in error bars in the graphs.
in-vitro cell cytotoxicity analysis
The cytotoxicity of the synthesized iron oxide nanoparticles was evaluated using 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay.100 μl of HEp2 cells were seeded in 96-well plates (5 × 10 4 cells/well) and they were kept for overnight incubation at CO 2 incubator.The condition of CO 2 incubator was maintained at a temperature of 37 °C and cell were humidified 5% CO 2 in the incubator for 24 h.
The iron oxide nanoparticles were then added to the cells at defined concentrations (2, 6, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 μg/ml) and incubated for 24 hours.After incubation, the media was discarded and 50 μl of MTT reagent (5 mg/ml) was then added per well and the plate was incubated for 4 hours.After incubation, the media with MTT was discarded from the wells and 100 μl of dimethyl sulfoxide (DMSO) was added to solubilize the formazan crystals formed.Readings were then taken in an enzyme-linked immunosorbent assay (ELISA) reader at 570 nm.Percentage viability of cells was calculated as the ratio of mean absorbance of triplicate readings with respect to mean absorbance of control wells as shown in the equation 2. readings of sample and I control is the mean absorbance of control.The error bars in the graph concludes the standard deviation of the statistical analysis of the triplicate experiments.
Histological studies
Histological evaluation was analyzed on a lobe of the liver tissue and a part of the specimen was fixed using 10% formalin and then embedded in paraffin wax, sectioned at 4l m thickness and were stained with hemotoxylin-eosin.Normal light microscopy was used to evaluate pathological changes of liver.
UV-visible spectroscopy
The spectra recorded from the FeNPs-GM solution, shows a shift in the onset of absorption observed in the sample and showed an absorbance peak at 224 nm, which was specific for the Iron oxide nanoparticles.This phenomenon of shift of absorption edge has been ascribed to a decrease in particle size.This results in a shift in the absorption edge to a lower wavelength region.Furthermore, nanoparticles are highly sensitive and functionally efficient because of smaller grain size and high surface to volume ratio as compared to the conventional materials in micrometer range (Figure 5).
SEM investigation
SEM analysis was used to confirm the morphology of the synthesized FeNPs-GM sample.SEM image of Galactomannan coated iron oxide nanoparticles demonstrates that these particles are smaller than 100 nm and have spherical shape (Figure 6).
EM image shows that the synthesized iron oxide galactomannan coated iron oxide nanoparticles and folic acid modified galactomannan-coated iron oxide nanoparticles conjugated with capecitabine.In the FTIR spectrum of FeNPs-GM, the peak at 3402 cm -1 and 3228 cm -1 are due to the stretching vibrations of O-H group.The peak at 2930 cm -1 and 1407 cm -1 are due to the stretching vibration of C-H group.The peak at 2174 cm -1 corresponds to the stretching vibration of C-O bond.The peaks at 1632 cm -1 and 1226 cm -1 are due to the C=O group.The peak at 1114 cm -1 corresponds to the stretching vibrations of C-N group attributed to aliphatic amines.The peak at 694 cm -1 corresponds to the characteristic peak of iron oxide nanoparticles [8].The FTIR spectrum of FeNPs-GM confirms the iron oxide nanoparticles are coated by the naturally synthesized polysaccharide, galactomannan.nanoparticles are well dispersed and roughly spherical in shape.The synthesized iron oxide nanoparticles are in the size range of 60-80 nm with mean size of 67 nm.
Particles size analyser
The size of FeNPs via green synthesis is found to be 167.2± 55.44 nm and the size Of FeNPs after surface functionalization is 202.3 ± 45.71 nm and surface activation of nanoparticles enhanced its size by forming a layer on the nanoparticles.Figure 7 shows the particle size of iron particles before and after functionalization.
FT-IR analysis
Figure 8 shows the FTIR spectrum of galactomannan coated iron oxide nanoparticles, folic acid modified groups respectively, indicate the presence of folic acid.
In the FTIR spectrum of FeNPs-GM-FA-Cap, the peak at 3751 cm -1 corresponds to the O-H group.The Sharp peaks at 2927 and 2851 cm -1 corresponds to the stretching vibration of C-H bond of alkyl group.The strong peak at 2365, 1420 and 1243 cm -1 are due to the presence of C-O group.The peak at 1850 cm -1 is the characteristic peak of carbonyl group of esters.The strong peak at 1637 cm -1 is due to the presence of C=O group attributed to CONH 2 group [11].The peak at 1313 and 1022 cm -1 is due to the presence of C-N bond in aromatic amine and aliphatic amine respectively.The peak at 953 cm -1 is due to the stretching vibration of O-H bond attributed to carboxylic acid.The characteristic peak of Fe-O bond at 670 cm -1 indicates the presence of iron oxide nanoparticles [12].When compared to the FT-IR spectrum of FeNPS-GM-FA and FeNPs-GM- The FTIR spectrum of FeNPs-GM-FA shows a peak at 3580 cm -1 , which corresponds to the stretching vibrations of O-H group attributed to isourea.The sharp peak at 1631 cm -1 indicates the presence of C=O group.The sharp peak at 1508 cm -1 is the characteristic peak of C-C group attributed to the stretching vibration of aromatic C=C.The peaks at 1429 cm -1 and 1148 cm -1 are due to the presence of C-O group attributed to alcohol and carboxylic acid respectively.The peak at 1082 cm -1 corresponds to the stretching vibration of C-N group attributed to aliphatic amines.The weak absorption band at 812 cm -1 is due to the vibration of C-H bondoscillations of β-mannopyranose residues of galactomannan [9].The peak at 665 cm -1 indicates the presence of magnetite [10] by 50-dFUrd.Capecitabine and 50-dFCyd had shown mild cytotoxic activity only at high concentrations.The cytotoxicity of the intermediate metabolites 50-dFCyd and 50-dFUrd was suppressed by inhibitors of Cyd deaminase and dThdPase, respectively, revealing that these metabolites become active only after their conversion to 5-FU.Generally, Capecitabine is converted into 5-FU by dThdPase in tumour cells, should be much safer and more effective than 5-FU.
Drug release
The drug release profile of Capecitabine from folic acid modified galactomannan functionalized iron oxide nanoparticles in PBS is given in Figure 11.The in-vitro drug release showed a slow, steady and controlled release of drug.Drug release profile shows a 30% release of capecitabine in 24 hours.Jin Hee Maeng, et al., observed similar results for doxorubicin loaded superparamagnetic iron oxide nanoparticles [14].Drug release profile showed 32% release of drug in 72 hours.The drug is released gradually over a period.This shows that the drug is released in a sustained manner.The slow, steady and controlled release of drug shows that the drug molecules are strongly bound to the polymer.From the study, it is concluded that capecitabine loaded with folic acid modified GM functionalized iron oxide nanoparticles is an effective carrier for the sustained drug delivery.X-ray image of swiss wistar rat Pathological analysis of Hepatocellular carcinoma (HCC) is based on macroscopic and microscopic aspects that are highly diversified and associated with prognosis for some FA-Cap, the shifts in bands from 2930 to 2927 cm -1 , 1632 to 1637 cm -1 and 1429 to 1420 cm -1 attributed to C-H, C=O and C-C group respectively, indicates that these groups are attached to the drug.The formation of new peaks at 2851, 2365, 1850, 1420, 1313, 1243 and 1022 cm -1 indicates the presence of capecitabine and the disappearance of peaks at 1508, 1148 and 812 cm -1 corresponding to aromatic C-C, C-O and aromatic C-H group respectively in FT-IR spectrum of FeNPs-GM -FA-Cap indicates that the corresponding groups are involved in the formation of FeNPS-GM -FA-Cap complex.
in-vitro cell cytotoxicity analysis
The extent of cytotoxicity from every single concentration of iron oxide nanoparticle was quantified as a percentage of cell viability including the absorbance values obtained as shown in the Figure 9.The percentages of cell viability above 80% are considered as non-cytotoxic; within 80%-60% are weak; 60%-40% are moderate and below 40% are strong cytotoxic [13].As observed in the Figure 9, all the percentages were high and consequently, the iron oxide nanoparticles were non-toxic at concentrations even up to 100 μg/ml.The viability range was within 83% to 71%.Thus, the invitro cytotoxicity studies clarified that the synthesized iron oxide nanoparticles did not have any toxic effect to the Hep2 cell line at the concentrations tested in the MTT assay.The prepared nanoparticles are well tolerated by Hep2 cells, making it suitable for various biological applications.
Recently investigations on iron oxides nanoparticles were increased in the field of nanosized magnetic particles (mostly maghemite, g-Fe 2 O 3 , or magnetite, Fe 3 O 4 , single domains of about 5-20 nm in diameter), among which magnetite is a very promising candidate since its biocompatibility has already proven [8].
Generally, in human cancer cell lines, the highest level of cytotoxicity was shown by 5-FU itself, followed cords and sinusoids appear very similar to healthy control.Treated group also shown increased cellularity, hyperchromatic nuclei, altered hepatocellular, contour, poorly maintained hepatocellular contour and dilated sinusoids.
Figure 12 reveals histological analysis of liver tissue sections from control group (1) animals revealed the normal architecture and cells with granulated cytoplasm and small uniform nuclei (Figure 12a).Group 2 DEN induced animals rat liver tissues revealed loss of their cell architecture, marked an ability to spread by intrahepatic veins, both hepatic and portal veins with significant tumor thrombi within portal vessels.Cytologically most of the tumor cells are slightly larger, have irregular shape of nuclei and numerous mitotic figures (Figure 12b).Group 3 FeNps capped with capecitabine treated animals showed normal architecture as well as some improved liver cell architecture indicating the therapeutic nature of capecitabine (Figure 12c).Because Capecitabine is a type of oral fluoropyrimidine carbamate, which is further converted into 5-fluorouracil (5-FU) molecule selectively in tumors through a cascade of three enzymes.This selectivity further supported by the FeNPs due their magnetic, hyperthermiea and EPR properties are make them effective usage in anticancer and drug delivery applications.A study reported that tissue localization of the three enzymes which are involving in the activation of capacitabine in humans, which was helpful for us to design the compound.Carboxylesterase was exclusively located in the liver and hepatoma, but not in other tumors and normal tissue adjacent to the tumors.There by it promoting the killing of cancer cells [16,17].
The main objective of nanosized drug delivery is accumulation of the drug molecules within tumors by EPR effect for the releasing of their therapeutic payloads.Hence, EPR effects are relatively potent, offering less than a 2-fold increase in delivery compared to critical normal organs.If the lifespan increases in circulation, which could help to extravasate nano drug into tumor through EPR effect.but at the same time, the drug can of them.After the administration of DEN carcinogen within one week they be tiny, discrete, translucent nodules on the capsular and surface cut surface of the remaining lobes.These results clearly indicate exposure of DEN chemical induces the changes in a few randomly located hepatocytes.The lesions continue to proliferate and become histologically in distinguishable from typical carcinogen induced hyperplastic liver nodules frequently described in the literature.Clinical evidence over several decade suggest that carcinogenesis is not a single step event but a gradual developmental process which may involves a series of sequential cellular alteration.Diethyl-nitrosamine (DEN) is known to induce liver cancer slowly with a single oral, intraperitoneal, intravenous administration.During the week following partial hepatocytes grow to become grossly visible as small translucent to grayish-white nodules, up to 1 mm in diameter, on the capsular and cut surface of the liver.The lesions are apparently induced by the DEN, for they are not formed in the absence of DEN pretreatment and they are numerically proportional to the initiating does of DEN [15].HCC typically form soft masses with a heterogeneous macroscopic appearance, polychrome with foci of hemorrhage or necrosis.They could be single or multiple with a size ranging from less than 1 cm to over 30 cm.Usually on cirrhosis, the size of HCC is smaller compared to those developed in non-fibrotic liver [6].On histology, the main hallmark of HCC is its resemblance to the normal liver both in its plate-like growth and its cytology [10].HCC is usually a hyper-vascularized tumor showing different degrees of hepatocellular differentiation.As compared to healthy control, untreated group reveals impressive inductive effect of carcinogen nonliver.Free compound group shows regression but is associated with poorly preserved hepatocellular architecture.Healthy control groups show normal cords of hepatocytes and sinusoids, untreated group shows hypercellularity, cellular and nuclear polymorphism and overtly hyperchromatic larger nuclei with increase nuclear cytoplasmic ratio.Treated groups shows Hepatic also extravasate into normal tissues albeit at a slower rate.Thus, methods that even temporarily increase the local EPR effect within the tumor are needed to improve the specific uptake of the drug within the tumor, thereby improving its therapeutic effect And FeNPs as such employed in hyperthermia applications.Iron magnetic nanoparticles used in the treatment of malignant tumours by hyperthermia (heat) method.In recent times, more advanced methods (hot water bath, pyrogens such as mixed bacterial toxins, perfusion heating, highfrequency radiation, magnetic fluid hyperthermia) were played vital role in heating and hopefully destroy, tumors [18].Magnetic field induced hyperthermia, one of the important therapies for cancer treatment, means the exposition of cancer tissues to an alternating magnetic field.Usually magnetic field did not absorb by the alive tissues and can be applied to deep region in the living body.If the magnetic particles are subjected to a strong variable magnetic field, some heat is generated because of magnetic hysteresis loss.The total amount of heat generated completely depends on the nature and properties of magnetic material and of magnetic field parameters.Magnetic particles embedded in the tumor site and placed within an oscillating strong magnetic field will heat up to a temperature directly proportional to the magnetic properties of the material, the strength of the magnetic field, the frequency of oscillation and the cooling capacity of the blood flow in the tumor site.When compared to normal cells, cancer cells could be destroyed at higher temperature than 43.1 °C., but the normal cells can be surviving at higher temperatures.Heat could be generated applying an appropriate magnetic field.The size of the magnetite crystals is submicrometric, so the powders or bulk of these biomaterials have comparable properties.These materials are not only biocompatible, but also bioactive and could be useful for bone tumors [19].
Conclusion
Green synthesis of metallic nanoparticles is a novel approaches and alternative for chemical and physical method of preparation of nanoparticles.Mimosa pudica used to synthesize the iron oxide nanoparticles.Iron oxide nanoparticles were successfully functionalized with Galactomannan and FA.These nanoparticles containing FA can be used to successfully target tumor cells expressing folate receptors.Anticancer drug Capecitabine was attached to FeNPs-GM-FA molecule for functionalization for drug delivery and targeting, offering an initial burst release and later sustained drug release at the tumor site effectively.The positive outcome of cell culture studies on iron nanoparticles and histological studies of hepatic tissue treated with functionalized FeNPs confirm a potential application in cancer therapeutics.
Figure 5 :
Figure 5: UV-Visible spectrum of iron nanoparticle via green synthesis.
Figure 7 :Figure 8 :
Figure 7: A) Iron nanoparticles average particle size; B) Particles average size of surface functionalized iron nanoparticles.
. The formation of new peaks at 1508, 1429, 1148 and 812 cm -1 corresponding to aromatic C-C, C-O, C-O of alcohol and aromatic C-H
Figure 9 :
Figure 9: Effect of various concentrations of iron oxide nanoparticles on HEp2 cell viability.
Figure 10 :
Figure 10: A) Control; B) Cells incubated with 2 μg/ml of iron oxide nanoparticles; C) Cells incubated with 40 μg/ml of iron oxide nanoparticles; D) Cells incubated with 100 μg/ml of iron oxide nanoparticles.
Figure 10
Figure10reveals the treatment of cells with iron nanoparticles.The synthesized iron oxide nanoparticles did not have any toxic effect to the HEp2 cell line at the concentrations tested in the MTT assay.The prepared nanoparticles are well tolerated by HEp2 cells, making it suitable for various biological applications.
Figure 11 :
Figure 11: Drug release profile of capecitabine from folic acid modified GM functionalized iron oxide nanoparticles. | 6,092.8 | 2018-12-31T00:00:00.000 | [
"Medicine",
"Chemistry"
] |
Evapotranspiration Estimation with the S-SEBI Method from Landsat 8 Data against Lysimeter Measurements at the Barrax Site, Spain
: Evapotranspiration (ET) is a variable of the climatic system and hydrological cycle that plays an important role in biosphere–atmosphere–hydrosphere interactions. In this paper, remote sensing-based ET estimates with the simplified surface energy balance index (S-SEBI) model using Landsat 8 data were compared with in situ lysimeter measurements for different land covers (Grass, Wheat, Barley, and Vineyard) at the Barrax site, Spain, for the period 2014–2018. Daily estimates produced superior performance than hourly estimates in all the land covers, with an average difference of 12% and 15% for daily and hourly ET estimates, respectively. Grass and Vineyard showed the best performance, with an RMSE of 0.10 mm/h and 0.09 mm/h and 1.11 mm/day and 0.63 mm/day, respectively. Thus, the S-SEBI model is able to retrieve ET from Landsat 8 data with an average RMSE for daily ET of 0.86 mm/day. Some model uncertainties were also analyzed, and we concluded that the overpass of the Landsat missions represents neither the maximum daily ET nor the average daily ET, which contributes to an increase in errors in the estimated ET. However, the S-SEBI model can be used to operationally retrieve ET from agriculture sites with good accuracy and sufficient variation between pixels, thus being a suitable option to be adopted into operational ET remote sensing programs for irrigation scheduling or other purposes.
Introduction
Evapotranspiration (ET) represents the loss of water from the Earth's surface to the atmosphere through the combined process of evaporation and transpiration. In general terms, the evaporation process occurs via open water bodies, bare soil, and plant surfaces, whereas the transpiration process occurs through vegetation or any other moisture-containing living surface [1]. Within the land-atmosphere interface, ET regulates the Earth's energy and water cycles [1][2][3][4][5][6]. As a result, its estimation is critical to the ideal design and management of irrigation systems, efficient irrigation scheduling, and a wide variety of water resource management efforts [7]. Although ET represents an essential component of the hydrological cycle, it is one of the least understood. It is estimated that 60% of the precipitated water returns to the atmosphere through ET [8]. Nonetheless, because of the complex physical and biological controls on evaporation and transpiration in addition to different land cover properties, ET estimates may diverge substantially [9].
Conventional measurements of ET (i.e., sap flow, weighing lysimeter, pan measurement, Bowen ratio system, eddy covariance system) have a limited use because they
Methodology
In this section, the application and validation of the S-SEBI model using Landsat 8 images to an agricultural region in Spain (Barrax) are presented. Figure 1 shows the flowchart of the methodology applied.
Remote Sens. 2021, 13, x FOR PEER REVIEW 3 Wheat, Barley, and Vineyard) and established a trusted validation for proper compreh sion of the method potentialities in generating novel ET products for future satellite m sions.
Methodology
In this section, the application and validation of the S-SEBI model using Lands images to an agricultural region in Spain (Barrax) are presented. Figure 1 shows flowchart of the methodology applied. The variables of the flowchart are presented in the next sections. In Figure 1, ND is the Normalized Difference Vegetation Index; T is the brightness temperature; SW is split-window method; Ts is the land surface temperature; ε is the emissivity; Rn is surface net radiation; G is the soil heat flux; TH and TLE are the temperatures correspond to dry and wet conditions; LET is the latent heat flux; Λ is the evaporative fraction; C the ratio between daily (Rd) and instantaneous (Rni) net radiation flux; and Chi is the r between hourly (Rhd) and instantaneous (Rni) net radiation flux.
A disaggregation algorithm for Ts data was included because of a high spatial va bility of the Barrax agricultural area and because we consider pixels of 100 m not rep sentative of some small plots, such as Vineyard or Barley and Wheat, areas of which less than 100 × 100 m. Disaggregation is recommended in order to retrieve a finer Ts p and more plot representation than a coarse Ts pixel, which can contain a mixture of ferent plots. The variables of the flowchart are presented in the next sections. In Figure 1, NDVI is the Normalized Difference Vegetation Index; T is the brightness temperature; SW is the split-window method; Ts is the land surface temperature; ε is the emissivity; Rn is the surface net radiation; G is the soil heat flux; T H and T LE are the temperatures corresponding to dry and wet conditions; LET is the latent heat flux; Λ is the evaporative fraction; C di is the ratio between daily (R d ) and instantaneous (R ni ) net radiation flux; and C hi is the ratio between hourly (R hd ) and instantaneous (R ni ) net radiation flux.
A disaggregation algorithm for Ts data was included because of a high spatial variability of the Barrax agricultural area and because we consider pixels of 100 m not representative of some small plots, such as Vineyard or Barley and Wheat, areas of which are less than 100 × 100 m. Disaggregation is recommended in order to retrieve a finer Ts pixel and more plot representation than a coarse Ts pixel, which can contain a mixture of different plots.
As the spatial resolution of thermal infrared pixels (100 m) is lower than visible/nearinfrared (VNIR) data (30 m), a disaggregation method was applied to Ts in order to meet the spatial resolutions of albedo and NDVI variables. To do so, a linear relationship between Ts and NDVI in a sliding 5 × 5 pixel window was performed to retrieve the Ts pixel at 30 m, following the methodology proposed by Jeganathan et al. [29].
Study Area Description
This study was performed at the Barrax site located in the west of Albacete province, Spain. The site is a Mediterranean climate test area with the heaviest rainfalls in spring and autumn and the lowest in summer ( Figure 2). The rainfall statistics show that the average annual rainfall is little more than 400 mm in most of the area, making La Mancha one of the driest regions in Europe [4,6,17,18,[30][31][32][33]. The Barrax area has been selected in many field campaigns for calibration/validation activities because of its flat terrain and the presence of large, uniform land-use units (approximately 100 ha), suitable for validating moderate-resolution satellite image products.
As the spatial resolution of thermal infrared pixels (100 m) is lower than visible/nearinfrared (VNIR) data (30 m), a disaggregation method was applied to Ts in order to meet the spatial resolutions of albedo and NDVI variables. To do so, a linear relationship between Ts and NDVI in a sliding 5 × 5 pixel window was performed to retrieve the Ts pixel at 30m, following the methodology proposed by Jeganathan et al. [29].
Study Area description
This study was performed at the Barrax site located in the west of Albacete province, Spain. The site is a Mediterranean climate test area with the heaviest rainfalls in spring and autumn and the lowest in summer (Figure 2). The rainfall statistics show that the average annual rainfall is little more than 400 mm in most of the area, making La Mancha one of the driest regions in Europe [4,6,17,18,[30][31][32][33]. The Barrax area has been selected in many field campaigns for calibration/validation activities because of its flat terrain and the presence of large, uniform land-use units (approximately 100 ha), suitable for validating moderate-resolution satellite image products.
In Situ Data
Barrax has a fixed station over a grass field with continuous land surface temperature (Ts) measurements taken by a radiometer that covers a footprint of 3 m² [34]. Besides Ts, this station provides other variables, such as wind direction and speed, soil flux, moisture and temperature, air temperature, and humidity, as well as net radiation. The net radiometer (model NR01) carries out separate measurements of solar (direct and reflected) and
In Situ Data
Barrax has a fixed station over a grass field with continuous land surface temperature (Ts) measurements taken by a radiometer that covers a footprint of 3 m 2 [34]. Besides Ts, this station provides other variables, such as wind direction and speed, soil flux, moisture and temperature, air temperature, and humidity, as well as net radiation. The net radiometer (model NR01) carries out separate measurements of solar (direct and reflected) and far infra-red (direct and reflected) radiations. A pyranometer measures the solar radiation flux from a field of view of 180 • and has a spectral response from 0.3 µm to 2.8 µm. A pyrgeometer measures the far infra-red radiation flux from a field of view of 180 • and has a spectral response from 4.5 µm to 50 µm.
The study area also has three continuous weighing lysimeters (see Figure 2) with electronic data readings: one lysimeter for Grass crops, one for rotating herbaceous crops (Wheat and Barley), and a permanent one for Vineyard. Each lysimeter is surrounded by a square protection plot of one hectare; the dimensions of the Grass and herbaceous crop lysimeter samples are 2.3 m 2.7 m to a side and 1.7 m depth with approximately 14.5 t total mass, and the Vineyard lysimeter sample is 3 m × 3 m to a side and 1.7m depth with 18.5 t total mass. The lysimeters have the necessary equipment to make a complete and accurate hydric balance as explained and tested by many authors [32,35]. The data are available in hourly measurements, which were used to validate the estimated ET calculated by the S-SEBI model between March 2014 and April 2018.
Satellite Data
We selected 62 Landsat 8 OLI/TIRS images to assess the efficiency of the S-SEBI model in estimating ET over different crops. Table 1 shows the days of years (DOYs) of the scenes used for each land cover and year evaluated. Grass has the largest amount of available in situ data for validation, thus being the land cover with more images selected.
Operational Equations
In order to apply the S-SEBI from remote sensing-based models, some variables are required. Table 2 exhibits the mathematical expressions used to estimate the Normalized Difference Vegetation Index (NDVI), albedo (α), land surface temperature (Ts), and land surface emissivity (ε). The equations were employed for all the Landsat scenes (Table 1) to obtain instantaneous LE in watts, which was subsequently converted to ET. Ti and Tj are the at-sensor brightness temperatures at the bands i (10) and j (11) in Kelvins; εi and εj are the emissivities for bands 10 and 11, respectively; ε is the mean emissivity, ε = 0.5 (εi + εj); ∆ε is the emissivity difference, ∆ε = (εi − εj); w is the total atmospheric water vapor content (in g/cm −2 ) [37,38] ε a + bρRED; FVC is the fractional vegetation cover and is given by = NDV I − NDV Is/NDV Iv − NDV Is ; ε s and ε v are the soil and vegetation emissivity values, respectively. [39] Remote Sens. 2021, 13, 3686 6 of 17
Evapotranspiration Estimation by the S-SEBI Model
The estimation of ET from remote sensing data is based on assessing the SEB through several surface properties, such as albedo, vegetation cover, and Ts [5]. When considering instantaneous conditions, the SEB is written as where Rn, H, and G are the surface net radiation, the sensible heat flux, and the soil heat flux, respectively, all are expressed in energy units (W/m 2 ), and LET is the latent heat flux and can be obtained according to where (Λ) is the evaporative fraction [6], adapted and tested [4,31], and it is described by where Ts is the land surface temperature, and T H and T LE are the temperatures corresponding to dry and wet conditions, all in Kelvin. Dry and wet temperatures are retrieved in function of the albedo value by plotting a scatterplot between surface temperature and albedo [6].
Once Λ is obtained, LET (see Equation (2)) requires the knowledge of Rn and G, which can be obtained according to Rg and Ra being the incident solar radiation and the longwave radiation, respectively, are both measured in W m −2 ; α is the surface albedo; ε is the surface emissivity; Ts is the land surface temperature; and σ is the Stefan-Boltzmann constant (= 5.67 × 10 −8 W m −2 K −4 ).
To obtain G, we considered the approach given by the authors [15,30], i.e., where NDVI is the Normalized Difference Vegetation Index [32].
Daily and Hourly ET
The comparison between ET obtained by the S-SEBI model on different crops and in situ lysimeter data was carried out considering both hourly (in mm/h) and daily (in mm/day) values. While lysimeter data are given as hourly and daily values, S-SEBI values are only instantaneous at the moment of the satellite overpass and are given in W/m 2 . Therefore, in order to match the time scales, it was necessary to convert the instantaneous values acquired through the images to hourly and daily values. The daily ET (ET daily ) is defined as the temporal integration of ET instantaneous values during a day and can be obtained using the C di [17,31], which consists of the ratio between daily (R nd ) and instantaneous (R ni ) net radiation flux, respectively, according to where λ is the latent heat of vaporization (2.45 MJ/kg); the soil heat flux (G) is considered equal to zero and not included in the equation [40] assuming that much of the energy that enters and reaches the soil during the day returns to the atmosphere at night through terrestrial longwave radiation; Λ is the evaporative fraction and can be considered constant during the day. Analogously, hourly ET (ET hourly ) in mm/h is obtained as where C hi is the ratio between hourly (R hd ) and instantaneous (R ni ) net radiation flux, and G i is the instantaneous soil heat flux (considering it constant and assuming that the impact on results is minimal and that Λ during the hour is also constant). For both conversions R n , R nh , and R nd have been retrieved from a tower flux located in the study area ( Figure 2) in order to reduce the uncertainties of hourly and daily estimations.
Statistical Metrics
The development of the algorithms and image processing was carried out in interactive data language (IDL). The operational application of the S-SEBI model requires the identification of the percentile boundary limits to be automatized. These limits are used to obtain the evaporative fraction, which is the basis of the method. We tested different percentile values (0.01; 0.1; 0.2) and selected 0.1% for the entire dataset because it demonstrated the best estimates all over the land cover types. Finally, to assess the performance of the S-SEBI, we used the root mean square error (RMSE), which allows one to quantify the difference between simulated and observed data. In addition, the mean standard deviation (MSD) and bias were also used to complement the statistical analyses.
Comparison of S-SEBI Estimated and Measured ET
The comparison of the S-SEBI hourly and daily ET against lysimeter data for each land cover type is shown in Figure 3a,b, respectively. Generally, the daily estimates had moderately superior performance relative to the hourly estimates in all the land covers assessed. Grass produced the best linear relationship with the in situ ET data. This may indicate that the relation is better when the land cover is more homogeneous. The biases of the hourly and daily ET estimated by the S-SEBI in comparison to the lysimeter data were also plotted and are exhibited in Figure 3c, d. When the bias is positive, the model overestimates the ET, which was observed mostly for dates with low values of ET. The hourly bias of the S-SEBI varied between -0.4 mm/h and 0.4 mm/h (Figure 3c), and the ET overestimation of the in situ values occurred essentially between 0.05 mm/h and 0.6 mm/h. On the other hand, when the in situ ET is higher (between 0.6 mm/h and 0.9 mm/h), the model tends to underestimate the ET. A similar random pattern was seen in the daily bias, which varied between −3.2 mm/day and 5.3 mm/day, producing values closer to zero (Figure 3d).
A difference of 12% (0.45 mm/day) was found between the S-SEBI model and the lysimeters, with an average daily ET for all the land covers of 3.55 mm/day and 4.01 mm/day, respectively. In contrast, the average hourly ET is 0.44 mm/h for the S-SEBI and 0.36 mm/h for the lysimeters, with a difference of 15% (−0.07mm/h). Different accuracy situations have been reported in the literature for remote sensing-based ET models in comparison to lysimeter data. Using the METRIC model, Chavez et al. [41] found similar but slightly larger errors for hourly ET in comparison to the daily values. An evaluation carried out in Tanjung Karang, China, used the SEBAL model and meteorological and lysimeter data over cultivated rice and found that the determination of ET by satellite data overestimates the values obtained from lysimeters by 10% [42]. In a semiarid climate in Las Tiesas, Spain, different models overestimated the lysimeter measurements between 3% and 70% depending on the method applied [43]. Mkhwanazi et al. [44] developed a modified SEBAL model that requires daily averages of limited weather data and validated it against lysimeter data over an Alfalfa field. The authors reported average underestimates with values up to 24% for the modified model and up to 38% for the original SEBAL algorithm. Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 18 A difference of 12% (0.45 mm/day) was found between the S-SEBI model and the lysimeters, with an average daily ET for all the land covers of 3.55 mm/day and 4.01 mm/day, respectively. In contrast, the average hourly ET is 0.44 mm/hour for the S-SEBI and 0.36 mm/hour for the lysimeters, with a difference of 15% (−0.07mm/hour). Different accuracy situations have been reported in the literature for remote sensing-based ET models in comparison to lysimeter data. Using the METRIC model, Chavez et al. [41] found similar but slightly larger errors for hourly ET in comparison to the daily values. An evaluation carried out in Tanjung Karang, China, used the SEBAL model and meteorological and lysimeter data over cultivated rice and found that the determination of ET by satellite data overestimates the values obtained from lysimeters by 10% [42]. In a semiarid climate in Las Tiesas, Spain, different models overestimated the lysimeter measurements between 3% and 70% depending on the method applied [43]. Mkhwanazi et al. [44] developed a modified SEBAL model that requires daily averages of limited weather data and validated it against lysimeter data over an Alfalfa field. The authors reported average underestimates with values up to 24% for the modified model and up to 38% for the original SEBAL algorithm. Table 3 summarizes the statistical metrics of the hourly and daily ET between the S-SEBI and lysimeter data. Good agreements were obtained from the satellite-based estimates, with RMSE varying from 0.1 mm/hour to 0.19 mm/hour for hourly and from 0.63 to 1.71 for daily ET, respectively. These results are in accordance with other validation exercises reported for the S-SEBI model worldwide [4,6,20,22,23,31,45]. Table 3 summarizes the statistical metrics of the hourly and daily ET between the S-SEBI and lysimeter data. Good agreements were obtained from the satellite-based estimates, with RMSE varying from 0.1 mm/h to 0.19 mm/h for hourly and from 0.63 to 1.71 for daily ET, respectively. These results are in accordance with other validation exercises reported for the S-SEBI model worldwide [4,6,20,22,23,31,45]. The performance of the hourly ET produced superior estimates for Grass and Vineyard, with an RMSE and MSD of 0.10 and ±0.09 for Grass and 0.09 and ±0.09 for Vineyard, respectively. Wheat and Barley had the worst hourly ET estimates, with an RMSE and MSD of 0.19 and ±0.16 for Wheat and 0.16 and ±0.09 for Barley, respectively. Knowledge of the hourly ET has several advantages, and its accuracy evaluation plays an important role in quantifying estimation errors with irrigation water management practices. However, the hourly satellite calibration is a typical source of uncertainty in satellite SEB models. Hashem et al. [46] compared the hourly ET with lysimeter data in Texas. By using the METRIC model, the authors found average RMSEs of 0.14 mm/h and 0.16 mm/h for dry and irrigated agriculture lands, respectively. Despite the fact that the METRIC model was developed with a focus on agriculture areas and is proven to perform very well for these land covers, its computation requires one to determine roughness length, which is a complicated variable to retrieve with enough accuracy from classic remote sensing methods [17]. Moreover, over crops in Texas, Gowda et al. [27] compared the performance of the hourly ET from the SEBS model with data from four lysimeters using a dataset of 16 Landsat 5 images. The authors reported high accuracy with an average RMSE of 0.11 mm/h. Nevertheless, they pointed out that a locally derived surface albedobased G model improved the G component estimates. The limitations of the empirical formulation used to derive G from remote sensing have already been emphasized in other works [23,24]. Furthermore, roughness length is also required in SEBS model computation, in addition to other meteorological inputs, such as air temperature, humidity, and wind speed measured at a reference height, which sustains the superiority hypothesis of the S-SEBI in terms of simplicity. The hourly biases of the land covers assessed were mostly negative except for Barley, which produced 0.08. This indicates that the hourly ET was predominantly underestimated.
The performance of the daily ET estimates, such as the hourly estimates, produced the best metrics for Grass and Vineyard, with an RMSE and MSD of 1.11 and ±0.98 for Grass and ±0.46 and 0.63 for Vineyard, respectively. The daily bias exhibited negative results for Wheat and Vineyard, with values of -0.50 and -0.43, respectively. Unlike the hourly metrics, the daily ET results of Wheat are notably better in comparison to Barley. However, it is worth mentioning that the amount of available data for Barley is reduced relative to the other land cover types, and, consequently, it may not have properly included the annual and pluriannual variability of ET. In order to evaluate the influence of weather conditions (particularly cloud cover impacts) on the S-SEBI model's accuracy, we calculated the statistical metrics and excluded the days with clouds, which are discussed in the next section.
Uncertainties in the S-SEBI Estimates
The concept of evaporative fraction is the basis of the S-SEBI model. However, its diurnal constancy may not be satisfied under cloudy circumstances [47]. Therefore, we selected 55 entirely cloud-free scenes to evaluate the performance of the algorithm under ideal conditions. Table 4 shows the statistical metrics obtained in the daily analysis. The results found demonstrate a considerable improvement in the ET estimates when the atmospheric conditions do not vary much during the day. In general, the average RMSE decreases from 1.25 mm/day to 0.86 mm/day when only ideal scenes are used. The low errors suggest that the model works very well for the estimation of ET in all the land covers. The RMSE was found to be 0.85 mm/day for Grass, 0.81 mm/day for Wheat, 1.32 mm/day for Barley, and 0.46 mm/day for Vineyard. The MSD indicates that the differences between model results and lysimeter data are less than 1 mm/day, which is in agreement with Sobrino et al. [31]. Table 4. Statistical analyses of the S-SEBI model performance with daily (mm/day) lysimetric data, excluding partial cloudy days (n = 55).
Grass
Wheat ( Typically, in the S-SEBI model, errors in the determination of TH and TLET lines (and consequently in the evaporative fraction) impact the obtention of the instantaneous LET, which directly affects the ET estimates. Afterward, the daily ET is extrapolated from instantaneous to daily ET by using the C di (Equation (6)). According to Singh and Senay [48], different methods of upscaling have their own bias. Yang et al. [49] demonstrated that in most of their dataset, variation of the evaporative fraction during daylight tended to be stable within the time window of 10:00 and 15:00 UTC. However, after this window, it is not constant and can affect the C di . According to some authors [14,50], there are many difficulties to convert instantaneous ET into daily ET, mostly due to the nonstable conditions of the evaporative fraction during a daylight period, which vary with the available energy, surface resistance, and other environmental variables. However, because in the S-SEBI model the daily ET is calculated using the available net flux radiation during the day, the daily ET estimates produced are reliable [21,31], which can be considered a strength of the methodology applied. Figure 4 illustrates the behavior of the solar radiation during different DOYs. The solar radiation data from the flux tower were analyzed on the DOY of greatest errors ( Typically, in the S-SEBI model, errors in the determination of TH and TLET lines (and consequently in the evaporative fraction) impact the obtention of the instantaneous LET, which directly affects the ET estimates. Afterward, the daily ET is extrapolated from instantaneous to daily ET by using the Cdi (Equation (6)). According to Singh and Senay [48], different methods of upscaling have their own bias. Yang et al. [49] demonstrated that in most of their dataset, variation of the evaporative fraction during daylight tended to be stable within the time window of 10:00 and 15:00 UTC. However, after this window, it is not constant and can affect the Cdi . According to some authors [14,50], there are many difficulties to convert instantaneous ET into daily ET, mostly due to the non-stable conditions of the evaporative fraction during a daylight period, which vary with the available energy, surface resistance, and other environmental variables. However, because in the S-SEBI model the daily ET is calculated using the available net flux radiation during the day, the daily ET estimates produced are reliable [21,31], which can be considered a strength of the methodology applied. Figure 4 illustrates the behavior of the solar radiation during different DOYs. The solar radiation data from the flux tower were analyzed on the DOY of greatest errors ( The "noises" observed in the solar radiation curve clearly reflect the differences between the observed and estimated daily ET. In a clear-sky day when the solar radiation does not show noises caused by clouds or large amounts of water vapor, the S-SEBI-based estimates exhibit an accuracy much lower than 1 mm/day. On 17 April 2014 (DOY 107), the difference between the in situ ET and calculated ET is 0.23 mm/day. In contrast, when the daily solar radiation curve presents some noises and the weather conditions vary widely during the day, the difference between the in situ ET and the model estimates is 2.92 mm/day for 6 November, 2014 (DOY 162), and 1.89 mm/day for 27 November 2014 (DOY 178). In addition to the solar radiation, seasonal drivers from the land surface can strongly affect the ET, making the estimates differ substantially. Yang et al. [49] examined remote sensing-based ET estimates from high-resolution data over Wheat in different months and reported an overall RMSE of 0.67 mm/day. The authors pointed out that in months with low coverage and row pattern at the turning green stage, the satellite-based ET accuracy is impacted. In contrast, when the crop is at the harvest stage, better estimates are produced. This occurs particularly because at the time that the normal crop physiological and ecological processes are gradually ending, the soil evaporation is over again, the main contributor to ET.
Variation of ET during the Daytime
At the Barrax site, the lysimeters are located in the center of 100 × 100 m plots, and the data are available hourly. As some in situ ET data were missing for Vineyard, they were not included. The average daily ET measured for the entire period was 5.4 mm/day for Wheat, 4.6 mm/day for Barley, and 3.7 mm/day for Grass. Given that differences in the thermal, wind, and weather conditions and the radiation regime between a lysimeter device and its surroundings can affect the measurements [51], we investigated the hourly average for each land cover type. Figure 5 displays the hourly averages of ET and the maximum values obtained from the lysimeters.
At the Barrax site, the lysimeters are located in the center of 100 × 100 m plots, and the data are available hourly. As some in situ ET data were missing for Vineyard, they were not included. The average daily ET measured for the entire period was 5.4 mm/day for Wheat, 4.6 mm/day for Barley, and 3.7 mm/day for Grass. Given that differences in the thermal, wind, and weather conditions and the radiation regime between a lysimeter device and its surroundings can affect the measurements [51], we investigated the hourly average for each land cover type. Figure 5 displays the hourly averages of ET and the maximum values obtained from the lysimeters. Overall, the ET exhibits typical fluctuations in shape during the day, varying between 7:00 and 20:00 UTC. The hourly ET for Grass ranged from 0.03 mm/h to 0.43 mm/h, with an hourly average of 0.24 mm/h and its maximum value at 13:00 UTC. For Wheat, the hourly ET ranged from 0.04 mm/h to 0.66 mm/h, with an hourly average of 0.36 mm/h and its maximum value at 14:00 UTC. Finally, for Barley, the hourly ET ranged from 0.05 mm/h to 0.52 mm/h, with an hourly average of 0.30 mm/h and its maximum value at 14:00 UTC. Yang et al. [52] reported noticeable daytime ET variations between 7:00 and 18:00, with a peak typically occurring at approximately 14:00 UTC.
Although between 13:00 and 15:00 UTC the ET measurements for each land cover are relatively constant, the maximum differences between curves are more significant in this period. However, at the time of the Landsat 8 overpass (10:42 UTC), the in situ ET values increased notably quicker. This behavior was observed for all the land cover types. In the S-SEBI model application, the conversion from instantaneous to daily ET through the C di assumes that at the time of the satellite overpass, the highest value of ET is being measured; nevertheless, the maximum ET values are seen after the Landsat 8 overpass, around 13:00-14:00 UTC. Consequently, the discrepancy between the hourly ET in situ and the instantaneous ET from Landsat 8 can be a potential source of uncertainty for ET validation. Figure 6 shows the distribution of the hourly and daily ET from the S-SEBI compared to lysimeter ET in situ values for the whole period. Similar patterns were found in daily ET for Grass, Wheat, and Barley fields between seasons, which demonstrates a clear seasonal pattern, with higher values in summer and lower values in winter due to the cold weather conditions [53]. Figure 6a,c illustrate the hourly and daily ET in the Grass field, respectively. The hourly ET ranged between 0.06 mm/h during the winter season and 0.8 mm/h in summer and spring seasons. In most cases, the modeled ET underestimates the values measured by the lysimeter, as while the average lysimeter ET is 0.39 mm/h, the predicted is 0.34 mm/h. The largest differences between predicted and observed daily ET were noted also in the summer season (DOY 170/2017), in which the lysimeter ET was 8.94 mm/day and the predicted ET was 5.3 mm/day. These results are in agreement with López-Urrea et al. [43], where FAO Penman-Monteith was applied and compared with lysimeter data. The authors pointed out that the model underestimated ET values mainly during periods of greater evaporative demand. Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 18 In Figure 6b,d, we depict the hourly and daily ET results in the Wheat and Barley fields. When the satellite-based hourly ET exceeds the lysimeters' observations, the daily ET tends to exhibit the same behavior. As a crop field is irrigated according to its water need to prevent stress, the only important factor that affects the ET results is the growing and harvesting season. As it was pointed at the end of Section 3.2, when low crop coverage is present (DOYs 82-123), the model shows more uncertainties in comparison to the late stages of the crop. The S-SEBI model also outperforms when very high and low ET values are achieved. This overtaking was already reported in other studies for the S-SEBI model. Käfer et al. [23] compared ET estimates derived from the S-SEBI with a neural networkbased model in Southern Brazil, which suggested that the S-SEBI values tend to decrease accuracy in estimating extreme ET values, commonly in the transition seasons between winter and summer.
Seasonally Distributed ET
The overestimates from the S-SEBI model, which were more pronounced in the summer-spring season, were already reported [12]. The authors claimed that, particularly during severe drought conditions, the parameterization will overestimate ET. The biggest difference between hourly ET occurred in the spring season (DOY 123/2014), in which the standard deviation was 0.39 mm/hour and the highest rate of water loss occurred. These findings are in accordance with Liu et al. [53], who observed the highest ET in May after the over-wintering period. The differences between estimated ET and lysimeter data can be explained by the evaporative fraction calculation in the S-SEBI model. Summarily, on DOY 123, for higher albedo values, the Ts does not increase significantly as expected; consequently, it generates a greater error in the Ts determination to dry and wet conditions. On DOY 163/2017 over the Barley field, a similar behavior was seen. This evidences the limitation of the S-SEBI model when operationally applied. The relationship between higher albedos and Ts is well documented in the literature. Sobrino et al. [31] and Gómez et al. [17] demonstrated that identifying the boundary limits to obtain the evaporative In Figure 6b,d, we depict the hourly and daily ET results in the Wheat and Barley fields. When the satellite-based hourly ET exceeds the lysimeters' observations, the daily ET tends to exhibit the same behavior. As a crop field is irrigated according to its water need to prevent stress, the only important factor that affects the ET results is the growing and harvesting season. As it was pointed at the end of Section 3.2, when low crop coverage is present (DOYs 82-123), the model shows more uncertainties in comparison to the late stages of the crop. The S-SEBI model also outperforms when very high and low ET values are achieved. This overtaking was already reported in other studies for the S-SEBI model. Käfer et al. [23] compared ET estimates derived from the S-SEBI with a neural networkbased model in Southern Brazil, which suggested that the S-SEBI values tend to decrease accuracy in estimating extreme ET values, commonly in the transition seasons between winter and summer.
The overestimates from the S-SEBI model, which were more pronounced in the summer-spring season, were already reported [12]. The authors claimed that, particularly during severe drought conditions, the parameterization will overestimate ET. The biggest difference between hourly ET occurred in the spring season (DOY 123/2014), in which the standard deviation was 0.39 mm/h and the highest rate of water loss occurred. These findings are in accordance with Liu et al. [53], who observed the highest ET in May after the over-wintering period. The differences between estimated ET and lysimeter data can be explained by the evaporative fraction calculation in the S-SEBI model. Summarily, on DOY 123, for higher albedo values, the Ts does not increase significantly as expected; consequently, it generates a greater error in the Ts determination to dry and wet conditions. On DOY 163/2017 over the Barley field, a similar behavior was seen. This evidences the limitation of the S-SEBI model when operationally applied. The relationship between higher albedos and Ts is well documented in the literature. Sobrino et al. [31] and Gómez et al. [17] demonstrated that identifying the boundary limits to obtain the evaporative fraction is the critical point of this method and reported that in some cases it reached 1.4 mm/day. In addition, differences between in situ and estimated ET can be related to the extension of the area evaluated, especially given the contrast influence in the landscape that may result in pixel mixing in the albedo and Ts determination. The fact that the cultivated area is smaller than the 30 meter pixel size presents scale issue to the Ts estimated and, therefore, the validation results. In this study, although we used a fixed percentile value for the whole dataset, the ET estimates produced a very high accuracy, and the cloudy effect clearly compromises the albedo-Ts relationship more significantly than the other factors mentioned.
Spatially Distributed ET
Remote sensing techniques have provided an efficient way to retrieve multi-year, spatially consistent, and temporally continuous ET products on the regional to global scale [5,23,25,31,54]. One of their main advantages is to provide estimates from the whole territory, capturing small spatial variations between pixels that allows one to assess the efficiency of the water use and irrigation and groundwater recharge projects or return flows [41]. Figure 7 exhibits the spatial pattern of daily and hourly ET obtained from the S-SEBI method by using a Landsat 8 image over Barrax in the spring season, 17 April 2014 (DOY 107). Overall, the S-SEBI model can capture the spatial variability of evaporative demand of the atmosphere over the whole study area. Specifically in the daily ET map (Figure 7a), the bare areas with lower ET (blue color) and crop areas with higher ET (red color) can be well distinguished. There were no differences between in situ measurements (lysimeter data) and from the S-SEBI model in Grass land cover. In contrast, over the Wheat field, a difference of 0.24 mm/day was found. In the hourly ET map (Figure 7b), the bare areas with lower ET are less prominent and discriminated from the other fields and irrigated areas. The hourly ET average was 0.6 mm/h, which is close to the hourly average ET of April (0.64 mm/h). The difference between in situ data and the S-SEBI model was 0.16 mm/h in Grass and 0.23 mm/h in the Wheat area. In addition to the smaller error obtained in the daily analysis discussed in Section 3.2, spatially, the daily analysis has more contrast in areas with higher ET and potential water deficit. These findings are important with regard to the water planning of agricultural areas, considering that effective water resource management requires an accurate estimation of the water use and availability to face challenges of water scarcity [55]. In addition to the smaller error obtained in the daily analysis discussed in Section 3.2, spatially, the daily analysis has more contrast in areas with higher ET and potential water deficit. These findings are important with regard to the water planning of agricultural areas, considering that effective water resource management requires an accurate estimation of the water use and availability to face challenges of water scarcity [55].
Conclusions
The ET is a key component of water balance, and despite the significant advances in the last decades, remote sensing-based models are not free from uncertainties, especially when applied over different conditions for which they have not been originally developed or calibrated for. Therefore, assessing efficiency in techniques for monitoring water use is a constant research topic. In this paper, we investigated the ET obtained operationally by the S-SEBI model from Landsat 8 data between 2014 and 2018 at the Barrax Site, Spain. Four different land cover types were evaluated (Grass, Wheat, Barley, and Vineyard) and validated against lysimeter observations.
In general, the daily estimates produced slightly superior performance relative to the hourly estimates in all the land covers, with an average difference of 12% and 15% for daily and hourly ET estimates, respectively. Grass and Vineyard showed the best performance, with an RMSE of 0.10 mm/h and 0.09 mm/h and 1.11 mm/day and 0.63 mm/day, respectively. Nonetheless, when only ideal scenes (without any cloud cover) are considered, the accuracy expressly improves, indicating that the model works very well for all the land covers in suitable conditions. Thus, the S-SEBI model is able to retrieve ET from Landsat 8 data with an average RMSE for daily ET of 0.86 mm/day.
In the operational application of the S-SEBI, identifying operationally the boundary limits of percentiles to obtain the evaporative fraction is challenging. Our findings have shown that assuming a fixed percentile value (0.1%) for different crops can produce enough ET accuracy. In addition, although the conversion from instantaneous to daily ET is frequently cited as a limitation of the remote sensing-based ET models, the mechanism used to extrapolate instantaneous ET to daily values resulted in improved ET estimates; therefore, we strongly encourage the application of the C di concept. In fact, the high accuracy of the in situ flux data used contributed to the good performance of the daily estimates. However, it is important to highlight that this is not a restriction, because hourly radiation data are available for the whole globe and can be easily obtained from several reanalysis products and used to generate trustable and continuous daily ET series [56].
The hourly ET obtained from the lysimeters provided a detailed analysis of the ET pattern during the day. Between 13:00 and 15:00 UTC, the ET measurements for all the land covers are relatively constant, and the maximum values occurred at 13:00-14:00 UTC. At the time of the Landsat 8 overpass (10:42 UTC), the in situ ET values showed a rapid increase. Because the C di assumes that at the time of the satellite overpass the highest value of ET is being measured, which it clearly is not, the discrepancy between the hourly ET in situ and the instantaneous ET from Landsat 8 can be a source of uncertainty. The overpass of the Landsat missions represents neither the maximum daily ET nor the average daily ET. Differently, more significant variations are seen 10:00-11:00 UTC, which contribute to increase errors in the estimated ET. In addition, it is worth mentioning that the Landsat pixel size also does not appropriately represent the test sites to validate ET; i.e., the spatial resolution of the TIR sensor of the Landsat satellite is not fully adequate for ET estimates. However, it is expected that with the new Sentinel projects and the improved resolution, these issues will be minimized.
The S-SEBI is a model of simple application and low dependence of complex inputs that can well capture the spatial variability of evaporative demand and produce robust daily ET maps over different crops without much effort. Hence, it can be used to operationally retrieve ET from agriculture sites with good accuracy and sufficient variation between pixels, thus being a suitable option to be adopted into operational ET remote sensing programs for irrigation scheduling or other purposes. Funding: This study has been funded by the Ministry of Economy and Competitiveness TIRSAT project (ESP2015-71894-R). R. López-Urrea thanks the funding obtained from the Ministry of Economy and Competitiveness (project AGL2017-83738-C3-3-R) and the Ministry of Education, Culture and Sports (JCCM) (project SBPLY/17/180501/000357), both co-financed with FEDER funds, and the RET-SIF project, PCI2018-093121 founded by Ministerio de Ciencia, Inovación y Universidades. | 10,089.8 | 2021-09-15T00:00:00.000 | [
"Environmental Science",
"Mathematics"
] |
Triggering of cancer cell cycle arrest by a novel scorpion venom‐derived peptide—Gonearrestide
Abstract In this study, a novel scorpion venom‐derived peptide named Gonearrestide was identified in an in‐house constructed scorpion venom library through a combination of high‐throughput NGS transcriptome and MS/MS proteome platform. In total, 238 novel peptides were discovered from two scorpion species; and 22 peptides were selected for further study after a battery of functional prediction analysis. Following a series of bioinformatics analysis alongside with in vitro biological functional screenings, Gonearrestide was found to be a highly potent anticancer peptide which acts on a broad spectrum of human cancer cells while causing few if any observed cytotoxic effects on epithelial cells and erythrocytes. We further investigated the precise anticancer mechanism of Gonearrestide by focusing on its effects on the colorectal cancer cell line, HCT116. NGS RNA sequencing was employed to obtain full gene expression profiles in HCT116 cells, cultured in the presence and absence of Gonearrestide, to dissect signalling pathway differences. Taken together the in vitro, in vivo and ex vivo validation studies, it was proven that Gonearrestide could inhibit the growth of primary colon cancer cells and solid tumours by triggering cell cycle arrest in G1 phase through inhibition of cyclin‐dependent kinases 4 (CDK4) and up‐regulate the expression of cell cycle regulators/inhibitors—cyclin D3, p27, and p21. Furthermore, prediction of signalling pathways and potential binding sites used by Gonearrestide are also presented in this study.
high capacity for structural modifications and high target specificity. [5][6][7][8] Unlike most conventional chemotherapies, many anticancer peptides have the capacity to specifically and selectively target cancer cells and they can also be used in combination with other anticancer therapeutics, with which the observed synergistic effects have been found to improve outcomes. 9,10 Nature has always been a capable and predictable source of remarkable pharmaceutical substances with potential usage for the treatment of many diverse diseases. It has been proven that peptides/proteins are generally the major components of venoms, and many of these have either shown high potential or indeed had such realised, to defeat diseases such as bacterial/fungal infections, cardiovascular disorders, diabetes and cancers. [11][12][13] However, less than 1% of the peptide/protein components of venoms have been well studied at present. 6 One of the reasons for this is due to the fact that traditional proteomic approaches to address this problem are slow. Recently, improvements in liquid chromatography-tandem mass spectrometry (LC-MS/MS) have made it more accurate, sensitive and amenable to high-throughput de novo sequencing of venom peptidomes/proteomes. [14][15][16] Also, the development of next-generation DNA sequencing technology can also facilitate higher throughput in this process and indeed is powerful enough and cost-efficient for ultrahigh-throughput transcriptome analysis. [17][18][19][20][21] Some venom researchers have started to apply these two approaches, but erroneous assembly is a major limitation of next-generation sequencing technology, while LC-MS/MS requires an existing database of structures to validate the de novo sequencing results. [22][23][24] Hence, a highthroughput platform combining transcriptome and proteome sequencing was established in this study and employed successfully to enable large-scale, high-throughput identification of novel bioactive peptides in venoms.
Based on this platform, we have identified a panel of novel potential anticancer peptides in scorpion venoms. Anticancer peptide research has been performed at a low level for around 50 years now with limited success and understanding of their mechanisms of action is still in the initial stage. To reveal the potential anticancer mechanisms of candidate peptide, a recently invented transcriptomecentric strategy was employed to predict their putative functions and targeted signalling pathways. Compared to traditional mechanistic study approaches, this was able to monitor the collective responses of all relevant genes without specific mechanistic or targeting hypotheses. [25][26][27][28][29][30][31] On the other hand, although the transcriptome-centric approach has been applied in some research, the enormous challenges in terms of data processing, storage and interpretation as well as sequencing quality control have been huge limitations which have hindered the translation from sequence data to clinical practice, but a few studies have succeeded in proving the concept. [32][33][34][35] Hence, here, we performed related in vitro, in vivo and ex vivo experiments to lend further substance to the validation of this approach.
In this study, we initially isolated a panel of potential anticancer peptides from venoms using this state-of-the-art high-throughput platform. Subsequently, a transcriptome-centric method was applied to address and to reveal the putative anticancer mechanism of the lead peptide candidate, followed by in vitro, in vivo and ex vivo experimental validation. In addition, we hypothesized as to the involvement of specific signalling pathways and potential binding sites through bioinformatic analyses and use of 3D modelling construction software. Finally, one peptide candidate (Gonearrestide) was identified to affect cancer cell proliferation in vitro and reduce tumour growth in vivo, while negligible cytotoxicity was observed on normal human epithelial cells and erythrocytes. These current data suggest that Gonearrestide has a high potential for development as an anticancer drug. In addition, the findings presented here have further validated the ever-increasing potential of this high-throughput platform and transcriptome-centric mechanistic study strategy to reveal additional novel anticancer peptide drug candidates.
| Transcriptomic procedures
Five mg sample from each lyophilized scorpion venom was dissolved in 1 mL of cell lysis buffer (Thermo Fisher Scientific). Polyadenylated mRNA was extracted by use of a Dynabeads â mRNA DIRECT TM Kit (Ambion by Life Tech), then subjected to a cDNA library construction procedure using a NEBNext â Ultra TM Directional RNA Library Prep Kit for Illumina â (New England BioLabs Inc.). According to the instructions, the cDNA library construction consisted of several main steps. First of all the mRNA fragmentation was achieved by incubating at 94°C with random primers. Then the RNA fragments were subjected to first strand cDNA and second strand cDNA syntheses.
After purification with 1.8X Agencourt AMPure XP beads, end repair of the cDNA library was performed by incubating with the end repair reaction buffer and the nucleotide A was added to the 3 0 end of the DNA fragments to avoid self-ligation. Therefore, the adapters with the nucleotide T at the 3 0 end were ligated to the DNA fragments. At last, the DNA fragments with adapters were enriched by PCR reactions and purified by AMPure XP beads. The quality of the cDNA library was verified using an Agilent 2100 Bioanalyzer (Agilent Technologies) with an Agilent DNA 1000 kit (Agilent Technologies).
The quantity of the cDNA library was validated by qPCR with a KAPA SYBR â FAST qPCR kit (KAPA Biosystems). The cDNA library was then loaded into a flow cell with oligos complementary to the adapters to generate clusters through bridge amplification. Finally, the transcriptome was obtained by performing RNA Sequencing on the Illumina MiSeq platform. The raw data obtained from the Miseq platform were analysed as follows. Firstly, the index primers used to identify different samples were removed. Secondly, the data were LI ET AL.
| 4461 transferred to the program FastQC 0.1.0.1 to filter out the reads with low quality and less than 25 nucleotides. The filtered data were saved as fastq files. At last, the clean reads were de novo assembled using Trinity 2.0.6 software to obtain the transcriptome with default parameters.
| Proteomic procedures
A second set of 5 mg lyophilized scorpion venom sample was dissolved in phosphate buffer (50 mmol/L, pH 7, containing 0.15 mol/L NaCl), and subjected to AKTA Avant 150 (GE Healthcare Life Science) fractionation using a Superose â 12 10/300 GL column (Sigma Aldrich) to filter out large proteins with molecular masses higher than 10 KD. After this, Tris (2-chloroethyl) phosphate (TCEP) was used to reduce disulphide bonds, and iodoacetamide (IAA) was used to alkylate free cysteine residues. At last, desalting was performed using PierceTM C18 Spin Tips (Thermo Scientific). Proteomics was performed using the Q Exactive TM Hybrid Quadrupole-Orbitrap Mass Spectrometer (Thermo Scientific) with a nano-LC system. Samples were loaded onto the Acclaim pepMap100, 75 lm 9 2 cm C18 trap column (Thermo Scientific) using LC-MS water (containing 2% ACN, 0.1% formic acid). Samples were trapped onto the column at 6 lL/min for 5 minutes for pre-concentration, then the trap column was connected to an EASY-Spray column, 15 cm 9 75 lm ID, 3 lm-C18 particle sizes (Thermo Scientific) by a 10 port valve automatically. Eluting was performed at a flow rate of
| Comparison between transcriptome and proteome
The software, PEAKS (version8.0) (Bioinformatics Solutions Inc., Waterloo, ON, Canada), was used to interrogate the transcriptome database with parameters set as: precursor ion mass tolerance, 3 ppm; fragment ion mass tolerance, 0.01 Da; no enzymes employed; a variety of post-translational modifications (PTMs) including cysteine carbamidomethylation and oxidation, were used and false discovery rate (FDR) was at ≤1%. The peptides identified high confidence and accuracy, constituted the prospective venomderived peptide libraries.
| Molecular cloning procedures
A third set of 5 mg lyophilized scorpion venom sample was dissolved in 1 mL of cell lysis/mRNA protection buffer, and polyadenylated mRNA was isolated from each by magnetic oligo-dT beads as described by the manufacturer (Thermo Fisher Scientific). The isolated mRNA was subjected to 5 0 -and 3 0 -rapid amplification of cDNA ends (RACE) procedures using a SMART-RACE kit (Clontech, UK).
The 3 0 -RACE reactions were purified and cloned using a TOPO â TA Cloning â Kit (Invitrogen) and sequenced using an ABI 3100 automated sequencer. The nucleic acid sequences were isolated by employing the primers below, which were designed to highly-con-
| Novel venom-derived peptide library construction and peptide synthesis
The prospective novel venom-derived peptide libraries were subjected to BLAST analyses against the NCBI non-redundant database and the peptide sequences which produced hits with the sequences on this were then subjected to Pfamscan online searching to identify whether the sequences aligned to any reported toxins. The peptide sequences reported before were removed manually during this step.
The novel peptides were manually filtered by removing very short sequences and finally, the venom-derived peptide library was constructed with all the peptide sequences selected as above. The
| Haemolysis assay
Human erythrocytes were washed with PBS until the supernatant was clear, and then samples of a 4% (v/v) suspension were treated with peptide concentrations ranging from 1 to 250 lmol/L at 37°C for 1 hour. Lysis of cells was assessed by haemoglobin release, measured by optical density changes at k550 nm, and calculated compared to positive controls. Positive control groups and negative control groups were treated with equal volumes of Triton X-100 and PBS instead of peptide, respectively. were stored at À80°C prior to use. Equal amounts of protein samples at each time-point, including those from the blank control group, were subjected to SDS-PAGE and then transferred to a membrane. Membranes were then blocked with 5% non-fat dry milk in TBST (0.1% Tween) for 2 hour at room temperature, and then incubated with primary antibodies (against Cyclin D1, Cyclin D3, CDK2, CDK4, CDK6, p18, p21, p27) at 4°C overnight. The next day, TBST (0.1% Tween) was used to wash membranes three times, after which secondary HRP conjugated antimouse/anti-rabbit antibody was incubated with membranes for 1 hour at room temperature. After washing with TBST (0.1% Tween) another three times, Immobilon Western HRP Substrate was employed for chemiluminescent detection in Western blots. Tumours were snap-frozen for further histological analysis. On the one hand, tumours were fixed and cut into slides. Immunohistochemical staining of tumour slides were performed by de-paraffinizing in xylene and rehydrating in graded ethanol, followed by incubation in sodium citrate buffer (pH 6.0) for high-pressure antigen retrieval. Afterwards, slides were incubated in 3% hydrogen peroxide to block endogenous peroxidase activity, and incubated with cell cycle checkpoint antibody CDK4 at 4°C overnight. On the second day, the slides were incubated with secondary antibody and subjected to diaminobenzidine staining. After counterstaining with 20% haematoxylin, slides were dehydrated and mounted on cover slips.
| LDH assay
The IHC-stained tissue sections were reviewed under a microscope.
In addition, mRNA and proteins were isolated from frozen tumours for qPCR and Western blot analysis. The procedures were for both techniques were described before.
| RNA sequencing with next-generation sequencing technology
In total, there were 514 974 and 625, 389 raw reads generated for the scorpion species, Androctonus mauritanicus (AMa) and Androctonus australis (Egypt) (AAu), respectively. As these two scorpion species do not have their genomes assembled so far, the transcriptome data were de novo assembled by use of Trinity software. Consequently, there were 112 235 and 46 360 nucleic acid sequences, respectively, obtained for each species (Table 1A). The transcripts were saved as Fastq files (S1 and 2).
| Isolation and de novo sequencing of proteomes through use of a highly accurate and sensitive LC-MS/MS system
The raw spectra generated from the AMa venom contained 20 606 peptides fragments. After alignment, the remaining 9225 peptide fragments obtained were filtered with the filtration parameter setting of an average local confidence of more than 50%. The de novo sequencing results including 3346 peptide fragments were saved as Excel files (S3 ; Table 1A). Similarly, from the AAu venom, we identified 2393 different peptide fragments after filtered from 7464 peptide fragments (S4 ; Table 1A).
| Comparison between respective transcriptomes and proteomes
In AMa transcriptome and proteome analysis, there were 1176 peptide fragments in the overlapping region between transcriptome and proteome databases for the two species, which aligned to 128 peptides (Table 1A). With the same method, 110 peptides were aligned from 924 peptide fragments in AAu transcriptome and proteome analysis (Table 1A). The overlapping peptides were regarded as the prospective venom-derived peptide libraries and saved as Excel files (S5).
To further validate our findings, we also compared AMa and AAu proteomes with an online scorpion protein database (UniProt). In total, there were 130 peptides matched with UniProt database, which indicated the robustness of our data.
| Molecular cloning
There were eight peptide sequences isolated through the molecular cloning approach, including three novel peptide sequences. All these eight peptide sequences were found in the overlapping region of the transcriptome and the proteome results, which validated the new high-throughput approach. The nucleotide and translated open-reading frames of the three novel sequences were saved ( Figure S1).
| Novel venom-derived peptide library construction and peptide synthesis
The overlapping regions described previously were subjected to a variety of bioinformatic analyses and the filtered results were saved ( Figure S2). As a result, novel venom-derived peptide libraries with 41 and 30 peptides were obtained for scorpion species AMa and AAu, respectively (S5). Twenty-two peptide sequences were initially selected to synthesize for use in further analyses (Table S1). Table S1) was found to have the most potent activity on human colon cancer cell line HCT116, thus it was chosen as a lead peptide for further investigation. The does-dependent anti-proliferation effect of Gonearrestide was shown in Figure 1A.
| Haemolysis assay
This demonstrated that Gonearrestide had negligible cytotoxicity on human erythrocytes with a haemolytic activity below 5% (positive control was regarded as 100%), indicating that Gonearrestide was a worthy candidate for further study with the view to its clinic application ( Figure 1B). Gonearrestide affected cancer cell proliferation through inhibition of growth ( Figure 1C).
| Determination of cellular location of peptide through use of confocal microscopy
We Taken together, it demonstrated that Gonearrestide was specifically bound to the cancer cell membrane, and induced subsequent reactions via membrane-related signalling pathways which will further be hypothesized and analysed in our "cell-peptide" RNA sequencing experiments.
| Apoptosis assay (Phosphatidylserine exstrophy detection)
Annexin V and PI staining along with flow cytometry can differentiate individual cells into different stages. The results of these experiments were shown in Figure 1E. The data showed that Gonearrestide did not induce apoptosis of HCT116 cells when compared to blank controls-a finding which was also consistent with our RNA sequencing data in this study.
IncuCyte live cell imaging system
As shown in Figure 1F, the proliferation of HCT116 cells treated with Gonearrestide was much slower than that observed for the blank controls. The results proved that Gonearrestide could inhibit cancer cell growth which again was consistent with our RNA sequencing data in this study.
| RNA sequencing revealed the biological function and signalling pathways altered by peptide treatment
As Gonearrestide had the best activity on the cancer cell line HCT116 with no obvious cytotoxicity on normal human cell lines and erythrocytes, it was chosen for further experiments to identify its molecular mechanism of action. There were three groups employed in this assay: HCT116 treated with Gonearrestide (HCT116_Gonearrestide), HCT116 treated with a negative control peptide (HCT116_NC) and HCT116 treated with PBS (HCT116_BC).
The negative control peptide was one of the previously identified peptides which showed no anticancer cell activity.
Approximately 40 million reads were generated per sample and around 90% of these were aligned to the human genome with a correlation value of 0.9 between and across replicates ( Figure S3). The top 500 variable genes (based on standard deviation) demonstrated that the replicates were consistent but slight differences were present between the blank control and the negative peptide groups ( Figure S4). Genes were determined as being significantly differentially expressed (DEG) based on a twofold log change and a q-value cut-off of absolute (0.6) and 0.05, respectively (S6). After filtration with the fold change and statistical significance, the remaining significantly differentially expressed genes were shown in Table 1B Figure 2C, such as phagosome, endocytosis and lysosome, which are all related to membrane reactions. Hence, we hypothesized that Gonearrestide worked through initial combination with cancer cell membranes, then produced subsequent effects.
Based on this, confocal imaging experiments were designed and conducted as described in Figure 1D. Gonearrestide was shown in Figure 3A and B. These data demonstrated that Gonearrestide arrested cancer cell cycle in G1 phase, and was consistent with our findings in Figure 2D which showed the cell cycle signals were actually down-regulated after Gonearrestide treatment.
| Identification of proteins involved in cell cycle processes by Western blotting
As Gonearrestide could arrest HCT116 cells in G1 phase, G1/S checkpoint protein antibodies were employed to identify the regula-
| Prediction of signalling pathways involved
Through combination of RNA sequencing data and biological in vitro/in vivo results, we hypothesized the signalling pathways LI ET AL.
| 4467 involved in cell cycle progression, which were shown in Figure 5A.
We believed that after Gonearrestide bound with the cancer cell membrane, cationic Gonearrestide could affect PIP3 by electrostatic attraction to its anionic trisphosphate group, resulting in the inhibition of the Akt pathway. PTEN, a lipid phosphatase that catalyses the dephosphorylation of PIP3 to produce PIP2, is a major negative regulator of Akt signalling. The inhibition of Akt was followed by the up-regulation of FOXO1/3, GSK-3b and p21, inducing the dysregulation of CDK4/6 and CDK2. The decline in CDK4/6 and CDK2 would inhibit the phosphorylation of retinoblastoma (RB) protein, which could release the transcription factor, E2F/DP, from the RB-E2F/DP complexes, thereby promoting cells entry from G1 to S phase.
Among all these genes, p27, p21, cyclin D3 and CDK4/6 were evaluated through Western blot assays, which further proved this prediction. On the other hand, after bioinformatics analysis, a series of biomarkers involved in peptide treatment related to colon cancer were also identified ( Figure S5).
| Hypothesis of potential binding site
It has been reported that phosphatidylserine (PS) and phosphatidylethanolamine (PE) can enhance membrane poration by a peptide with anticancer properties. 48
| DISCUSSION
Venom from animals has been proven to be a useful source of drug candidates in natural drug discovery to fight against diseases. 49,50 Especially for venom-based peptide/toxin, it has been paved new insights into therapeutic and diagnostic potential for cancer treatment in the last decade. 51 snake venom from Walterinnesia aegyptia and Vipera ammodytes meriodionalis, respectively, induced apoptosis on a broad spectrum of cancer cell lines. [52][53][54][55] Furthermore, the combination of WEV and silica nanoparticles efficiently enhanced the in vivo suppressive effect in mouse models. [52][53][54] To increase the identification of potential venom-sourced anticancer peptides, a high efficiency and low-cost screening platform is urgently required. In this study, a high-throughput screening platform consisting of transcriptome and proteome sequencing is described and has been of proven efficacy. Based on the use of this platform, complete peptide libraries of venoms from the scorpions, Androctonus mauritanicus (AMa) and Androctonus australis (Egypt) (AAu), have been constructed. To confirm the validity of this platform, a traditional cloning approach was also applied in parallel. The traditionally-derived cloning data provided evidence of the robust nature of the described high-throughput screening platform. The coupling of transcriptomic and proteomic/peptidomic approaches using bioinformatics produced venom-derived peptide panels, which could be used to explore the potential therapeutically useful peptides present in respective venoms. 58 Within the scorpion peptide panels, bioinformatics filtration and MTT screening were initially applied to detect novel candidate anticancer peptides. As a result, peptide 13(Gonearrestide) was identi-
CONFLI CTS OF INTEREST
The authors confirm that there are no conflict of interest. | 4,845.4 | 2018-07-11T00:00:00.000 | [
"Biology"
] |
Prediction of Drug–Target Interaction Using Dual-Network Integrated Logistic Matrix Factorization and Knowledge Graph Embedding
Nowadays, drug–target interactions (DTIs) prediction is a fundamental part of drug repositioning. However, on the one hand, drug–target interactions prediction models usually consider drugs or targets information, which ignore prior knowledge between drugs and targets. On the other hand, models incorporating priori knowledge cannot make interactions prediction for under-studied drugs and targets. Hence, this article proposes a novel dual-network integrated logistic matrix factorization DTIs prediction scheme (Ro-DNILMF) via a knowledge graph embedding approach. This model adds prior knowledge as input data into the prediction model and inherits the advantages of the DNILMF model, which can predict under-studied drug–target interactions. Firstly, a knowledge graph embedding model based on relational rotation (RotatE) is trained to construct the interaction adjacency matrix and integrate prior knowledge. Secondly, a dual-network integrated logistic matrix factorization prediction model (DNILMF) is used to predict new drugs and targets. Finally, several experiments conducted on the public datasets are used to demonstrate that the proposed method outperforms the single base-line model and some mainstream methods on efficiency.
Introduction
In recent years, the discovery of new drugs has enormous technology advancement and research investment. However, an intended target is rarely bound to the drugs. This may lead to off-target effects and extend drug development time. As a consequence, there is a necessary need for researchers to develop new drugs in effective ways. Drug repositioning [1] is one of the essential and important part in the discovery of new drugs. Herein, it should be pointed out that one of the fundamentals for computational drug repositioning is to accurately predict drug-target interactions. There are abundant research studies for DTI prediction over the past several decades including chemical genetic and proteomic methods such as affinity chromatography [2] and expression cloning approaches [3]. However, because of laboratory experiments and physical resources, these methods can only process a limited number of possible drugs and targets. Therefore, computational prediction approaches [4,5] have received lots of attention when they can lead to a much faster assessments of possible DTIs.
Mei et al. [6] proposed one of the approaches to predict drug-target interactions computationally. A neighbor-based interaction-profile inference was used for both drugs and targets. KRONRLS-MKL [7] researched a linear combination of multiple similarity measures to model the all similarity between drugs and targets. However, these models used a simple linear combination technique to predict DTIs. In fact, such a linear setting may not be appropriate when the linear relationship is not evident. In view of this bottleneck, regularized least squares integrating with kernel fusion technique model (RLS-KF) [8] employed a nonlinear kernel diffusion technique to combine different kernels and then used the diffused kernel to perform DTIs prediction. As a result, the model has a better performance than the linear combination models. However, when testing with 10-fold cross-validation for the whole dataset, this model failed to produce satisfactory results.
Recently, a neighborhood regularized logistic matrix factorization (NRLMF) [9] was developed to predict DTIs by using logistic matrix factorization and a neighborhood smoothing method. The NRLMF model showed an encouraging result based on the 10-fold cross-validation. Moreover, the dual-network integrated logistic matrix factorization (DNILMF) [10] based on NRLMF used matrix factorization to predict drug-target interactions over drug information networks and showed significant improvements over other methods on standard benchmarking datasets. Other models such as the DTI-CDF and DTI-MLCD used machine learning-based methods. The DTI-CDF [11] used pseudoposition specific scoring matrix (PsePSSM) to extract the evolution information of protein sequence and added path-category-based muti-similarities feature (PathCS) based on the heterogeneous graph of DTIs. The DTI-MLCD [12] utilized the community detection method to facilitate muti-label classification. Nevertheless, in this case, the difficulty lies in overdependence on known drugs and targets information, and the latent information between drugs and targets might be absent. In view of this problem, the more advanced prior-knowledge-based approaches have been proposed to satisfy various DTI tasks.
The current prior-knowledge-based approaches in this context are arguably the DDR [13], the NeoDTI and the TriModel. The DDR used a multiphase procedure to predict drug-target interactions from relevant heterogeneous graphs. In this effort, nonlinear fusion was employed to combine different similarity indices as well as random walk features from the input graphs. The NeoDTI [14] supported information about drugs and targets. The TriModel [15] approached the DTI prediction problem as a link prediction in knowledge graphs. In contrast, existing prior-knowledge-based prediction methods such as DDR are best suited to finding new associations between well-studied drugs and targets (useful for instance in the drug repurposing context). In the real word, under-studied drugs and targets can be more easily obtained than well-studied drugs and targets. Therefore, there is a critical need for methods that combine both priori knowledge and the ability to predict under-studied drug-target interactions.
Motivated by the previous studies [10,16], a novel dual-network integrated logistic matrix factorization DTI prediction scheme via relational rotation knowledge graph embedding (Ro-DNILMF) approach is proposed in this article. This model combines knowledge graph embedding and DNILMF. Firstly, we add the tanh function as an optimization function into knowledge graph embedding to produce better results in this task. Secondly, we construct an interaction adjacency matrix by knowledge graph embedding model based on relational rotation (RotatE) [16] to improve information integrity. Finally, we add the interaction adjacency matrix into DNIMLF to predict interactions between new drugs and new targets.
The remainder of this article is organized as follows. We briefly introduce basic concepts and related work in Section 2, such as the DNIMLF and RotatE. Section 3 details the proposed Ro-DNILMF model for drug-target interactions prediction task. Experimental results and discussions are presented in Section 4, and the conclusion and the future work are prospected in Section 5.
Principle of the DNILMF
DNILMF is a predicting drug-target interactions model proposed by Hao et al. [10]. It inherits a majority of features and indicates the superiority of the neighborhood regularized logistic matrix factorization (NRLMF) [9]. The logistic matrix factorization of DNILMF is especially suitable for binary variables and the diffused kernels matrices considering the drug-target profile information to predict the new drug or target. Many researchers have made some work of DNILMF in recent years [17,18], and the architecture of DNILMF is shown in Figure 1. Firstly, the target sequence similarity matrix, chemical structure similarity matrix and interaction adjacency matrix are used as input data. Secondly, to infer new drugs and targets information, the Gaussian kernel matrix and the latent variable matrix are presented by the interaction adjacency matrix. Thirdly, the final kernel matrix is composed of integrating drug or target neighbor information. Finally, the final kernel matrix is added into the logic function to yield interaction probabilities between drugs and targets.
of DNILMF is shown in Figure 1. Firstly, the target sequence similarity matrix, chemical structure similarity matrix and interaction adjacency matrix are used as input data. Secondly, to infer new drugs and targets information, the Gaussian kernel matrix and the latent variable matrix are presented by the interaction adjacency matrix. Thirdly, the final kernel matrix is composed of integrating drug or target neighbor information. Finally, the final kernel matrix is added into the logic function to yield interaction probabilities between drugs and targets.
Data Preparation
The given input training data consist of the target similarity matrix, the drug similarity matrix and the interaction adjacency matrix. The target sequence similarity matrix is denoted by (similarity scores among proteins for both datasets are computed using a normalized version of SmithWaterman score [19]), which is a × square matrix (number of targets, ). The drug similarity matrix is denoted by (similarity scores among compounds for both datasets are computed using the SIMCOMP tool [20]), which is a × square matrix (number of drugs, ). The interaction adjacency matrix is denoted by , where
Definition
In the DNILMF model, "known drug", "new drug", "known target" and "new target" are defined as follows [8]. A "known drug" refers to a drug that has at least one interaction with targets (e.g., D1 in Figure 1A,B, respectively), while a "new drug" refers to a drug that does not have any interaction with targets (e.g., D1 in Figure 1C,D, respectively) in the dataset. A "known target" refers to a target that has at least one interaction with drugs (e.g., D1 in Figure 1A,C, respectively), but a "new target" refers to a target that
Data Preparation
The given input training data consist of the target similarity matrix, the drug similarity matrix and the interaction adjacency matrix. The target sequence similarity matrix is denoted by S ct (similarity scores among proteins for both datasets are computed using a normalized version of SmithWaterman score [19]), which is a N × N square matrix (number of targets, N). The drug similarity matrix is denoted by S cd (similarity scores among compounds for both datasets are computed using the SIMCOMP tool [20]), which is a M × M square matrix (number of drugs, M). The interaction adjacency matrix is denoted by Y cn , where Y cn [d, t] = 1 if drug d interacts with target t, and Y cn [d, t] = 0 otherwise, as shown in Figure 1A-D.
Definition
In the DNILMF model, "known drug", "new drug", "known target" and "new target" are defined as follows [8]. A "known drug" refers to a drug that has at least one interaction with targets (e.g., D1 in Figure 1A,B, respectively), while a "new drug" refers to a drug that does not have any interaction with targets (e.g., D1 in Figure 1C,D, respectively) in the dataset. A "known target" refers to a target that has at least one interaction with drugs (e.g., D1 in Figure 1A,C, respectively), but a "new target" refers to a target that does not have any interaction with drugs (e.g., D1 in Figure 1B,D, respectively) in the dataset.
Latent Matrix and Gaussian Kernel Matrix Construction
The goal of this model is to use known drugs and known targets to derive new drugs and new targets information. Specifically, the algorithm deduces the known drug/target interaction profiles to build a new drug/target latent matrix and the Gaussian kernel matrix. The known drug/target interaction profile (denoted separately by Y u and Y v for the known drug u interaction profile and the known target v interaction profile) are inferred by Y cn . For example, for a known drug u, the interaction profile is calculated by its nearest neighbors in which their interactions are extracted from Y cn . The known target v interaction profile, Y v , is calculated in a similar way. After that, the new drug/target latent variable matrix (denoted separately by D i and T j for the new drug i latent variable matrix and the new target j latent variable matrix) is calculated by Y u /Y v . The formulations are as follows: where S iu cd is the similarity score between new drug i and known drug u and S jv ct is the similarity score between new target j and known target v. Once drugs/targets profiles are inferred for all new drugs and targets, the Gaussian kernel matrices denoted by K gd (d i , d x ) (x = 1, 2, 3, . . . , M) and K gt t j , t z (z = 1, 2, 3, . . . , N) are calculated as Formulas (3) and (4). Those are where Y t . is the new target interaction profile, Y d . is the new drug interaction profile and ϕ is the kernel bandwidth.
Final Diffused Matrix Construction
To add the similarity network information between drugs and targets into the model, the final diffused matrices for drugs and targets (denoted by S d for drugs and S t for targets) are combined with the similarity matrices S ct , S cd and the Gaussian kernel matrices K gd d i , d j , K gt t i , t j . These matrices are normalized and symmetrized. The resulting matrices are status similarity matrices, which are denoted by P (1) , P (2) , P (3) and P (4) , respectively for S ct , S cd , K gd d i , d j , and K gt t i , t j . Status similarity matrices are iterated with a given iteration step number, t, for drugs and targets, respectively. After the iteration process is finished, the final diffused matrices are generated. For details of the calculation procedure, the previous studies [21] can be referred.
Interaction Probabilities Score Calculation
The interaction probability score is key to the predicting interaction between drugs and targets. A high score indicates a higher chance of a drug-target interaction. To obtain the interaction probability score, a logistic function is used to yield scores between drugs and targets with the above final drug diffused matrices S d and the final target diffused matrices S t . The formulation is as follows: where α, ρ, τ are the corresponding smoothing coefficients with the summation of them as 1 and T T denotes the transpose of T.
RotatE
RotatE is a knowledge graph embedding model by relational rotation in complex space. It is able to model and infer three patterns (i.e., symmetry/antisymmetric, inversion, and composition) from the observed facts. The process of the RotatE method can be illustrated as follows. Firstly, in order to initialize knowledge graph embeddings, three types of relation patterns are defined. Then, after the distance between the source entity to the target entity is calculated, self-adversarial negative sampling is used to optimize embeddings. Finally, the score function is proposed to measure the salience of a candidate triplet.
Three Relation Patterns Definition
Specifically, for given triplet (h, r, t), h represents the source entity, t represents the target entity, and r is the relation between h and t. RotatE defines each relation as a rotation from the source entity to the target entity. Relation types are symmetry/antisymmetric, inversion, and composition. According to the existing literature [22], three types of relation pattern definitions are as follows: The relation r 1 is inverse to relation r 2 if ∀h, t The relation r 1 is composed of the relation with r 2 and r 3 if ∀h, t, z
Embeddings Optimization
RotatE initializes its embeddings with random noise. It updates them by self-adversarial negative sampling so as to score the true triplets much higher than the corrupted false triplets. The negative sampling loss function is obtained by: where σ is the optimization function, γ denotes the fixed margin, Tri n is the number of triplets, Θ(·) is the embedding, p h i , r i , t i represents the weight of the negative sample and d r (Θ(h), Θ(t)) is the distance function. p h i , r i , t i is calculated as Formula (7), that is where β is the temperature. The distance function is as follows: where · is Euclidean distance and denotes the Hadamard product.
Score Function Definition
The score function scores true triplets much higher than the corrupted false triplets. To measure the salience of a candidate triplet (h, r, t), the score function is defined as follows: DNILMF can achieve good performance on new drugs and targets. However, it does not incorporate prior knowledge, which is important to enhance predictive accuracy. RotatE can achieve good performance on known drugs and targets, but it is not suited to finding new associations between new drugs and targets. Therefore, to improve the DNILMF performance, a novel DTIs prediction method combined with DNILMF and RotatE called Ro-DNILMF is proposed in this article.
Architecture
In this section, we describe the proposed model Ro-DNILMF for drug-target interactions prediction. This scheme adopts the knowledge graph embedding model to integrate prior knowledge. As the basic prediction model, DNILMF is used to predict interactions between new drugs and targets. It is graphically illustrated in Figure 2. Three main stages are included: data preparation, constructing the interaction adjacency matrix, and training DNILMF model. Firstly, all of the input data are integrated into triples. Then, the RotatE model is trained to optimize embeddings by the negative sampling loss function. The self-adversarial temperature method in the negative sampling loss function is used to choose temperature. The interaction adjacency matrix is generated by the score function so as to integrate prior knowledge into the prediction model. Finally, the new interaction adjacency matrix is applied on the DNILMF model. Latent variable matrix and the final diffused matrix are integrated into logistic function so as to obtain the interaction possibilities between new drugs and targets.
Embedding Initialization
As illustrated in Figure 2, it is necessary for all triplets to initialize embeddings by RotatE. The entity embeddings, (ℎ) and ( ), are initialized by random noise. The relation embeddings, ( ), are calculated based on Euler's identity:
= cos + sin
Relation types include symmetry/antisymmetric, inversion, and composition. If a relation r is symmetry or antisymmetric, each element of its embeddings ( ), i.e., , satisfies: If two relations and are reverse, each element of their embeddings, and
Data Preparation
The knowledge graph embedding model requires data to be modeled in a triplet form, where the objective is to predict new links between entities. In the case of drug discovery, the input data include each triplet (h, r, t), the target sequence similarity matrix, S ct , and chemical structure similarity matrix, S cd .
Embedding Initialization
As illustrated in Figure 2, it is necessary for all triplets to initialize embeddings by RotatE. The entity embeddings, Θ 0 (h) and Θ 0 (t), are initialized by random noise. The relation embeddings, Θ 0 (r), are calculated based on Euler's identity: Relation types include symmetry/antisymmetric, inversion, and composition. If a relation r is symmetry or antisymmetric, each element of its embeddings Θ 0 (r), i.e., r i , satisfies: If two relations r 1 and r 2 are reverse, each element of their embeddings, r 1i and r 2i , satisfy: If a relation r 3 is a combination of two relations r 1 and r 2 , each element of their embeddings, r 1i , r 2i and r 3i , satisfy:
Embedding Optimization
In order to update embeddings, self-adversarial negative sampling is used to train distance d r (Θ(h), Θ(t)) to reduce the distance of true triplets and enlarge the distance of corrupted false triplets. The negative sampling loss function is obtained by Formula (6). According to the problem of inefficiency for the traditional temperature of handcrafted sampling, a method called self-adversarial temperature is adopted to choose the temperature with the current training level. The negative sampling probability is calculated by Formula (7), and the temperature, denoted by β, is obtained by where β 0 is initial temperature and ω is the sigmoid function. The final values of each triplet embedding (Θ(h), Θ(r), Θ(t)) are generated by Formulas (6) and (8).
Interaction Adjacency Matrix Construction
To construct the interaction adjacency matrix, the score function, f RotatE , is trained to score triplet (Θ(h), Θ(r), Θ(t)) by Formula (9) and select new relations. If f RotatE has a higher score than the minimum passing score denoted by ξ, the relation r is added into the interaction adjacency matrix, Y cn [h, t] = 1 as a new element; otherwise, Y cn [h, t] = 0. The interaction adjacency matrix integrates prior knowledge, which is good preparation for DTIs prediction in the next stage.
Predicting DTI with DNILMF
As shown in Figure 2, the interaction adjacency matrix Y cn is constructed by RotatE. It is integrated into DNILMF as one of input matrices, together with S ct and S cd .
Latent Variable Matrix and Gaussian Kernel Matrix Construction
Combined with the above interaction adjacency matrix Y cn , the drug i latent variable matrix denoted by D i and the target j latent variable matrix denoted by T j are generated to predict new DTIs. The important steps are summarized as follows: (1) the interaction profile is built. For a known drug u, the interaction profile, Y u , is calculated by its nearest neighbors in which their interactions extracted from Y cn . For a known target v, the interaction profile, Y v , is calculated in the same way; (2) the latent variable matrix is calculated by the multiplication of the similarity score with interaction profile. According to Formulas (1) and (2), the latent matrices, D i and T j , are calculated by the following equations: where Y u and Y v are separately the known drug u interaction profile and the known target v interaction profile. According to Formulas (3) and (4), the Gaussian kernel matrices, denoted by K gd (d i , d x ) (x = 1, 2, 3, . . . , M) for drug i and K gt (t i , t z ) (z = 1, 2, 3, . . . , N), for target j can be calculated by where Y t . is the drug/target interaction profile. Thus, after the above calculation, D i , T j , K gd (d i , d x ), and K gt (t i , t z ) are constructed.
Final Diffused Matrix Construction
In the DNILMF model, the final diffused matrix is constructed to integrate neighbor information between drugs and targets. The final diffused matrix is calculated by the Gaussian kernel matrix and the similarity matrix. Specifically, for a new target, the similarity matrix S ct is first converted into the kernel matrix according to previous studies [23]. By normalizing and symmetrizing both the target kernel matrix and the target Gaussian kernel matrix, the status matrix, denoted by P (1) and P (2) , is constructed for the target kernel matrix and the target Gaussian kernel matrix, respectively. The final diffused matrix is calculated by the multiplication of local similarity matrix L for each P matrix with the status matrix after t iterations. The local similarity matrix for each P matrix is calculated by the following equation: where N i denotes the nearest neighbors of target i and k is the number of nearest neighbors. It can be noted that this operation makes the similarities among non-nearest neighbors to zero. P (1) t+1 and P (2) t+1 are calculated by the following equation: where P (1) t+1 is the status matrix of the target kernel matrix after t iterations, and P (2) t+1 is the status matrix of K gt t i , t j after t iterations. To make P (1) t and P (2) t symmetrical, in each iteration, the status matrices, P (1) t and P (2) t , are further changed as follows: where I denotes the identity matrix. After t steps, the final target diffused matrix, S t , is calculated by P (1) t and P (2) t . For a new drug, after applying the same steps, we can also obtain the final drug kernel matrix S d .
Interaction Probability Calculation
Using the latent variable matrices and the final kernel matrices, the interaction probabilities P between new drugs and targets are yielded. The equation is as follows:
Data Preparation and Experimental Settings
To demonstrate the effectiveness of our proposed scheme, it is thoroughly evaluated on the Kyoto Encyclopedia of Genes and Genomes (KEGG) dataset [24], DrugBank dataset [25] and Yamanishi_08 dataset [26], respectively.
Dataset Preparation
The KEGG dataset is a large benchmark dataset covering metabolismus, cellular processes, diseases, drug pathways, genetic information processing, environmental information processing, and organismal systems. The total training drug sample is 10,979, the target sample is 13,959, and the interaction sample is 12,112.
The DrugBank dataset can be considered as both a bioinformatics and a cheminformatics resource. The total training drug sample is 1482, the target sample is 1408, and the interaction sample is 9881 in our experiment.
The Yamanishi_08 dataset represents the most frequently used gold standard datasets in the previous state-of-the-art models. It is used to validate the proposed model for DTIs prediction. The dataset is classified into four groups: enzymes (EN), which has 445 drugs and 664 targets; ion channels (IC), which has 210 drugs and 204 targets; G-protein coupled receptors (GPCR), which has 223 drugs and 95 targets; and nuclear receptors (NR), which has 54 drugs and 26 targets. All of samples are trained in our experiment. The information of datasets is shown in Table 1.
. Experimental Environment
This presented method can be easily performed on a laptop. All experiments are conducted on the laptop configured by NOIDIA GeForce MX250, 8G memory, Intel Core i5-1021 CPU 1.60-GHz processor, and the operating system is Window 1064 bit.
Results and Discussion
In this section, we comprehensively evaluate the superior performance of the proposed method in many aspects: parameter setting, the optimization function determination of Ro-DNILMF, performance of the score function in Ro-DNILMF, performance of Ro-DNILMF under different samples, and comparative results with some mainstream prediction methods.
The Optimization Function Determination of Ro-DNILMF
In order to improve the computational efficiency of the loss function, the optimization function is used. This function can map the distance discrete values to a certain range. This experiment gives the performance of optimal function including sigmoid function and tanh function. The sigmoid function is a common optimization function that maps the distance between the fixed margin γ and the distance d r to [0, 1]. The formulation is as follows: The tanh function extends the mapping range to [-1, 1] based on the sigmoid function. The formulation is as follows: Mean Reciprocal Rank (MRR) and Hit at N (H@N) are standard evaluation measures for the Yamanishi_08 dataset.
The results of the optimization function based on the tanh function and sigmoid function are shown in Table 3. It shows that the best MRR scores of the sigmoid function and the tanh function are 0.723 and 0.743, respectively. The H@1 and the H@3 score of the sigmoid function are lower than the tanh function. In a Hit@10 comparison, the tanh function tops the sigmiod function by at most 0.093. In conclusion, the results of the tanh function are better than the sigmoid function (e.g., the highest score of the tanh function is 0.884, while the highest score of the sigmoid function is 0.817). We think it is caused by the distance between the fixed margin γ and the distance d r . The tanh function can calculate the distance both positive and negative (−1, 1) and the sigmoid function can only calculate positive ones (0, 1). The blue part 0.817 is the best performance of the sigmoid function and the blue part 0.817 is the best performance of the tanh function.
Performance of the Score Function in Ro-DNILMF
To measure the salience of the score function in Ro-DNILMF, this part trains different embedding models including TransE [28], ComplEX [29] and RotatE on the DrugBank dataset. The score function in TransE is −h + r − t, and the score function in ComplEX is Re r, h, t , where Re(x) is a real vector component. The score function in RotatE is shown in Formular (9). Figure 3 shows Hit@N with different embedding models trained by the best optimal parameters. In Figure 3a, the highest hit score is RotatE (79%) and the maximum difference is 30%. In Figure 3b, the highest hit score is RotatE (88.4%) and the maximum difference is 26%. In Figure 3c, the highest hit score is RotatE (88.5%) and the maximum difference is 14%. These results show that the values of the RotatE model are higher than the ones of any embedding models. It is caused by RotatE, which defines each relation as a rotation from the source entity to the target entity, and relation types determination will produce better generalization results.
Performance of Ro-DNILMF under Different Samples
In order to test the prediction performance of the Ro-DNILMF model under different samples, area under curve of receiver operating characteristic (AUC) and area under precision-recall curve metrics (AUPR) are evaluated on the KEGG dataset. This experiment increases the number of training samples from 0 to 2000 with 100 training samples each time. As can be seen from Figure 4, the Ro-DNILMF model is more robust than the DNILMF model in the case of fewer samples. When the training sample is 100, the AUC score of the Ro-DNILMF model is 0.903, while the AUC score of the DNILMF model is 0.59. When the training sample is 1000, the AUPR score of the Ro-DNILMF model is 0.96, while the AUPR score of the DNILMF model is 0.72. When the training sample is 1500, the AUC score of the Ro-DNILMF is 0.965, while the AUC score is 0.892. When the training sample is 2000, the AUPR score of the Ro-DNILMF model is 0.972, while the AUPR score of the DNILMF model is 0.945. These results show that the Ro-DNILMF model converges significantly faster than the DNILMF model with the increasing number of training sam-
Performance of Ro-DNILMF under Different Samples
In order to test the prediction performance of the Ro-DNILMF model under different samples, area under curve of receiver operating characteristic (AUC) and area under precision-recall curve metrics (AUPR) are evaluated on the KEGG dataset. This experiment increases the number of training samples from 0 to 2000 with 100 training samples each time. As can be seen from Figure 4, the Ro-DNILMF model is more robust than the DNILMF model in the case of fewer samples. When the training sample is 100, the AUC score of the Ro-DNILMF model is 0.903, while the AUC score of the DNILMF model is 0.59. When the training sample is 1000, the AUPR score of the Ro-DNILMF model is 0.96, while the AUPR score of the DNILMF model is 0.72. When the training sample is 1500, the AUC score of the Ro-DNILMF is 0.965, while the AUC score is 0.892. When the training sample is 2000, the AUPR score of the Ro-DNILMF model is 0.972, while the AUPR score of the DNILMF model is 0.945. These results show that the Ro-DNILMF model converges significantly faster than the DNILMF model with the increasing number of training samples. cision-recall curve metrics (AUPR) are evaluated on the KEGG dataset. This experiment increases the number of training samples from 0 to 2000 with 100 training samples each time. As can be seen from Figure 4, the Ro-DNILMF model is more robust than the DNILMF model in the case of fewer samples. When the training sample is 100, the AUC score of the Ro-DNILMF model is 0.903, while the AUC score of the DNILMF model is 0.59. When the training sample is 1000, the AUPR score of the Ro-DNILMF model is 0.96, while the AUPR score of the DNILMF model is 0.72. When the training sample is 1500, the AUC score of the Ro-DNILMF is 0.965, while the AUC score is 0.892. When the training sample is 2000, the AUPR score of the Ro-DNILMF model is 0.972, while the AUPR score of the DNILMF model is 0.945. These results show that the Ro-DNILMF model converges significantly faster than the DNILMF model with the increasing number of training samples.
Comparison with Other Mainstream Methods
We further compare the presented method with other state-of-the-art methods, such as BLM-NII, KRONRLS-MKL, NRLMF and DNILMF. The comparative results are shown in Figure 5. Note that all of the comparative methods are tuned with optimal parameters as previous works [10,[30][31][32]. The performance of each method is tested on the Yamanishi_08 dataset, and it is evaluated with AUC and AUPR. As can be seen from
Comparison with Other Mainstream Methods
We further compare the presented method with other state-of-the-art methods, such as BLM-NII, KRONRLS-MKL, NRLMF and DNILMF. The comparative results are shown in Figure 5. Note that all of the comparative methods are tuned with optimal parameters as previous works [10,[30][31][32]. The performance of each method is tested on the Yamanishi_08 dataset, and it is evaluated with AUC and AUPR. As can be seen from Figure 5, the scores of BLM-NII and KRONRLS-MKL are also lower than the scores of the other methods. NRLMF and DNILMF take higher AUC and AUPR scores on the EN dataset. For the proposed method, although it has a bit of a lower score than the NRLMF and DNILMF methods on the EN dataset, its AUPR score and AUC score can obviously achieve the highest ones on other three datasets (AUPR score: 72.6%, 91.2% and 62.5% on other three datasets, AUC score: 94.5%, 98.6% and 91.3% on other three datasets). To verify the contribution of RotatE, we compare the performance of RotatE with previous knowledge graph embedding models on the Yamanishi_08 dataset, including
Comparison with Other Combination Models
To verify the contribution of RotatE, we compare the performance of RotatE with previous knowledge graph embedding models on the Yamanishi_08 dataset, including TransE, DisMult [33], HolE [34], ComplEx [29], and ConvE [35]. In this experiment, these embedding models, including RotatE, are combined with DNILMF and NRLMF, respectively. For all combined models, the AUC and AUPR scores are shown in Table 4. Although Ro-DNILMF has better performance than the combination model of RotatE and DNILMF caused by the optimization function, the combination model of the RotatE model and the DNILMF model outperforms the other combined models. It is noted that almost all of the combination models outperform the baseline model. We think it is caused by the knowledge graph embedding model added to the prediction models. New information of samples will produce better performance. The green part is the performance of the Ro-DNILMF model and the blue part is the best performance of the other combination models.
Conclusions and Future Work
Ro-DNILMF is an efficient drug-target interactions prediction model, which was designed based on RotatE and DNILMF. This method used RotatE to learn efficient vector representation for both drugs and targets, and it constructed the interaction adjacency matrix to integrate prior knowledge. Our study trained DNILMF to predict new drugs/targets interactions. This method faced an increasingly prior knowledge problem in the real world. The prior knowledge was combined with predicting new drugs/targets, and the prediction accuracy was surprisingly improved.
What is more, the tanh function was added into RotatE to greatly increase generalization capability. Experiments conducted on the benchmark datasets proved that the proposed method achieved high efficiency and better effectiveness than many other popular methods. Our experiments also showed that prediction model with knowledge graph embedding can improve accuracy.
In future work, we will further explore the relationship of drug-target interactions and annotation information, and we will even extend this method to many complicated applications. Last but not least, the selected prediction of our model will be validated in laboratory experiments to demonstrate the clinical relevance of our results. | 8,106 | 2022-08-01T00:00:00.000 | [
"Computer Science"
] |
Best Strategy: Lower Risk & Higher Return
. People have an innate desire for money. Gold and bitcoin, these two high-return investments are popular in the world. We built XGBoost-based regression prediction model and mean-absolute deviation model based on the mean-variance model. We use machine learning and construct an XGBoost regression model for prediction [1]. With the forecast data from above model, we build a mean-absolute deviation model using the final assets as the objective function to maximize the goal.
Introduction 1.1 Background
In 2009 bitcoin, a new trading currency, was born, from its inception, a bitcoin was just less than $0.01, in 2017 the huge gains in the bitcoin trading market has been comparable to stock gains, has reached $20,000 a piece, along with the huge gains, its riskiness also emerged immediately after the daily trading price reached its peak, and then a plunge of greater than 50% occurred, many people in Overnight riches, there are also many people in the nothing.
Gold, the natural metal, with its excellent non-oxidizing, lustrous and shiny natural properties already predicts that it will be an excellent item for trading.Unlike some other assets, gold is more liquid and its quotes change more rapidly, and sometimes these changes can have a substantial impact on the daily price of gold.
For both types of currencies, traders have to develop strategies in order to hedge their risks to a certain extent and maximize their profits.[2]
Assumptions and Justifications
• Investors are a rational group that seeks to maximize profits.
• The investor knows before investing that the investment return is a variable that follows a normal distribution and uses the standard deviation or variance of its investment return to represent the risk of the investment.• Investors want to minimize risks and maximize benefits.
• Return on investment, risk is the main factor that influences investors to make investment decisions.• Investors are rational.
• Markets are time-sensitive.
• All investors are considered to be in the same single investment period.
• If the gold market is open, then gold and bitcoin must be traded at the same day.
Model Building
The purpose of our model is to achieve a more accurate prediction of the daily gold and bitcoin trading prices, so that it can provide an effective reference for the actual traders, when to buy, when to sell, when to hold, and only by predicting the prices can we make good trading decisions and thus maximize the benefits.
We use XGBoost to build the model, and certain parameters need to be set before modeling.[3] The objective function to be optimized consists of two parts.
XGBoost will have a prediction score on each leaf node, generally called a leaf weight, denoted by or.[4] This leaf weight is the prediction value of this tree for all samples on that leaf node.Each tree has its structure, which can be measured by the depth of the tree, the number of leaf nodes, and the position of the leaves, which can be denoted by denoting the leaf node where the sample is located, and by denoting the leaf weight of the sample falling to the first coconut node of the tth tree, whereupon there is: A model is built with time as the independent variable and transaction unit price as the dependent variable, which is first trained using a portion of the given data and then predicted for the remaining cases.
Predicted Results
It is easy to see from the two line graphs that the results are fitted more perfectly, both for gold and bitcoin.Regarding the prediction of gold, there are almost equal data with a dozen or so at some points, and even at the place where the difference between the predicted and actual values is the largest, the difference is less than $100, which shows that the fit is almost perfect; the prediction of bitcoin is more outstanding, which shows that except for some individual points, the folds of the predicted and actual values almost coincide, which is more evidence of the perfectness of the fit, and for the differences of We will use the optimization model to make further and more accurate predictions for the individual parts.
In particular, when dealing with anomalous data for Bitcoin, we compared two processing methods, directly eliminating and retaining the anomalous data, with the following comparison of the predicted results after processing.
It is not difficult to see that the prediction results generated after retaining the outlier data fit better with the true value, which is not difficult to understand when combined with the reality.In reality, market disturbances inevitably occur, huge changes in the global economy, massive buying and selling by companies or individuals can have an extremely large impact on the price, so when these disturbances occur, certain values will show a significant over-average, i.e. become outliers, but here we choose to retain them because the gold and bitcoin trading markets are risky and highly susceptible to disturbances, and directly eliminating outliers would destroy the integrity of the data and make the processed data not reflect the change in price over time in real situations.
Model Optimization Using Genetic Algorithms
Genetic algorithm is a kind of stochastic search algorithm with the help of natural selection and natural genetic mechanism in the biological world, which can automatically acquire and accumulate knowledge about the search space during the search process, and adaptively control the search process to find the optimal solution.[5] The genetic algorithm represents the solution of the problem as a "chromosome", which starts from a bunch of chromosomes and uses the principle of survival of the fittest to select the chromosomes with high adaptability for replication, and generates a new generation of "chromosomes" that are more adaptable to the environment through two genetic operations: crossover and mutation."As the genetic algorithm runs from generation to generation, those highly adapted models will grow exponentially in the offspring, and finally the most adapted chromosome will be obtained, i.e., the optimal solution of the optimization problem [6].According to the modeling principle of xgboost, it is known that the mean square error MSE and the coefficient of determination are the main factors of prediction accuracy, so the genetic algorithm is chosen to search out the two best parameters of XGBoost.The genetic algorithm uses genetic operators to operate on individuals in the population, and by continuously exchanging chromosomal information, the population evolves so that individuals with good fitness values are retained and those with poor fitness values are gradually eliminated in the evolutionary process.[7]
Model Selection
Since we have a combination of cash, gold, and bitcoin at the same time, a multi-objective evolutionary algorithm is the main method to solve the multi-objective optimization problem so that each objective can reach the optimal set of equilibrium solutions as much as possible.This also means that: we sell gold or bitcoin when the predicted return is larger at this point, and we can buy it when the opposite is true.We assume that gold and bitcoin are bought and sold at the same time, so that we can determine the date of the transaction (buy and sell) based on the return combined with the risk factor, i.e., the variance (date), and it should be noted that gold is not traded on the day of rest, so the G in the triplet should be kept constant and only bitcoin is calculated.
Since the mean-variance model is a static model that cannot match the changes of the stock market in real life, we can invoke a new investment algorithm model, the mean-absolute deviation model, which uses absolute deviation instead of variance to modify the original model, which not only retains the advantages of the original model and is more adaptable to market changes, but also can use some methods to correct the new model to get the better results we want in terms of return.[8] We used the XGBoost model for prediction and genetic algorithm for optimization, and later we chose the mean-absolute deviation model for risk analysis and evaluation to determine when the risk of the transaction is minimal, and later we also optimized this model, followed by genetic algorithm optimization of the objective function and multiple iterations of the results to achieve the closest true value.
Model Building
The mean of the historical real rate of return is used as an estimate of the expected rate of return on total income, and the variance of the expected rate of return on gold or bitcoin is used to quantify the risk assessment.
Historical real rate of return calculation: The larger the variance, the greater the deviation between the actual return and the expected return, indicating that the investment risk in this matter is greater and it is not appropriate to buy at this time.
The expected rates of return are: ( Two market conditions: • Bitcoin and gold markets open at the same time. ( ) ( ) This is partly what happens when the market for Bitcoin opens and the market for gold closes, and the target equation is still the total return.Constraint 1 is based on the principle that the number of bitcoin transactions must not exceed the number of holdings.Constraints 2 and 3 respectively represent the gold trading when the commission may not be greater than the yield, otherwise no trading will take place.Although gold cannot be traded at this time, we still list the constraints about gold to avoid interference and improve accuracy.[9] It is worth noting that gold should continue to be the same amount as the previous day, and not change until the next available trade.
• Gold and Bitcoin Yield Comparison:
Fig. 1 Comparison of Gold and Bitcoin Daily Yields By figure1, we calculate the daily returns to determine who is more stable in terms of change between gold and bitcoin, it is clear that gold is more stable than bitcoin.
• Comparison of Expected Increase: According to the question, we can only use the daily prices of gold and bitcoin so far to determine the trading strategy for the next day.We did this by predicting the gold and bitcoin prices afterwards, and based on the predictions we made a chart of the future price increase of gold and bitcoin.[10] We can clearly see that the orange color is the data already given in the title, while the blue color is what we predicted based on the previous data, and we can make a comparison between the predicted return and the COMMISSION.With the data obtained from the prediction, we find that gold and bitcoin are gradually increasing.See figure 2. We have done the image analysis for gold and bitcoin buying and selling by risk prediction.We have calculated the return on gold and bitcoin, and we can observe by the expected return that we should sell when the price is high, and we should buy when the price is low, so that it is in line with the facts.For example, if I buy gold on the first day at a lower price, but the next day the price of gold rises, so that if I sell my total assets will increase, but if I buy at a high price and sell at a lower price, so that the total return will be a loss.If the absolute value of the difference between tomorrow's price and today's actual price obtained from the forecast is lower than the threshold we set, then no trade will be made.
• Total Revenue Analysis: This is a graph of the relationship between total assets and dates.Total assets is the final return we calculate according to the algorithm.In the graph, each small color block represents a date and an amount, different colors distinguish different dates and different amounts are sorted by the size of the color block.The amount corresponding to the top left block is the largest, but it is not our total assets as of September 10, 2021.It is a very realistic investment problem because there are risks, ups and downs, and we may not always get the maximum return on September 10, 2021.See figure 3.
Fig. 2
Blue represents purchase.Yellow means sale • Transaction Forecast: | 2,832.2 | 2023-06-08T00:00:00.000 | [
"Computer Science"
] |
Voice Conversion Based Augmentation and a Hybrid CNN-LSTM Model for Improving Speaker-Independent Keyword Recognition on Limited Datasets
Keyword recognition is the basis of speech recognition, and its application is rapidly increasing in keyword spotting, robotics, and smart home surveillance. Because of these advanced applications, improving the accuracy of keyword recognition is crucial. In this paper, we proposed voice conversion (VC) - based augmentation to increase the limited training dataset and a fusion of a convolutional neural network (CNN) and long-short term memory (LSTM) model for robust speaker-independent isolated keyword recognition. Collecting and preparing a sufficient amount of voice data for speaker-independent speech recognition is a tedious and bulky task. To overcome this, we generated new raw voices from the original voices using an auxiliary classifier conditional variational autoencoder (ACVAE) method. In this study, the main intention of voice conversion is to obtain numerous and various human-like keywords’ voices that are not identical to the source and target speakers’ pronunciation. Parallel VC was used to accurately maintain the linguistic content. We examined the performance of the proposed voice conversion augmentation techniques using robust deep neural network algorithms. Original training data, excluding generated voice using other data augmentation and regularization techniques, were considered as the baseline. The results showed that incorporating voice conversion augmentation into the baseline augmentation techniques and applying the CNN-LSTM model improved the accuracy of isolated keyword recognition.
I. INTRODUCTION
In recent years, the use of speech for human-machine interactions and devices that support voice communication has increased rapidly owing to advancements in digital technology. Currently, most hand-based human-to-machine interactions are being replaced by computer vision and speech recognition technology in an advanced way. If the size of the training data is limited, the speaker-independent keyword spotting is a very challenging task owing to overfitting problems. Considering this difficulty, this paper focuses on voice conversion (VC)-based augmentation to increase the training The associate editor coordinating the review of this manuscript and approving it for publication was Longzhi Yang . dataset size for deep learning algorithms and to improve speaker-independent keyword recognition. The identification of keywords is applicable for controlling robotics, speechto-text, home surveillance (door and TV control), military activities (air force), keyword verification (unknown keyword detection), personal digital assistance (car driver and chatbot), Google search by voice, personal virtual assistance (Siri, Google Assistant, Cortana, and Alexa), aerospace applications, keyword spotting, and security [1], [2], [3], [4], [5], [6], [7], [8]. For instance, voice-based automated smart home surveillance is useful for assisting elderly and disabled people.
VC has become very sophisticated and has many applications, such as generating new voices for text-to-speech (TTS) [9], [10], hiding the identity of the speaker, music conversion [11], [12], accent conversion [13], emotion conversion [14], [15], speech enhancement [16], film industry, gaming technology, and voice restoration [17]. VC is useful for people who lose their voice organs either due to nature or disease. Challenges of VC competition have been initiated and released in recent years to improve VC performance. Three VC challenges [18], [19], [20] have been addressed to date. Traditional VC methods use Gaussian mixture models (GMM), but the converted speech quality is often degraded owing to over-smoothing. To overcome this problem, a minimum distance spectral mapping (MDSM)-based GMM has been proposed [21]. The GMM-based VC is a statistical conversion method based on the maximum-likelihood estimation of spectral parameter feature statistics [22]. Recently, researchers who participated in VC challenges used different neural network approach models, such as the encoder-decoder model (Zero-Shot Voice Style Transfer with Only Autoencoder Loss, vector quantized variational autoencoders, cyclic variational autoencoder), one-shot VC, generative adversarial network (GAN) (CycleGAN-VC, StarGAN-VC, and Adaptive GAN or AdaGAN), parallel spectral mapping (Tacotron), and one-shot VC [20].
The basic goal of VC is converting the source speaker's accent to the targeted speaker's accent accurately with the full linguistic content. A large amount of data is needed for an accurate voice conversion process. If we convert the voice accurately, it is not helpful for data augmentation because we have almost the same existing voice on the limited dataset. In our scenario, the generated voice should be the modified accent of the existing voices with the full linguistic content. Many state-of-the-art VC methods [23], [24], [25] have been proposed and implemented for parallel and non-parallel VC. It is possible to train the parallel VC in a limited dataset [26]. If the performance of VC is not precise enough, voice augmentation for VC is possible. Different augmentations techniques for VC were proposed such as attention-based speaker embeddings for one-shot VC and data augmentation-based non-parallel VC [27], [28].
The main contribution of this paper is applying the advanced parallel VC techniques to real applications, specifically to increase the training data size and usage of state-ofthe-art machine learning algorithms for speaker-independent keyword recognition. We consider that the very high similarity between the converted voice and the existing target voices has no significant implication for data augmentation. We realized that exact VC is not useful for voice-based augmentation. The converted voice should be a modified version of the target and source speakers' pronunciation, while the linguistic content of the keyword is maintained as it is. The proposed VC is carried out across a limited number of nonnative English speakers. We reduced the training time of the VC for reducing the accurate voice conversion performance. Since the VC model degrades the quality of results for never seen voices, the trained data has been fed to the trained model during the conversion phase to simplify the challenge of the huge training data demands of VC. These techniques distinguished our approach from the VC-based augmentation of related works [36], [37], [38]. The test data of VC is already included in the training data of VC. Several speakers are not required necessarily for our VC process. Dataset-I was collected and formulated for three non-native English speakers' countries. The test data for dataset-II contained four different native language speakers, whereas the training data contained only the same native language speakers. Both dataset-I and dataset-II were organized for speakerindependent keyword recognition challenge, which is arduous relative to the speaker-dependent on limited dataset. The significance of the proposed voice augmentation technique was compared with the ordinary voice recognition augmentation and regularization techniques. Although the related works [30], [31], [33], [34] showed that the CNN model is an exemplary model for vocabulary-size speech recognition, we have proven that the fusion CNN-LSTM model is superior to the pure CNN and pure LSTM for two separate datasets. The LSTM model improved the inconsistent performance of the CNN model when CNN and LSTM were hybridized together. Since the LSTM controls the exploding gradient problems [29], we noted that replacing the fully connected layer of the CNN with LSTM reduced the vanishing gradient problem. Finally, we realized that selecting the optimal mel-spectrogram segmentation frame size values for the time distributed CNN-LSTM model has a significant impact on model performance and it needs very critical experimental investigation to achieve desirable model performance with an optimized computational time. The mel-spectrogram features are well-organized in the form of 2-D sequential frames that is very learnable and suitable for our CNN-LSTM model. A delicate CNN-LSTM framework is also designed carefully for feature extraction and classification, which could take less computation time during model training and testing. The frame size was obtained using a deep experimental analysis.
The rest of this paper is organized as follows. We described the related works in Section II. The proposed methodology is described in Section III. The dataset setup is explained in Section IV. In Section V, the results and a discussion are presented. Finally, the conclusion of this study is summarized in Section VI.
II. RELATED WORKS
Many studies have been proposed for keyword identification by applying the CNN model to mel-frequency cepstral coefficients (MFCC) and spectrogram speech signal features. Li and Zhou [30] proved that a CNN outperformed a deep feed-forward network for six-command voice recognition using MFCC feature extraction. The six commands (''up'', ''down'', ''left'', ''right'', ''unknown keyword'', and ''silence'') were selected and used from Google's TensorFlow speech commands dataset for their experiment. Waqar et al. [31] proposed speech command recognition using CNN to control popular snake games. The authors used VOLUME 10, 2022 a limited dataset for only four direction speech commands (''Up'', ''Down'', ''Left'', and ''Right''). The MFCC features of the speech commands and the CNN algorithm were proposed to recognize these four speech commands. The experimental results showed that the proposed algorithm achieved high recognition accuracy. Similarly, Wubet and Lian [32] showed that CNN is better than the SVM model for keyword recognition, and surprisingly, a hybrid of CNN-SVM outperformed pure CNN and pure SVM. Cayir and Navruz [33] investigated the influence of a limited size dataset for voice command recognition using 12 different voice commands (''down'', ''forward'', ''follow'', ''go'', ''left'', ''on'', ''off'', ''right'', ''stop'', ''up'', and ''yes''). Their experimental results showed that when the test dataset included native Turkish speakers, the test accuracy was 94.64% for a large dataset and 64.81% for a small dataset. In contrast, when the test dataset included foreigners' voices, the test accuracy declined to 63.29% for the large dataset and 33.18% for the small dataset. They examined and confirmed the above-listed results using a CNN on the MFCC features. The results indicated that the test accuracy rates increased as the training dataset size increased and the accent of the diversified voice was expanded. Yang [34] compared a speech recognition of command words performances using a deep neural network (DNN) and recurrent neural network (RNN) for 10 command voice recognition using MFCC feature extraction. The 10 commands (''yes'', ''no'', ''up'', ''down'', ''left'', ''right'', ''on'', ''off'', ''stop'', and ''go'') were selected and used from Google's TensorFlow speech commands dataset for their investigation. The result showed that CNN outperformed compared to DNN and RNN. Furthermore, Fendji et al. [35] have mentioned and summarized the last two decades' study of automatic speech recognition (ASR) using limited vocabularies and sentences. Overall, most of the recently proposed models have shown that the CNN model is an exemplary model for vocabulary-size speech recognition. The comparison of the related works and the proposed model are summarized in Table 1 (a). Besides, the related works that employed VC data augmentation for speech recognition in limited data are summarized in Table 1 (b). VC-based data augmentation has been used by several researchers in recent years. Shahnawazuddin et al. [36] proposed a VC-based data augmentation to improve children's speech recognition in limited data scenarios. In this study, the acoustic attributes of adults were converted into children's speech using a cycle-consistent GAN. Word error rates (WERs) were significantly reduced by VC-based data augmentation. However, our VC scenario does not involve exact VC processing; rather, it is the process of obtaining a human-like modified voice version of the source and target speakers' pronunciation. Singh et al. [37] used VCbased data augmentation for ASR using CycleGAN and also compared its performance with the baseline system. The experimental results showed a good improvement after 200 hours of CycleGAN-based new adult speech with a reduction of 5.58% in WER compared to the baseline system. Furthermore, the collection of other augmentation and CycleGAN-converted adult speech showed the highest reduction of 7.44% in WER compared to the baseline system. Baas and Kamper [38] proposed a VC-based augmentation to improve the speech recognition system for limited data of the low-resource languages. Authors augmented the unseen and cross-linguistic low resource-limited data using a good resource language of the VC training model.
III. PROPOSED MODELS
The proposed model was developed using ACVAE-VC for voice-based data augmentation and a hybrid CNN-LSTM model for feature extraction and classification, as depicted in Fig. 1. The minimum mean-square error log-spectral amplitude estimator algorithm [39] is applied for noise reduction. The VC-based augmentation and a hybrid of CNN-LSTM network are briefly described as follows.
A. VOICE CONVERSION-BASED DATA AUGMENTATION
Data augmentation is the process of creating new, slightly altered samples from the original samples to escalate the training set, which can be regarded as a type of regularization method. Geometric transformation (affine transformation), generative adversarial networks (GAN), and autoencoder networks are common methods for generating more spectrogram images to reduce the overfitting problems of speech recognition in all machine learning algorithms. In addition, dropout, batch normalization, transfer learning, and oneshot learning are regularization techniques and exceptionally common ways of reducing the overfitting problem in deep neural networks [40]. Most research has shown that affine transformation has significantly improved the performance of overfitted models when compared to others. We considered geometric transformation, batch normalization, and dropout as the baseline for comparison with the proposed augmentation technique.
We proposed the ACVAE VC model [41] for VC processing. Although Kameoka et al. [41] used ACVAE for non-parallel VC and they aimed to generate exact accent translation on phrases and sentence utterances, we prepared and used the keyword dataset for parallel VC to keep the linguistic content of voices perfectly and to obtain a moderately modified version of target and source speakers' accents. We noted that VC-based voice augmentation should not be the exact pronunciation conversion, but the linguistic content of the keywords should be accurately maintained. Our work is speaker-independent keyword recognition (test data is completely from never seen speakers) and the number of speakers is limited. This limited number of training speakers leads to a limited dataset size for speaker-independent keyword recognition and an overfitting problem. Therefore, we need to diversify the training speakers' accents to make them look like many different speakers. Consider that we have a limited number of speakers (A and B) who speak each keyword several times, as we specified in Section IV. VC among these speakers is possible to generate new artificial speakers D and E. Speaker A to B conversion yields speaker D, whereas B to A conversion gives speaker E. The proposed VC model uses a sequence of mel-cepstral coefficients computed from a spectral envelope sequence obtained using WORLD [42]. In the autoencoder model, the encoder network generates a set of parameters (mean and variance) for the conditional distribution P φ (z|x) of a latent space variable z from the input data x, whereas the decoder network generates a set of parameters (mean and variance) for the conditional distribution P θ (x|z) of data x from the latent space variable z. In regular CVAEs, the encoder and decoder are free to ignore c by finding distributions satisfying P ϕ (z|x, c) = P ϕ (z|x) and P θ (x|z,c) = P θ (x|z). Class category c can be represented as a single one-hot vector identification of classes in ACVAE. A gated linear unit (GLU)-based CNN auxiliary classifier was introduced and applied next to the decoder to avoid VAEs problems. The classifier predicted the attribute classes of the decoder outputs [41].
As we mentioned in the introduction Section, we have found that the exact accent translation is not useful for our work because our target is acquiring various human-like voices and keeping the linguistic content for raising the number of training data. To get these successfully modified voice versions, the maximum iteration of exact VC was reduced. The noise has been reduced before and after the VC process. If there is any noise in raw data, it highly affects the VC quality. In this work, the principal goal of VC is for generating a human-like (natural) and a variant voice. Therefore, we didn't give attention to exact VC processing rather gave more caution to acquire the natural voice and to keep the linguistic content. Since our target is not designing an accurate model for VC, we used the trained data on the ACVAE training model to produce various human-like keyword voices. It was implemented across non-native English speakers' accents each other for all datasets. We considered females to females, females to males, males to males, and males to females VC to get a more generalized voice and to reduce the test data accent variation which is a big tackle of speaker-independent speech recognition. All selected speakers are both source and target speakers for ACVAE, but the same speaker cannot be both source and target at the same time. Finally, the converted voices and original voices are mixed and converted to a 2-D spectrogram by using a short-time Fourier transform (STFT) with a 23 milliseconds frame size and at a sample rate of 16000 Hz. The sample mel-spectrogram image result of VC-based augmentation is depicted in Fig. 2.
B. PROPOSED HYBRID CNN-LSTM MODEL
The proposed feature extraction and classification model was developed using a fusion of the CNN and LSTM models. Although the pure CNN model has demonstrated exceptional achievements in many applications [43], [44], [45], [46], the LSTM is integrated into it to achieve a good performance. The 2D CNNs have been proposed for the extraction of deep features of spectrograms. The 2D mel-spectrogram was split into an equal-size sequence of 16 frames. All sequences of frames are still 2D mel-spectrogram features and they are fed to 2D-CNNs sequentially based on the labeled sequence number in Fig. 3. First, frame 1 was fed into the CNN, which extracted the basic features of frame 1 and generated a flattened vector called Flatten 1. Next, frame 2 was fed into the CNN, which extracted the basic features of frame 2 and generated a flattened vector called Flatten 2. Similarly, all remaining frames were fed into the CNN, and flattened vectors were generated based on their sequence order. Although the original dimension of the mel-spectrogram was large, it was resized to 64×64×3 to reduce the computational time and space. We verified that reducing the original size to 64×64×3 pixels had no significant impact on the accuracy metrics. As a result, all 16 frames were 64×4×3 in size.
After many inspection methods to find an appropriate CNN architecture, we have found that a CNN architecture with two convolutional layers and one max-pooling layer was performed expertly. Because the segmented frame length was short, it was not possible to use many convolution layers preceding the max-pooling layers. Max-pooling layers were placed after the two convolutional layers to downsample the convolution dimension. A rectified linear unit (ReLU) activation function was applied between the convolution layers. In addition to VC-based data augmentation and affine transformation, batch normalization and dropout regularization were applied to pure CNN, pure LSTM, and CNN-LSTM to prevent the models from overfitting problems and for convenient comparison.
In this study, we fused a state-of-the-art LSTM deep learning algorithm with the sequentially flattened layer of the CNN. LSTM is employed for deep feature extraction and classification. It has shown advanced performance for sequential data prediction and classification in many applications [47], [48], [49], such as time series trend forecasting, image classification, speech classification, and sentiment analysis. Similarly, hybrid CNN and LSTM models [50], [51], [52] have improved pure CNN and pure LSTM models.
The LSTM consists of operations, activation functions, and states for receiving inputs over time. At each time step, an input vector is fed into the LSTM. We used LSTM for global temporal information extraction and classification using the extracted features of the CNNs. In a fully connected (FC) layer of LSTM, a softmax activation function was applied and used as the classifier. The CNN extracted features are carefully organized time series data for the LSTM input time series data for the LSTM input. The flattened vectors of the CNN are fed to the LSTM with 16 time steps, as depicted in Fig. 3. The CNN flattened vector output V (t=i) was assigned to the CNN's frame i input, where t is the time step, and i is the frame number. Each flattened vector is fed to the interconnected LSTM networks as x i at t = i.
LSTM consists of an input gate, a forget gate, and an output gate, which are represented by i t , f t and o t , respectively. It has a cell state (c) and a hidden state (h), which are the long-term memory and short-term memory, respectively. In the LSTM gates, σ is the element-wise sigmoid function and tanh is the element-wise tangent activation function. The LSTM gates processed the flattened input vector (x t ∈ R N ×1 ) at t timestep with the previous short-term memory (h t−1 ), where N × 1 is the size of vectors. Finally, the new cell state and the new short-term memory are computed according to: where c t−1 is the previous cell state,ĉ t is the candidate cell state, c t is the new cell state, and is an element-wise product operator. The spectrogram input was segmented in the vertical direction, but the horizontal segmentation was not as good as the vertical direction. When the number of frames is high, the frame length is too small. Conversely, when the number of frames is low, the frame lengths are large. Selecting a large frame length is preferred for a good trainable CNN model, whereas many segmented frames are required for a good learnable LSTM model. However, the CNN-LSTM model requires a good adjustment of the frame size to design a worthy model. We simplified the complication by selecting an optimal and more generalized 2 i number of frames per single spectrogram and frame length for a 64×64×3 spectrogram image: where i = 0, 1, 2, . . . , 6, and L is the length of the melspectrogram. Because frame segmentation was applied vertically on each spectrogram, the frame width was kept the same as the spectrogram width. We compared the performance among all 2 i frames experimentally, and we realized that a frame size of 16×64×4×3 per single spectrogram adjustment is surprisingly the best CNN-LSTM input from other frame sizes. From the selected frame size, 16 is the number of frames, 4 is the width of the frames, 64 is the height of the frames, and 3 is the number of channels (red, green, and blue) for each spectrogram. After many inspection methods for finding the optimized CNN-LSTM architecture, we configured the proposed model as shown in Table 2. A comparison between CNN, LSTM, and the proposed model to be persuasive, well-configured pure CNN, and pure LSTM models with a well-adjusted parameter setting were also designed.
The parameter settings of the proposed model are listed in Table 3. In this study, we considered a well-recommended optimizer and cost function.
IV. DATASET SETUP
To ensure the generality of the proposed models, one private dataset was prepared and one public dataset was selected. The proposed models were applied separately to both datasets. The dataset description is as follows: A. DATASET SETUP I All keyword voices were collected from non-native English speakers' countries, namely, Ethiopia, Taiwan, and India. The Most of these keywords were recorded from environments with background noise. The keyword voices were recorded at a sampling frequency of 16000 Hz, bit depth of 16 bits, and a monotype channel. The recording parameters of the datasets were fixed for all records. The recording time interval for the English keywords was between 1 and 1.5 seconds. After the recording, the audio files were stored as WAV files. All voices were recorded on laptop computers and Aver Media Microphone devices. All voices were collected from individuals with normal health status, and no person spoke emotionally during data collection. The voices of all but three speakers were recorded indoors. The total number of speakers was 8 Indian (5 females and 3 males), 10 Ethiopian (7 males and 3 females), and 12 Taiwanese (8 males and 4 females). Each keyword was spoken 20 times by all speakers. The dataset preparation method was purely speaker-independent. The 24 speakers were selected as limited training data and half of these limited training data (12 speakers) were assigned as very limited training data. The remaining six speakers were for test in both cases. The training and test data were collected separately, as illustrated in Fig. 4.
In our scenario, 12 speakers (four Taiwanese, four Ethiopian, and four Indian) and 10 speakers were selected from dataset setup-I and dataset setup-II for VC processing, respectively. A total of 12×11×12×20 = 31,680 and 10×9×10×50 = 45k new voices were generated for dataset setup-I and dataset setup-II, respectively, as shown in Fig. 5 and Table 4.
B. DATASET SETUP II
We also used the AudioMNIST dataset to evaluate the performance of the proposed model. Originally, the AudioMNIST consisted of 30000 audio recordings (9.5 hours) of spoken digits (0-9) in English, and each digit was spoken 50 times by 60 different speakers [53]. Since this study aims to improve speaker-independent keyword recognition on limited data, only 10 German speakers (6 male and 4 female) were assigned to the training data and 8 speakers (5 male and 3 female) were selected and assigned to the test data. All training data were selected from German native speakers, whereas test data were from German (three males and two females), South African (one male), Tamil (one female), and Arabic native speakers (one male).
Affine augmentation is a popular data augmentation technique for image recognition and spectrogram-based speech recognition using geometric transformations. We have used this very powerful augmentation technique as a baseline augmentation for evaluating the performance of the VC-based augmentation techniques. In this baseline augmentation, the affine transformation parameters are configured carefully for the comparison to be very convenient and unbiased. The 10 different mel-spectrogram images are generated for each of the original training samples during the baseline augmentation. For the proposed VC + baseline augmentation, 3 different mel-spectrogram images are generated from each real sample voice by applying baseline augmentation beside many voices which are generated using the VC methods.
V. RESULTS AND DISCUSSION
The experimental results were investigated using PyTorch for VC, Kera framework on the frontend, and Tensor-Flow framework as a backend for deep learning classification models using the Python programming language on the graphics processing unit (GPU). We used the NVIDIA GeForce RTX 2080 Ti GPU with 11 gigabytes (GB) of dedicated memory, where RTX stands for Ray Tracing Texel eXtreme and T is Titanium. Compute Unified Device Architecture (CUDA) Toolkit for the GPU-accelerated applications and NVIDIA CUDA deep neural network (cuDNN) GPUaccelerated libraries for deep neural networks were installed and configured on Windows 10 Intel 64-bit operating system. The original dataset setup-I is limited by itself, and half of this limited dataset is removed to further obtain a very limited dataset. We considered both limited and very limited as the baseline for comparing it to the proposed VC-based voice augmentation technique. Many voices were generated by the VC algorithm using the voices of a few speakers. The VC model was trained two times with the same model architecture for dataset-I and dataset-II separately. We assigned 2000 epochs for VC training phases to obtain a modified accent between the target and source speakers. A mean opinion score (MOS) subjective evaluation method [41] is selected for the naturalness and similarity evaluation of the converted voice. Five persons evaluated the naturalness and accent similarity between 25 converted sample voices and target voices. The evaluation score is 5 for excellent, 4 for good, 3 for fair, 2 for poor, and 1 for bad VC. Since we used the training data of parallel VC as test data again, the average MOS result is good for the naturalness and fair for the similarity. We examined the proposed model on two separate dataset setups to ensure that it performed well. In this study, the experiments for dataset-I were carried out for two cases, which are limited and very limited data.
In limited cases, all collected data (24 speakers) were taken as the original training data, and all 12 speakers' voices were converted to each other. The final dataset contained a mix of both original and converted voices. Performance comparison of the models and a summary of the results for limited data are presented in Table 5 and Fig. 6. The performance of the model is measured as follows: where TP is the true positive, TN is the true negative, FP is the false positive, and FN is the false negative. For very limited cases, we retained only half of the original training data (12 speakers). This is used to show how much VC is very useful for very limited data, as Table 6 and Fig. 7 show the result summary. The performance of the deep learning models was significantly improved by the proposed VC augmentation technique on very limited training data. Overall, the proposed model performed 94.2 % accuracy for keyword recognition on dataset setup-I. For dataset setup-II, all training voices (10 speakers) were selected for VC, and the results are shown in Table 7 and Fig. 6. The proposed VC augmentation method and CNN-LSTM model showed superior results on both dataset setups.
The deep learning models on a mix of original training data and converted data surprisingly improved the accuracy when compared to their performance on pure original data. For instance, the mix of 12 speakers' voices and their converted voices had better performance than the pure 24 speakers in the CNN model, as presented in Tables 6 and 7. Therefore, instead of collecting a large amount of data from many speakers, it is possible to compensate for this using VOLUME 10, 2022 VC augmentation techniques. The overall results showed that the pure CNN and pure LSTM models were highly affected by the limited training dataset size when compared to our proposed CNN-LSTM model. Table 6 reported that the pure LSTM and the proposed models' performance are superior compared with the CNN model for very limited data without data augmentation techniques. Finally, we conclude that applying augmentation and regularization techniques to a mixture of both original and converted data enhanced the deep learning performance. We observe that the pure CNN performance has no stability for the testing data at different training iterations, whereas the proposed model has shown better consistency.
For good result analysis, we used the popular nonparametric statistical models' performance comparison techniques. The Wilcoxon signed-rank test is recommended for pairwise models' performance comparison, whereas the Friedman test, the Friedman aligned ranks test, and the Quade test for multiple algorithms [54], [55]. We chose the Wilcoxon signed ranks test for pairwise models' performance comparison, as Table 8 has reported. The Friedman test, the Friedman aligned ranks test, and the Quade test for three algorithms' performance comparison is depicted in Table 9. All these techniques were performed on the accuracy of all three different datasets. The significant level (p-value) < 0.05 indicates that one model is better than the other. All non-parametric statistical model performance comparisons' results showed that the proposed models were better than others.
The execution time analysis is very useful for trade-off the accuracy and computational time on the given models. The execution time of each model is shown in Table 10.
The execution time of the proposed algorithm (CNN-LSTM) is fast compared to pure CNN and pure LSTM models. The dataset-I (limited and very limited) and dataset-II training execution times are reported in 500 and 100 epochs, respectively.
VI. CONCLUSION
This paper presented a VC-based augmentation and CNN-LSTM model for robust speaker-independent keyword recognition. Many new modified versions of the original training voice were generated to increase the amount of training data. The experimental results showed that VC-based augmentation and the hybrid CNN-LSTM model improved speaker-independent keyword recognition. The mix of the original training data and converted data has comparable performance to affine transformation augmentation. The combination of affine transformations and VC augmentation has become more robust. The CNN-LSTM model has better accuracy and consistency than the pure CNN and pure LSTM. For very limited data without data augmentation techniques, the CNN model was highly affected compared with the pure LSTM and the proposed model. Extending this work for continuous speech recognition in a limited dataset size is under consideration for future work with some essential improvements to the current methodology. | 7,432.6 | 2022-01-01T00:00:00.000 | [
"Computer Science"
] |
Green silver nanoparticles of Phyllanthus amarus: as an antibacterial agent against multi drug resistant clinical isolates of Pseudomonas aeruginosa
Background Pseudomonas aeruginosa infection is a leading cause of morbidity and mortality in burn and immune-compromised patients. In recent studies, researchers have drawn their attention towards ecofriendly synthesis of nanoparticles and their activity against multidrug resistant microbes. In this study, silver nanoparticles were synthesized from aqueous extract of Phyllanthus amarus. The synthesized nanoparticles were explored as a potent source of nanomedicine against MDR burn isolates of P. aeruginosa. Results Silver nanoparticles were successfully synthesized using P. amarus extract and the nature of synthesized nanoparticles was analyzed by UV-Vis spectroscopy, transmission electron microscopy, energy dispersive X-ray spectroscopy, dynamic light scattering, zeta potential, X- ray diffraction and fourier transform infra-red spectroscopy. The average size of synthesized nanoparticles was 15.7, 24 ± 8 and 29.78 nm by XRD, TEM and DLS respectively. The antibacterial activity of AgNPs was investigated against fifteen MDR strains of P. aeruginosa tested at different concentration. The zone of inhibition was measured in the range of 10 ± 0.53 to 21 ± 0.11mm with silver nanoparticles concentration of 12.5 to 100 μg/ml. The zone of inhibition increased with increase in the concentration of silver nanoparticles. The MIC values of synthesized silver nanoparticles were found in the range of 6.25 to12.5 μg/ml. The MIC values are comparable to the standard antibiotics. Conclusion The present study suggests that silver nanoparticles from P. amarus extract exhibited excellent antibacterial potential against multidrug resistant strains of P. aeruginosa from burn patients and gives insight of their potential applicability as an alternative antibacterial in the health care system to reduce the burden of multidrug resistance. Electronic supplementary material The online version of this article (doi:10.1186/s12951-014-0040-x) contains supplementary material, which is available to authorized users.
Background
Pseudomonas aeruginosa, a gram negative bacterium, is the leading cause of morbidity and mortality in burn patients as they are more susceptible to infections because of immune-suppression and loss of cutaneous coverage [1]. Since P. aeruginosa has innate potential to develop resistance, virtually to any antibiotics to which it is exposed, due to the presence of multiple resistance mechanisms and it becomes a multidrug resistant (MDR) strain.
Infections caused by MDR P. aeruginosa are often severe; life threatening and these strains have frequently been reported as the cause of nosocomial infections. These MDR have been emerged as a major problem in burn units as burn injury disrupts both the normal skin barrier and many of systemic host defence mechanism which make burn patients the ideal hosts for opportunistic infections [2]. The importance to prevent these infections has been recognized since its inception thus it becomes difficult to treat the infection caused by P. aeruginosa MDR strains due to their narrow range of susceptibility to antimicrobial agents. Therefore, currently, researchers started to develop alternative therapies to aid patients to recover from the infections. In future, these alternatives may be useful in treating not only burn infections but other antibiotic resistant infections as well.
Nanotechnology provides a good platform to modify and develop the important properties of silver metal in the form of nanoparticles having promising applications as an antibacterial agent [3,4]. Silver nanoparticles have high surface area to volume ratio and the unique chemical, physical properties [5,6]. Nowadays, they have been widely used as an effective bactericidal agent against broad spectrum of bacteria, including antibiotic resistant strains [7]. Hence, researchers are shifting towards nanoparticles in general and silver nanoparticles (AgNPs) in particular to solve the problem of emergence of MDR bacteria [8]. Also the development of biological approach for the synthesis of nanoparticles is evolving in to an important branch of nanotechnology [9,10]. The biological method has advancement over chemical and physical method as it is cost effective and ecofriendly [11,12]. Phyllanthus amarus is an important plant of Indian Ayurvedic system of medicine, belongs to the family Euphorbiaceae. It is a small herb well known for its medicinal properties and has been used worldwide [13].
This study aims to explore the efficacy of synthesized silver nanoparticles from P. amarus as a potent source of nanomedicine against MDR burn isolates of P. aeruginosa and establish the therapeutic antibacterial potential of plant with nanotechnology; thereby justify the folklore claim of the plant used in the traditional system of Indian medicine.
Synthesis of AgNPs
The AgNPs were successfully synthesized using aqueous plant extract of P. amarus by mixing with silver nitrate solution (1mM). The colour changes from pale yellow to dark brown (Additional file 1: Figure S1). This was observed due to the reduction of Ag + and it indicates the formation of AgNPs.
Characterization of Ag nanoparticles
The synthesis of AgNPs was confirmed by UV-VIS spectrophotometer (Shimadzu). The UV-VIS absorption spectra of the AgNPs were monitored in a range of 300-800 nm. A strong peak specific for the synthesis of silver nanoparticles was obtained at 420-430 nm. Additional file 2: Figure S2 shows the absorption spectra of AgNPs synthesized by P. amarus. The TEM results ( Figure 1) showed that all synthesized AgNPs were spherical in shape with 24 ± 8 nm size and found to be well dispersed in aqueous medium. EDX characterization has shown absorption of strong silver signal along with other elements, which may be originated from the biomolecules that are bound to the surface of silver nanoparticles. EDX performed by energy and intensity distributions of X-ray signals generated by focused electron beam on a specimen. From EDX spectra, showed in Figure 2, it is clear that silver nanoparticles reduced by P. amarus.
Dynamic light scattering (DLS) technique and zeta potential has been used to determine the size of particles and measure the potential stability of the particles in the colloidal suspension respectively. Figure 3 and Figure 4 have shown the DLS and zeta potential graph of AgNPs of P. amarus with an average size of 29.78 nm and the particles carry a charge of -11.9 mV respectively. Silver nanoparticles generally carry a negative charge. All silver nanoparticles synthesized from P. amarus showed negative charge and were stable at room temperature. The particle size and nature of AgNPs was determined by XRD. The mean particle diameter of AgNPs was calculated using the Debye-Scherrer's equation. An average size of the silver nanoparticles synthesized by P. amarus was 15.7 nm ( Figure 5 and Table 1). The FT-IR spectrum of AgNPs from P. amarus showed the characteristics absorbance bands ( Figure 6) due to aldehydic C-H stretch (2,915 and 2,848 cm -1 ), C-O stretch (1,634 cm -1 ), N-H (1517 cm -1), 1462 cm -1 N-O stretch (1,377 cm -1 ) and C-O stretch (dialkyl) (1,169 cm -1 ), C-N (1,037 cm -1 ), C-H stretch (718 cm -1 ).
Antibacterial assay
The 15 multidrug resistant strains of P. aeruginosa isolated from burn patients tested at various concentrations of AgNPs i.e. 12.5, 25, 50 and 100 μg/ml to determine the antibacterial effect by agar well diffusion method. The AgNPs showed (Additional file 3: Figure S3) antimicrobial activity against all the tested pathogens. The antibacterial activity is concentration dependent as it increased with the concentration of AgNPs ( Figure 7). The zone of inhibition measured in a range of 10 ± 0.53 to 21 ± 0.11 mm. MDR Strain1 was found ( Figure 8) to be most susceptible where zone of inhibition ranged from 13 ± 1 to 21 ± 0.11 mm at AgNPs concentration of 12.5 to 100 μg/ml. MDR strain 10 was least susceptible with 10 ± 0.53 to 13 ± 0.41mm zone of inhibition.
Minimum Inhibitory Concentration (MIC)
The MIC of AgNPs from P. amarus against MDR strains of P. aeruginosa was 6.25-12.5 μg/ml. MDR strains 6, 10,12,13,14 and 15 showed the MIC values of 12.5 μg/ml. The remaining nine MDR strains have shown the MIC at 6.25 μg/ml (Table 2) which is lower than standard antibiotic.
Discussion
The biosynthesis of nanoparticles has received considerable attention due to the growing need to develop environmentally benign technologies in material synthesis [14]. The phytochemicals derived from plant products serve as a prototype to develop less toxic and more effective medicines for controlling the growth of microorganisms [15]. These compounds have significant therapeutic application against human pathogens. Numerous studies have been conducted with the extracts of various plants for screening of antimicrobial activity in search of new antimicrobial compounds [16]. P. amarus was also reported to have antibacterial efficacy against some drug resistant pathogenic bacterial strains [17]. But there are still limited studies regarding antibacterial activity of AgNPs from this plant. The beauty of the present study is that AgNPs reduced by P. amarus were highly effective against MDR burn isolates of P. aeruginosa in term of novelty. We synthesized AgNPs from P. amarus, which is easily available in rainy season, safe, non-toxic and have a variety of secondary metabolites that can help in the reduction of silver ions. The main mechanism considered for the process is plant-assisted reduction due to phytochemicals. The main phytochemicals involved are terpenoids, flavones, ketones, aldehydes, amides, and carboxylic acids. Flavones, organic acids, and quinones are watersoluble phytochemicals that are responsible for the immediate reduction of the ions [18]. Studies have revealed that P. amarus contain mainly phyllanthin, hypophyllanthin, phyltertralin and many more other phytochemicals [19]. It was also suggested that the phytochemicals are involved directly in the reduction of the ions and formation of silver nanoparticles [20]. Though the exact mechanism involved in each plant varies as due to the presence of different phytochemicals which are involved in the reduction of the ions leads to the synthesis of AgNPs. A strong peak was obtained at 420-430 nm showing the absorption spectra of AgNPs synthesized by P. amarus. Further EDX has shown absorption of strong silver signal along with other elements that are bound to the surface of silver nanoparticles. TEM, XRD, DLS revealed the size and zeta potential contributed towards the stability of AgNPs [21]. FTIR confirms the presence of different functional groups absorb characteristic frequencies of IR radiations [22].
The exact mechanism by which silver nanoparticles employ to cause antimicrobial effect is not clearly known.
However, there are various theories suggested about the action of AgNPs on microbes to cause the antimicrobial effect. The AgNPs have ability to anchor to the bacterial cell wall and subsequently penetrate it, thereby causing structural changes in the cell membrane like the permeability of cell membrane and death of the cell. There is formation of 'pits' on the cell surface where accumulation of the nanoparticles takes place [23]. The formation of free radicals by AgNPs may be considered to be another mechanism by which the cells die [24,25]. It has also been proposed that there can be release of silver ions by the nanoparticles [26], and these ions can interact with the thiol groups of many vital enzymes and inactivate them [27]. The bacterial cells in contact with silver absorb silver ions, which inhibit several functions in the cell and damage the cells.
In recent years, due to the development of resistant strains, antibiotic resistance also has been increased. MDR P. aeruginosa strains from burn patients are causing serious infections and exhibit innate resistance to many antibiotics. These can develop new resistance after exposures to antimicrobial agents. Some antimicrobial agents are extremely irritant and toxic. The studies on drug resistant bacteria in this facet are still limited. Also AgNPs have gained insight as an excellent antimicrobial agent due to its non-toxic effect on human cells in its low concentration and weaker ability to develop resistance towards silver ions [28][29][30].
The various researchers showed that AgNPs of P. amarus were found to be good antibacterial agent. Humberto et al. [31] showed the antibacterial activity of AgNPs against multidrug-resistant P. aeruginosa, E. coli, Streptococcus sp. and S. pyogens. Kathireshwari et al. [32] showed the antimicrobial activity against multi drug resistant human pathogens from leaf mediated synthesis of AgNPs using Phyllanthus niruri. Durairaj et al. [33] studied the antibacterial activity of purchased AgNPs (size 20-30 nm) against 10 isolates of P. aeruginosa comprising of 5 MDR strains with an inhibition zone of 11 mm observed with10 μg dose of the nanoparticles. In our results, AgNPs showed excellent antibacterial activity which is better than our previous study [34], which showed the good antibacterial activity of AgNPs prepared using T. cordifolia aqueous extract against P. aeruginosa MDR strain from burn patient with maximum concentration of 200 μg/ml. However, there is vital need and much interest in finding ways to formulate new types of safe and cost-effective biocidal materials [22]. Therefore, in this study, we used different plant as biomaterial and evaluated its antibacterial effects. The synthesized AgNPs showed significant antibacterial activity at concentration of 12.5-100 μg/ml against MDR strains of P. aeruginosa isolates. The MIC of AgNPs was found to be in a range from 6.25-12.5 μg/ml, almost nine MDR strains have shown the MIC at 6.25 μg/ml which was lower than that of the standard antibiotic (10 μg). As infection of P. aeruginosa always remains one of the most challenging concerns in burn units and the synthesized AgNPs of P. amarus are highly effective antibacterial agent against these MDR burn isolates.
Conclusion
In conclusion, we have demonstrated that AgNPs from P. amarus exhibit excellent antibacterial potential against MDR P. aeruginosa strains isolated from burn patients. Therefore these AgNPs may act as ecofriendly antibacterial agent against these nosocomial strains and can provides a potent alternative nanomedicine in the health care system to reduce the burden of multidrug resistance.
Synthesis of silver nanoparticles from plant extract Preparation of the extract
The whole plant of Phyllanthus amarus was collected locally from Botanical Garden, M.D. University, Rohtak, Haryana, India. It was thoroughly washed in distilled water, cut into fine pieces. 10g of fresh plant material was boiled into 100 ml sterile distilled water for 10 minutes and filtered through Whatman's No.1 filter paper. The extract was stored at 4°C for further experiments.
Synthesis of AgNPs from plant extract
For synthesis of AgNPs, the above plant extract of P. amarus was used and 15 ml of this extract was added to 200 ml of aqueous silver nitrate solution (1mM). This solution was kept for 20 minutes at 70°C (in water bath). The plant extract act as reducing as well as stabilizing agent in the solution and leads to the formation of AgNPs.
Characterization of synthesized AgNPs
The seven different characterization techniques were used for AgNPs. At first, AgNPs were characterized by UV-VIS Spectroscopy using Shimadzu UV-VIS Spectrophotometer. The scanning range for the samples was 300-800 nm. The double distilled water used as a blank reference. To remove any free biomass residue or compound that is not the capping ligand of the nanoparticles, after complete reduction, silver nanoparticles were concentrated by repeated centrifugation (3 times) of the reaction mixture at 15,000rpm for 20 min. The supernatant was replaced by distilled water each time. Thereafter, the purified suspension was freeze dried to obtain dried powder. The shape and size of AgNPs was determined by transmission electron microscopy (TEM). A drop (2 ul) of water dissolved synthesized nanoparticles was placed on a copper grid. The images were obtained with a Tecnai, Twin 200 KV (FEI, Netherlands) at a bias voltage of 200 kV used to analyze samples. The composition of the AgNPs was determined using the Energy Dispersive X-Ray Spectroscopy (EDX) coupled to the TEM. The size distribution or average size of the synthesized AgNPs were determined by dynamic light scattering (DLS) and zeta potential measurements were carried out using DLS (Malvern). For DLS analysis the samples were diluted 10 folds using 0.15M PBS (pH 7.4) and the measurements were taken in the range between 0.1 and 10,000 nm. X-Ray Diffraction (XRD) was done with the help of by X-Pert Pro Diffractometer. The X-ray diffraction data were obtained using step scan technique and with Cu-Ka radiation (1.500 Å, 40 kV, 30 mA) in h-2h configuration. The AgNPs were coated on to the glass substrate and after drying, the sample was analyzed by X-ray diffractometer. The crystallite domain size was calculated using the Debye-Scherrer's formula. Finally, Fourier Transform Infra-red Spectroscopy (FTIR) was used for detection of different functional groups. The dried AgNPs were analyzed by ALPHA FT-IR Spectrometer (from Bruker, Germany) for the detection of different functional groups by showing peaks from the region of 4000 cm -1 to 500 cm -1 .
Multi drug resistant clinical isolates of P. aeruginosa from burn patients
Fifteen clinical isolates were obtained from the various samples of burn patients receiving in Microbiology Department of Pt. B.D.S. Post Graduate Institute of Medical Sciences, Rohtak, Haryana, India. The purity and identity of each isolate was confirmed in laboratory by standard microbiological methods [35][36][37]. The sources of the clinical isolates were urine, wounds, blood, and body fluids of burn patients. The approval of SRAC (Scientific & Research Advisory Committee) of the institute was taken for the study with reference no. UHS/OSD/ 2010/1 dated 27/02/2012. The 10 most cost-effective antibiotics routinely used to treat P. aeruginosa infections were employed in the susceptibility test. The antibiotics included were amikacin, aztreonam, ceftizoxime, cefepime, gentamicin, imipenem, netilmicin, ofloxacin, piperacillin and tazobactum. For isolation of MDR strains, these antibiotics were used and susceptibility was checked by Kirby-Bauer disc method [38]. The strain which were resistant to 6 or 7 antibiotics was taken as MDR strain. | 4,033.4 | 2014-10-01T00:00:00.000 | [
"Chemistry",
"Environmental Science",
"Medicine"
] |
Regional inequality of resident income and its determinants: A case study of Zhejiang Province, China
This paper focuses on the regional inequality of resident income in local China at the county or district level, and Zhejiang Province is set as the empirical case. It takes a geographic approach to detect the spatial distribution pattern of resident income, and explore the relationship with regional-specific socio-economic factors. The analytical framework proposed by us has been proved appropriate by the case study. Our study results show that in terms of the resident income level, there exists great regional gap in Zhejiang with the northeast wealthy cluster and much poorer cluster in the southwest. The disposable income of residents is mainly determined by commerce prosperity, urban intensity and technological capacity of local areas, while the effect of regional income, household deposits and industrial production are much less or no significant. Our findings for Zhejiang lead us to suggest that those local states seeking to improve people’s livelihood and income should not solely rely on the industrial or manufacturing expansion, but pay more attention to business environment, urban construction and indigenous innovation. Also, to narrow the significant regional gap of resident income, extra efforts should be made to push the regional cooperation system in economic development.
Introduction
Income inequality is a socio-economic issue of global concern. The neoclassical convergence hypothesis summarizes the general law of its evolution, but the explanation for developing countries or transition economies is often unsatisfactory (Wei et al., 2017). In China, due to the unique economic structure and domestic environment, the problem of inequality is particularly prominent and complicated. The prevailing view is that the steep rise in income inequality of China is closely related to economic reforms (Gao et al., 2019a, b;Sutherland & Yao, 2011;Xie & Zhou, 2014). The transition from a planned economy to a market-oriented one consequences a surge in the inequality of national income distribution with obvious rise in Gini index (Molero-Simarro, 2017). According to Barry Naughton (2007) ''there may be no other case where a society's income distribution has deteriorated so much, so fast''. Although the distribution system is often regarded as the fundamental cause (Zhang, 2020), some specific situations and realistic reasons for income inequality have also attracted scholars' attention such as urbanization (Wang et al., 2019a, b;Yuan et al., 2020), financial development (Li, 2020;Su et al., 2019), administrative management (Zeng et al., 2018) and social policy (Gao et al., 2019a, b). Wang et al. (2014) discussed profiles of income inequality in China along three dimensions: interhousehold disparity, regional divides, and urbanrural gaps. They examined the wide driving forces behind rising inequality including policy biases, location or geographic factors, globalization, and education, as well as the effect of government interventions.
The interhousehold disparity is considered as the micro source and basic form of income inequality in China, and relevant study has been widely conducted (Anderson et al., 2019;Li & Sicular, 2014;Xie & Jin, 2015). Paul et al. (2017) investigated the effects of household income sources on the level and rise of inequality in urban China, based on the householdlevel data from the Chinese Household Income Project Surveys (CHIPS). Their empirical results show the contribution of wages and salaries to inequality has declined over the years, but business income also has turned into an inequality reducing force after the middle 1990s. It has many implications for the policy options or intervention to narrow the interhousehold disparity. Household income inequality in rural areas also got much attention, and it is found associated with some different factors like agricultural activities, ecological protection projects, and farmers' physical assets (Leng et al., 2020;Xiang et al., 2020;Zhang et al., 2019). Zhang et al. (2019) believe local off-farm work and out-migration with remittances are the two principal income sources and both add to inequality. Although human capital, natural capital and physical capital all play roles in the generation of income and inequality in rural China, the factors affecting inequality from agricultural and non-agricultural activities are different.
Apart from the interhousehold disparity, urbanrural gap and regional inequality are much more intuitive in China, and show diverse spatial patterns with great significance. Wu and He (2018) pointed out urban-rural gap and regional inequality are longstanding problems in China and result in considerable number of studies. Their empirical results indicate the dominant characteristics in the income distribution dynamics, that persistence and immobility, as well as the separate convergence clubs in urban and rural areas. The pattern of urban-rural gap proves in three regional groups, namely the eastern, central and western regions, and geographical poverty traps exist in both urban and rural prefectural areas. Tian et al. (2016) revisited the regional income inequality in China comprehensively, from a perspective of club convergence. They found more interesting geographic patterns that instead of one convergence at the national level, provincial incomes are converging into two clubs: seven east-coastal provinces (Shanghai, Tianjin, Jiangsu, Zhejiang, Guangdong, Shandong, and Fujian) and Inner Mongolia are converging into a high-income club, and the remaining provinces are converging into a low-income club.
In particular, the urban-rural gap is regarded as a significant factor with impacts on income distribution in China (Luo et al., 2020;Wang et al., 2020). Many scholars believe there is no developing country whose income gap between urban and rural areas contributes more to overall income inequality than China's. According to the WORLD INEQUALITY REPORT 2018, the urban-rural gap of China continues to grow in the past decades, but it is within-region inequality that spurs overall growth in inequality. It also shows despite the increase of inequality both in urban and rural China, the level of income inequality in China as a whole is markedly higher at the national level than it is within urban China or rural China considered alone. Ma et al. (2018) investigated income inequality between rural and urban residents in the reforming era of China based on both urban-rural flow and the accumulated income Gini coefficient. They demonstrated the positive effect of urbanization process on the decline of the Gini coefficient.
In this paper, we focus on the regional inequality of resident income in local China that is the county or district level. The purpose is to investigate the effect of spatial heterogeneity on resident income and its association with regional-specific factors. The conception of resident income is defined as per capita disposable household income, and we believe it is interrelated with the uneven spatial development in China. Although the issue of our study still belongs to the category of regional inequality , the urban-rural gap can also get involved for discussion within the analytical framework due to the different built-up levels of local areas. The study aims to contribute to an enhanced understanding of geographic distribution pattern of resident income levels and its relationship with regional-specific factors in local China. As few studies take the approach like us, it can hopefully enrich the relevant empirical results. In the practice, we will establish an evaluation system based on statistical data at the county and district level in China, and then take Zhejiang Province as an example for testing and analysis.
Theoretical framework
As mentioned previously, there have been numerous literatures reporting the income inequality research in China. As far as regional inequality is concerned, most studies are based on the measurement and analysis of per capita gross domestic product (GDP per capita) and the added value, or so-called per capita national income (He et al., 2019;Huang & Wei, 2019;Li & Fang, 2014). This indicator undoubtedly has broad macroeconomic implications and can indeed reflect some essential feature of the regional economy, such as total factor productivity (TFP) (He et al., 2017a, b, c). However, it does not fully represent the people's livelihood and income. How to measure the income level of local residents in a reasonable manner and detect such income inequality spatially is the motivation of our research. Another consideration is the geographic scale. The interregional or interprovincial inequality across the country has been extensively examined and summarized as the east-west gap and coastal-inland gap (Hao & Wei, 2010;He et al., 2017a, b, c). But the intra-provincial inequality is still less known in China, and few studies are conducted in such smaller scale. The spatial association or geographic pattern of the income distribution in a fine distance thus deserves further research.
As such, this study adopts a geographic-economy framework to assess the regional inequality of resident income in local China. The geographic aspect focuses on the effect of spatial heterogeneity on the income level of residents. It aims to explore the regional differences of resident income and the potential pattern of the geographic distribution. The economy perspective is dedicated to understanding the spatial interrelations among regional development, economic prosperity and people's livelihood. Most people are engaged in various economic activities in the locality to make life and acquire wealth from the society. So, the regional macroeconomic performance is generally regarded to have the positive relationship with resident income. And it happens through the numerous humaneconomy interaction channels such as wage labour, business operation and financial investment. On the whole, the integrative works attempt to seek a socioeconomic explanation for the geographic distribution pattern of resident income level. The quantitative analysis allows us to compare the contribution of different explanatory factors and find the major ones. At the same time, another purpose of our study is to provide some implications or advice for somewhere struggling in regional poverty or low-income status. We hope that the conclusions of this case can have a wide range of practical significance. As a small-scale empirical study, we pay particular attention to the spatial autocorrelation in the distribution of resident income and the relationship with geographic environment. The research methods, and background information of the study area will be given later.
Data survey and mapping
We use the indicator of per capita disposable household income (DHIN per capita) to measure the income level of residents in local areas of China. It is an important item of household sample surveys conducted by statistical departments across China. The household sample survey conducted with each administrative area as an independent unit has two separate parts of urban and rural. But it has developed into an integrated version which no longer artificially distinguishes resident status in survey. This is a major statistical system reform that China promoted in 2012 in order to adapt to the development of urban-rural integration (Iacob, 2013). Disposable income is a conception different from national income. It refers to the amount of money that that all of the individuals in the household sector have available for spending or saving after income distribution measures (for example, taxes, social contributions and benefits) have taken effect. It comes from the fact-finding surveys and covers the sum of all income sources of the household including wages and salary income, net business income, net property income and net transfer income. So, the Index of DHIN per capita can well reveal the livelihood and average income of local residents.
We make a data mapping of DHIN per capita and geographic area on the ArcGIS platform, in order to analyse the geographic characteristics. The starting point of our thoughts is spatial economic agglomeration, a common phenomenon especially in China (Li & Li, 2018;Liu et al., 2018;Wei et al., 2020a, b), may consequence the spatial disparity of people's livelihood and income. This may be manifested in certain geographic pattern, such as spatial segregation, autocorrelation and clustering. To detect the effect of spatial heterogeneity, we will use Moran's I and Getis-Ord General G statistics for the pattern analysis, and Hot Spot Analysis (Getis-Ord Gi*) for clusters mapping (Getis & Ord, 2010;Mitchel, 2005;Wooldridge, 2006). It will quantitatively assess the spatial dependency of data distribution, and judge the pattern, clustered, random or dispersed, as well as high-low value clusters, based on significance statistics. As far as our study issue is concerned, it will help verify the geographic polarization and clustering of resident income which bonds with some tough problems in current China like unbalanced development, regional disparity and poverty.
Analytical design and modeling
The issue of regional inequality in resident income has long been a concern in China. Existing literatures have extensive explanations in the view of people's livelihoods, regional characteristics, and urban-rural differences, but they are rarely based on an integrated analysis. So, their results vary because different perspectives, methodologies and data sets are employed. Although most evidence proves reasonable, some conclusions are so partial without the covering of explanatory factors as much as possible. Using a data set in the most current of 89 local areas in Zhejiang, one of China's model province, in this paper we try a macro approach to find determinants of the regional inequality in resident income at county or district level, and we seek to explain how geographic heterogeneity has influenced resident livelihood or welfare, mainly manifested in disposable income. As the research samples involve both counties (a little built-up areas) and complete urban districts, the regional differences in the general sense and specific urban-rural divide can be incorporated into a unified empirical framework (Table 1). The theoretical starting point is the basic hypothesis that the vast majority of individuals obtain income from society by participating in various types of economic activities directly or indirectly, which can be roughly divided into production, commodity exchange (sales) and technological creation. The accumulation of existing wealth or assets will bring continuous returns and constitute part of the resident income generally. Besides, regional development and national wealth can cause an unignorable effect on the overall performance of all kinds of economic operations, which is expected to affect resident income as consequence. In this study, we posit disposable household income per capita (DHINpc) as the dependent variable and choose several explanatory variables with various impacts on resident income through major income sources including wage labor, business operation and deposits returns, as well as factors determining the economic performance (e.g., development stage, technology and urban-rural divide).
Dependent variable
1. Disposable household income per capita (DHINpc). This variable is derived from the per capita disposable income of urban and rural households, which has been widely regarded as one of the major indices of people's welfare or livelihood in China. As mentioned earlier, the data comes from the upgraded household sample survey, which no longer deliberately classifies residents as urban or rural. In the study, DHINpc denotes the average per capita income of all households in each county or district. We employ this variable to explore the geographic characteristics of resident income and examine regional determinants of income inequality in China at the county or district level.
Independent variables
2. Per capita regional domestic product (LRDPpc). Resident income often depends on regional economic development and the national income distribution. LRDPpc has been widely employed to examine the economic development of specific areas (He et al., , 2017a, b, c;Li et al., 2020). We postulate a positive relationship between resident income and LRDPpc.
3. Household deposits per capita (LHDPpc). The returns of assets and vested wealth is one of the basic sources and components of resident income. Household savings deposits can continue to bring capital returns, although it may be tiny compared to immovable property appreciation, but it is widespread for most residents. This variable is defined by the balance of savings deposits of rural and urban residents divided by the de facto population in each county or district area.
4. Built-up areas per capita (BUILTpc). It is widely acknowledged that region-specific degree of urbanization or the level of city scale has effects on resident income (Liang & Gao, 2020;Yuan et al., 2020). The urban-rural divide is also regarded as a main type of income inequality in China (Wang et al., 2019a, b;Zhu et al., 2020). BUILTpc denotes the per capita share of built-up area in each county or district. It is designed to characterize the differences of local areas in urban intensity.
5. Industrial production (INDUS). As a basic economic activity, industrial production is closely related to the supply of jobs, fiscal taxation and the creation of wealth for the entire society. In the developing world, the larger the scale of manufacturing industry, the larger is the working opportunity and employment, which can benefit the overall livelihoods of people. So, the output value of industrial enterprises of each county or district is expected to be positively associated with resident income. The industrial enterprises whose annual revenue of 20 million RMB or more from their main operations are regarded above designated size in statistic b The sum of retail sales of consumer goods sold by wholesale and retail, cate-ring and lodging to residents, social groups or institutions is total retail sale of consumer goods 6. Commerce prosperity (COMME). In addition to participating in production or processing, a considerable number of local residents are engaged in various business activities and operations. The profits generated in commodity transactions are the main source of income for business participators. So, commerce prosperity of each area is an important factor of people's livelihood and the variable is expected to have a high relationship with resident income. 7. Technological capacity (TECHN). Strong technological capacity in a region can markedly spur indigenous innovation, increase productivity and the general economic returns. The higher the degree of technological capacity, the higher is the profitability of social production. The scale of innovative activities implies the number of research & development staffs engaged in technological creation. The high yield of regional innovations means that there are many hightech companies, organizations or communities in the area. This may be a foreseeable cause of regional inequality in resident income.
Since the purpose is to seek an explanation of geographic differences in resident income, crosssectional data analysis will be applied in the study to verify the hypothesis proposed earlier. The authenticity and explanatory power of the data are the basis of proofs in empirical research. Therefore, we use the original data without any mathematical transformation for the analysis. Taking account into the lag of economic effects, we use the 2018 data of explanatory variables and 2019 data of the dependent variable. We employ multicollinearity, autocorrelation, and heteroscedasticity tests to validate statistical assumptions of our regression models. And a general pooled regression model is specified as follows: where subscript i refers to individual county or district, a is the intercept, b i is the regression estimator, and e i is the error term.
Study area
Our empirical work starts in the Zhejiang Province. It is not only because of the economic leading status but also the distinctive intra-provincial inequality in Zhejiang. As shown in Fig. 1, Zhejiang is situated on the southeast coast of China with Hangzhou as the provincial capital. Although it is one of the smallest provincial administrative zones in China, Zhejiang is one of the most densely populated and wealthy areas as well. Zhejiang has the fourth largest economy in China, and is one of China's major export bases, accounting for around 13 percent of China's total exports (National Bureau of Statistics of China 2019). It was a pioneer in China's reform and opening-up, and carried out market-oriented reform more than 40 years ago, one of the first provinces in China to do so. Over the years, its private economy has achieved leapfrog growth in scale and strength, nurturing a great number of successful enterprises, and makes Zhejiang famous for mercantile culture in China. The region is noted for hills and waters, and the terrain slopes from southwest to northeast. The terrain is dominated by hills and mountains, accounting for 70.4% of the province's total area. Plains only account for 23.2%, and most of them are concentrated in the northeast and coastal areas (Fig. 2). Due to the great terrain differences, the economic and social development of various parts of Zhejiang Province presents distinct regional inequalities. Under the interplay of the first and second nature causes, the northern plain area has been the economic and cultural centre of Zhejiang for hundreds of years, with densely distributed cities, population and strong industries, while the southern mountainous or hill areas are far less developed.
Geographic polarization and clustering of resident income
We used the Moran's I and Getis-Ord General G statistics to evaluate the spatial distribution pattern of resident income in various areas of Zhejiang. The Moran's I statistic measures spatial autocorrelation based on both feature locations and feature values simultaneously. It calculates the Moran's I Index value and both a z-score and p-value to evaluate the significance of that Index. The General G statistic measures the concentration of high or low values for a given study area. It is a most appropriate tool when looking for unexpected spatial spikes of high values. The results of our calculation (Table 2) show that for both indices, the p-value is statistically significant and the z-score is positive. It means the null hypothesis of complete spatial randomness can be rejected. The implication of Moran's I tells us that spatial distribution of high values and/or low values in the dataset is more spatially clustered than would be expected if underlying spatial processes were truly random. The statistic of General G further proves the spatial clustering of high values. The observed value of General G statistic is very little and approaching zero. That is because both the high and low values cluster tend to cancel each other out in the calculation. In another words, there exists both high and low-value clusters, but the degree or significance of high cluster is a little larger than that the low cluster. Then, the Hot Spot Analysis (Getis-Ord Gi*) was used to calculate the Getis-Ord local statistic (z-score) for each feature in the dataset. This tool works by looking at each feature within the context of neighbouring features. And the results of z-scores and p-values can tell us where features with either high or low values cluster spatially. Although some general features of the spatial distribution of resident income have shown in the data plotting (Fig. 3), whether they are statistically significant remains to be tested. So, we used the Hot Spot Analysis to make such local autocorrelation test. The analysis result was displayed on the input map (Fig. 4). The hot spot (remarked red), with statistical significance, means a feature has a high value and be surrounded by other features with high values as well, which forms the high-value cluster spatially. The implication of cold spot (remarked blue) is just the converse version. The output results of our statistical calculation clearly show that the resident income levels within the study area show significant spatial divide and polarization. And there presents the Fig. 1 The location and intra-provincial divisions of Zhejiang diametrically opposite clusters, that is, the high-value cluster in the northeast and the low-value cluster in the southwest. The regional and environmental differences can provide a general explanation for such geographic gap in initial, that the northern part of Zhejiang is mostly plains with a large population and dense cities, while the southwest is mostly mountainous, with inconvenient transportation, sparse population and backward economy. These facts were widely mentioned by Ye (2004, 2005), Dai andZhang (2011), andYue et al. (2014).
Regional determinants of the income levels
In order to seek a regional-specific explanation for the resident income inequality, we applied the analytical The spatial statistics are carried out in the WGS84 51 N projection coordinate system. The fixed distance band or threshold is set to 100 kms model designed previously and the Ordinary least squares (OLS) method was used to perform the regression calculations. OLS is the best known of all regression techniques. It provides a global model of the variable or process we are trying to understand or predict. Prior to the data analysis, all possible violations of statistical assumptions were checked. And no heteroscedasticity and multicollinearity were detected. Table 3 summarizes the regression results generated after conducting the OLS estimation. Generally, results of the OLS diagnostics were satisfactory and show that the regression model is acceptable. The no significance of Koenker (BP) Statistic rejected the inconsistency hypothesis (either due to non-stationarity or heteroskedasticity) of the relationship modeled by us. To test for the overall model significance, Joint F-Statistic was examined and it proves the nearly 100% significance of the analytical model we built. The Jarque-Bera Statistic has no statistically significance. It rejected the statistical assumption that model predictions are biased (the residuals are not normally distributed). The adjusted R 2 value is 0.816, indicating that the explanatory variables in the model explain most of values in the dependent variable. The Variance Inflation Factor (VIF) are all below the threshold (7.5) as consulted. It implies there is no notable issue of collinearity among all explanatory variables. Based on the regression coefficients, it can be found that the effect of most of the explanatory variables on resident income remains significant, except that the industrial production (INDUS). Builtup areas per capita (BUILTpc) and Commerce prosperity (COMME) have strong positive correlation with resident income levels of local areas particularly, which should be the major reason for the regional inequality of resident income. Besides, the correlation of technological capacity (TECHN) and the income level is much stronger than that of per capita regional domestic product (LRDPpc) and household deposits per capita (LHDPpc). This means the technology power and innovation can produce apparent impacts on resident income, which cannot be underestimated.
Implications of the regression results
Our statistical results regarding determinants of regional inequality in the resident income (Table 3) are analyzed more here. Based on both the strength and significance of the coefficient, commerce (scale or prosperity) is the most fundamental factor that determines the income level of local residents. Industrial production remains a positive correlation with resident income, but it fails to get the statistical significance compared with other variables. This finding concurs with those produced by Lardy (2016), who mentioned that the economic development in contemporary China is going towards a consumption-driven growth path. And this causes the commerce expansion and the rise in service industries. In the field survey of Zhejiang, we also found that quite a large number of local residents make life by wholesale and retail trades, catering and lodging services, which occupies a big share of regional employment. Although industrial production or manufacturing still contributes a lot to the national and regional economy, the almost unlimited supply of labor makes workers' wages very low, or namely cheap labor, as described by Lewis's twosector theory (Lewis, 1954). Also, there is a specific phenomenon of migrant workers in East China, as mentioned in many literatures (Gu et al., 2020;Yang et al., 2020), that many industrial enterprises depend much on the massive cheap labor from the middle and west of China, but few of them get registration in the local resident status. These should be the reasons why the assumption that industrial production affects the income level of local residents through employment and labor wage cannot be true. The observed effect of BUILTpc on HDINpc is the second highest among that the explanatory variables, and it is more than 90% significant. It confirms our hypothesis that the geographic difference in urban intensity has an impact on resident income. The coefficient of TECHN is much smaller than that the COMME and BUILTpc, but it still has a certain strength with more than 95% significance. This confirms the positive contribution of technological capability to resident income levels of local areas, and implies technological innovation can not only drive regional economic growth but bring additional economic benefits to the people's livelihood. Besides, although the significant correlation with HDINpc, the coefficient of LRDPpc and LHDPpc are incredibly tiny and even not in the same order of magnitude compared with that the other variables. It means the impact of the regional disparity in general (wealth or development) on the disposable income of local residents is very limited. This may be a consequence of the still strong public sector in Chinese regional economy. In the case, the resident disposable income is often out of sync with or lagging behind the regional development and economic growth, as the government, state-owned enterprises and relevant organizations have a large share in the social wealth allocation.
Conclusions
This study supplements research findings on resident income inequality in China with the geographic pattern detection and econometric analysis of the local areas in Zhejiang. Our own findings may deepen the knowledge, and help scholars or policymakers come to understand the regional inequality in resident income and its determinants at the county or district level of China. The geographic characteristics of the income distribution in the study area have been revealed as well, that the significant spatial polarization and clusters. It means the great regional gap of resident income in local areas. The disposable income of local residents is mainly influenced by the regional commerce prosperity, urban intensity and technological capacity. But industrial production does not have a significant correlation with the income levels, as supposed. Other factors such as LRDPpc and LHDPpc are less important. This is consistent with the employment status of the grassroots in China. That quite a large part of local residents make life and acquire wealth by diverse commercial activities like trades, services or business operations.
Concomitantly, our empirical results may offer some hints for narrowing income gap, pushing regional convergence, and achieving common wealth. First, in order to effectively increase the resident income in poverty-stricken areas, the focus on accelerating up industrial development is not sufficient for the government in the current situation, and how to better the business environment and facilitate the growth of regional commerce should get more attention. Some advanced communication technologies or methods are useful to spread the commercial propaganda (e.g., tourism, investment and exhibition) and enlarge trade channels of local firms. This has been proved by many recent literatures (Couture et al., 2021;Muktar et al., 2018;Wei et al., 2020a, b) that the positive role of ICTs and E-commerce in local business and people's livelihoods. Second, Urban construction still deserves attention for local states, especially in rural or less-developed areas. The increase in the built-up density based on population size can contribute to the agglomeration of economic factors or resources, and produce positive effects on resident income. Third, for metropolitan and developed areas, technological innovation should be the focus of them in pursuit of higher income. Meanwhile, extra effort can be made to push the regional cooperation system of innovative activities. This can promote the spatial spillover of technological capabilities, drive the leapfrog development of backward areas, and narrow the widening trend of income gap hopefully. Last but not the least, for most developing countries or regions, although industrialization is a necessary process, the government should still strive for economic diversification, and indigenous innovation in particular, rather than over-reliance on manufacturing, especially low-tech processing industry. This can prevent falling into the low-income or poverty traps and benefit the long-term well-being of the people.
Funding Not applicable
Availability of data and material The data involved in this article comes from the statistical yearbooks of local authorities, and the author can provide them if requested.
Declarations
Conflicts of interest The author declare that they have no conflicts of interest.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | 7,439.6 | 2021-06-20T00:00:00.000 | [
"Economics"
] |
Controlling the Sign Problem in Finite Density Quantum Field Theory
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the"telegraphic"approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign problem regime.
Introduction
The sign problem is known to be one the most important challenges of modern physics. In theoretical particle physics, it prevents us from simulating finite-density QCD with standard Monte-Carlo methods. Hence most of the QCD phase diagram cannot be explored by firstprinciple techniques, such as lattice QCD. Many reviews can be found, see for example [1,2,3,4,5,6,7,8,9].
Dropping the phase factor of the quark determinant exp{iφ} from the functional integral results in a theory, say with partition function Z P Q , that is accessible a e-mail<EMAIL_ADDRESS>b e-mail<EMAIL_ADDRESS>by standard importance sampling Monte-Carlo simulations. Very early on, it became clear that Z P Q and the partition function of the full theory Z are only comparable for the smallest values of the chemical potential µ [10]. The deviation is quantified by the so-called phase factor expectation value where ∆f is the free energy difference between the full and the phase quenched theory and V is the volume (see e.g. [10]). The knowledge of this phase factor would give access to the partition function Z(µ) (we assume that Z P Q (µ) has been obtained by standard methods). In this work, we study its expectation value, e iφ P Q : it is a very small number, generically very hard to measure due to the statistical noise, which only decreases proportionally to the square root of the number of Monte-Carlo configurations. Our approach is based on the density-of-states method and in particular on the LLR formulation [11,12], which is ideally suited to calculate probability distributions of observables: it features an exponential error suppression [12] which can result in an unprecedented precision for the observable (see e.g. for an early example [13]). It is based upon a non-Markovian Random Walk, which immediately provides two main advantages: it bears the potential to overcome the critical slowing down for theories close to a first order phase transition [14,9], and it is not restricted to theories with a positive probabilistic weight for Monte-Carlo configurations. In fact, the method has been successfully applied to the Z 3 theory at finite densities [15] and QCD at finite densities of heavy quarks [16]. In both cases, the probability density ρ(φ) of the phase φ has been obtained to very high precision. The phase factor expectation value is then arXiv:1703.04649v1 [hep-lat] 14 Mar 2017 given by e iφ P Q = dφ ρ(φ) exp{iφ} dφ ρ(φ) . (2) Despite of high quality numerical result for ρ(φ), the challenge remains to extract a very small signal from the above Fourier transform. An approach, put forward in [15,16], is to first represent the numerical data for ln ρ(φ) by a fit function and then to calculate the Fourier transform of the fit function (semi-)analytically.
The method produces reliable results if all the numerical data are well represented by the fit function with a small number of fit parameters [15,16]. With the advent of high precision data for ρ(φ), the main obstacle for gaining access to quantum field theories at finite densities is the above Fourier transform. The method used in [15,16] hinges on the fact that a fit function which faithfully represents the data could be found. This might not be generically the case.
In this paper, we propose three alternatives to this direct method. In Section 3 we present the first approach, called Gaussian approximation. No fitting procedure is required, instead the phase factor is computed directly from the data. Within this framework, the integral in the numerator of (2) is known analytically. The second approximation, presented in Section 4 is what we call the "telegraphic" approximation. This approach can be implemented either on the fit function or directly on the data (although it might require new simulations). The integral is replaced by a simple difference. In Section 5, we introduce a third method, the "Advanced Moment expansion", which can be seen as a variant of a cumulant expansion [17,18,19,20]. It is a systematic expansion in the deviation from the uniform distribution and as such is expected to work better in the strong sign-problem regime. We will provide evidence that the universal coefficients decrease exponentially with increasing order, providing a rapid convergence if the moments are bounded. Although the convergence is faster in the strong sign-problem regime, for the phase factor expectation value we find an excellent agreement already at the third order of the expansion, regardless of the strength of the sign problem. In this case we still rely on a fitting procedure for the density of states. However the direct computation of the Fourier transform (2) is not needed, only the elementary moments are required. Before going through the details of these methods, we present the framework and the numerical details of our simulations in the next section. Our conclusions are presented in 6 2 Generalities and Framework
Full theory and phase quenching
We consider a generic theory with a partition function and with a complex "matter" determinant: With the help of the density of states the partition function can then be recovered by a 1dimensional Fourier transform: We also introduce the so-called phase quenched counter part by = ds ρ(s) .
The expectation values of an observable A in the full and in the phase quenched theory are given as usual by implying the well-known relations In terms of the density, the phase factor expectation value is given by (2).
Extensive density of states
For theories for which the imaginary part arises from a local action an extensive phase x ∈] − ∞, ∞[ can be defined as the sum of the local phases. This has been e.g. the case for the finite density Z 3 and for heavy dense QCD [15,16]. For fermionic theories with the phase φ[U ] arising from the (non-local) quark determinant, an extensive phase can still be defined as pointed out in [21]: The definition of an extensive phase factor has proven to be important to achieve the precision needed for the Fourier transform. If ρ E (x) denotes the corresponding probability distribution, the phase factor expectation value in (2) is obtained by The density of states ρ(s) can be easily recovered from the extended density ρ E (x). To see this, we subtract from x a multiple of 2π until s ∈ [−π, π[, s = x − 2π n, n ∈ Z, and split the integration domain in intervals of size 2π: and identify: Also note that
Volume dependence of the density
We here consider the class of theories for which the phase of the Gibbs factor is proportional to the chemical potential µ and for which this is the only µ dependence. Scalar theories do not fall into this class since the real part of the action also acquires a µ dependence, but fermion theories in the ab initio continuum formulation might fall into this class. For these theories, let us study the dependence of ρ E (s) on the physical volume V . We make explicit the µ dependence of the phase factor expectation value and point out that the partition function is positive for all µ: Note that we have z(0) = 1 and that we will assume that Note that since z(µ) is obtained by a Fourier transform of ρ, see (2), the density of states can be recovered from z(µ) by the inverse Fourier transform (up to a normalisation constant Z P Q ≥ 0) As argued in [21], z(µ) can be viewed as a partition function with free energy density f (µ) (a necessary condition is that z(µ) ≥ 0), leaving us with the volume dependence: where the coefficients c k are volume independent. Inserting (20) into (18), we find with an expansion in inverse powers of V : If we define a "scaling" variable by x = s/ √ V , the deviation from a Gaussian distribution decreases with increasing volume:
Numerical details
We use the data obtained in our previous work [16] but have also generated new simulations for reasons that we explain below. We summarise here the parameters used for the numerical simulations and the methods to obtain the density of states. The interested reader will find more details in the aforementioned reference. The lattice parameters are 8 4 lattice, β = 5.8, κ = 0.12 .
and we let the chemical potential µ vary between 1.0421 and 1.4321. We identified the "strong sign problem region" as being 1.1 < µ < 1.4. We for each value of µ, we split the domain of the phase s ∈ [0, s max ] in n int small interval of size δ s and on each interval k, we compute the LLR coefficients a k . In practise we choose s max ∼ 36, δ s = 0.896 and n int = 40, except for a few values of the chemical potential, for which we need a better resolution. The corresponding values are reported in Table 1. We reconstruct the probability density function for discrete values of the phase In [16] we performed a polynomial fit of ln(ρ E ) and computed (13) by a semi-analytic integration (we refer to this method as "Exact").
Although the fits are of very good quality and very stable, for three values of the chemical potential, we have also ran new simulations with δ s = π/5. As shown below, these new data allow us to compute ρ(s) directly from the data (without relying on any fitting procedure) and will be very useful to check the methods presented here. We have implemented this technique for three different values of the chemical potential. This is illustrated in Figures 1,2 and 3, where we see that the different methods give compatible results.
Finally, we mention that we use around 1000 configurations and that the statistical errors are estimated with the bootstrap method, using 500 samples. Naturally we have checked that the errors are stable with respect to the number of samples.
The Gaussian approximation
The smallness of e iφ P Q arises from large cancellations in (2). It was pointed out be Ejiri [17] that these cancellations can be avoided by using cumulants of the phase factor: In fact, numerical results suggest that the probability distribution is Gaussian to a good extent [17,22,23,24], which would imply that only the cumulant φ 2 c is nonvanishing. It has been argued in [21] that higher cumulants are suppressed by factors of the volume V and The density obtained directly from the data or from fitting the extensive density ρ E , in the low density-region where the sign problem is weak. that, however, higher order cumulants are important for the medium and high range of chemical potentials. Throughout this paper, we define the Gaussian approximation as the approximation of the extended density of states by a normal distribution: The phase factor expectation value (2) is then analytically obtained: We extract the parameter from the standard expectation value by where the subscript E indicates that the expectation values are defined with respect to the extended density ρ E . We test this approach for heavy-dense QCD with partition function (7). We find the expectation value in (27) directly from the data: we take the density obtained through (23) and compute the expectation value s 2 E using a trapezoidal approximation. We obtain in this way an estimate for the phase factor expectation value (26) without invoking any fitting procedure. Our numerical findings are summarised in Figure 4. We find that the Gaussian approximation provides a surprisingly good approximation over the whole range of chemical potentials µ. Even in the strong sign-problem regime at intermediate values µ, the cancellations are well emulated and the approximate result only underestimates the true result by roughly a factor 2.
Methodology
As can be seen in Figure 3, ρ weakly depends on its arguments in the strong sign-problem regime and for large volumes. In this case, a Poisson re-summation of (15) should yield a rapidly converging series: The sum over ν in (28) becomes: Note that we find in view of (13) If the sum over ν is rapidly converging, we find approximately: In the strong sign-problem regime, the amplitude of the cosine is very small, and therefore we see that ρ(s) is almost a constant. Equation (33) then offers the possibility to extract the phase factor expectation value, i.e., Using (15), we therefore find: We call this the telegraphic approximation. It emerges by neglecting higher contributions c ν of the Poisson sum. In order to get a feeling for the resulting systematic error, we adopt, for now only, the Gaussian approximation (25) and find: This implies that the correction to ρ(s) in (33) is of order: where we have used (26) and (32). At least in the strong sign-problem regime, for which e iφ P Q is very small, we expect the telegraphic approximation to work very well.
We finally point out that the telegraphic approximation can be improved in a systematic way. The order of the approximation is defined by the number of harmonics entering the density of states. E.g., in 3rd order we have: with the unknowns e iφ P Q and c, d. We generate three equations by evaluating ρ(s) at s = 0, π/3, π and solve the linear set of equations for the unknowns. We are predominantly interested in the phase factor: which can be easily converted to a discrete sum over discrete set of points of ρ E (s) using (15) .
Numerical implementation
Again, we use Heavy-Dense QCD to test this approximation. Having in hands the density of state -either ρ E obtained from the fit or ρ from the date through (15) -it is straightforward to implement numerically (35). If we take the results from the fit, we find that this approximation provide results extremely close to the "exact" ones: except for a few values of µ in the weak sign problem regime, the results (central value and variance) are actually indistinguishable. For example, for µ = 1.0821, we find ln e iφ exact P Q = −1.992175 ± 2.910279 × 10 −3 , We show our results for the various µ in Table 2 and Figure 5. We have also implemented this approximation for our new simulations where δ s = π/5, such that we can compute ρ(s) directly from the data (without relying on any fitting procedure). In that case we have ρ(s) for s = π/10, 3π/10, . . ., but do not have ρ(0) nor ρ(π). Therefore we use a variant of (34): In that case we find Using the same data, the "exact" results obtained through the fit yield Although in the strong sign-problem regime µ = 1.2921, we could not extract a signal only from the data, for the two other values of µ we find a decent agreement.
5 The advanced moments approach
General formulation
The starting point is the expansion of the density-ofstates: The coefficients d j depend on the underlying theory, and N 0 ≥ 2 will define the order of the expansion. Our conjecture is that the coefficients d j are suppressed by powers of the volume with increasing j. For QCD, this conjecture is supported by the strong coupling expansion and the hadron resonance gas model [21]. There is also some numerical evidence by the WHOT-QCD collaboration [22,23,24]. Last but not least, this conjecture becomes true for the limited class of theories considered in subsection 1.2. Using (47) in (14), we can express the phase factor expectation in terms of the theory-dependent coefficients d j : where d 0 has dropped out upon integration, and where The values I 2k can be efficiently calculated by the recursion with the initial condition I 0 = 0. Our strategy to access the coefficients d j in an actual numerical simulation is to calculate combinations as the simple moments s 2n . Using the truncation (47) for a given N 0 , we find: Keeping in mind that we have s 2n+2 available from a numerical simulation, the idea is to choose a set of n-values and to consider (51) as a linear set of equations to obtain the unknowns d j . Note that for n = −1, s 2n+2 = 1 = 0 follows from the symmetry ρ(−s) = ρ(s) and does not contain theory specific information. We hence choose n = 0, . . . , N 0 − 1 and obtain Inserting this into (48), we obtain: We now have at our fingertips the moment expansion of the phase factor for a given order N 0 . We have not yet achieved a systematic expansion, featuring increments of decreasing size (when we increase the order N 0 ). To this aim, we define the first advanced moment M 4 for N 0 = 2 by such that, at leading order: We then define recursively for N = 2, . . . , (N 0 − 1): and finally achieve the systematic expansion: We stress that the coefficients α 2n+2 are universal, i.e., the only dependence on the theory under investigations enters via the moments M k . Last but not least, we would like to have an explicit representation of the advanced moments M in terms of the simple expectations values s n . We define: By construction of the advance moments, we have the normalisation γ kk = 1. Although for high order N 1 the intermediate coefficients γ N i can become very large (we will show this below), the field theories of interest, i.e., finite density quantum field theory in the strong sign-problem regime, should give advanced moments within bounds. In this case, the convergence is then left to the coefficients α n . Inserting (62) into (59), we find after a renaming of indices where we have changed the order of the double sum. We therefore find the recursion: where 1 ≤ n ≤ N and 2 ≤ N ≤ N 0 − 1. The recursion can be solved in closed form for i ∈ {2, . . . , N 0 } and j ∈ {1, . . . , N 0 }:
The first advanced moments
For illustration purposes, we will explicitly calculate the first few advanced moments. The main task is to obtain the coefficients k (N ) i , which emerge from the solution of a linear set of equations, see (55)).
For the leading order N 0 = 2, we find Hence, the first advanced moment, see (56), is given by: At next to leading order, i.e., N 0 = 3, we have π 5 5 π 7 7 π 9 9 π 7 7 π 9 9 The solution of the corresponding linear system is given by From (66), we then find for the coefficients γ leaving us with: Up to order N 0 = 3, the phase factor expectation value is given by: We have computed the moment coefficients up to order N 0 = 5. We find for the coefficient matrix (k ≥ 2, i ≥ 1): and for the lead coefficient in front of the advanced moments: We finally perform a consistency check. For a truncation of the density-of-states at order N 0 , all the moments up to M 2N0 contribute to the the phase factor expectation value at this order, see (61). If we consider (47) as exact for the moment in the sense that all simple moments s 2n are calculated with this density, then the phase factor expectation value is obtained exactly by summing all contributions including the term containing M 2N0 . Since this result is already exact, all moments M 2k with k > N 0 must vanish. For example, assume that the density is given by then e.g. M 6 (and all higher moments need to vanish for all choices for d 0 and d 1 . This devises a consistency check. We find for the present example: Inserting these simple moments into M 6 , (76), we find that all terms cancel and that M 6 indeed vanishes for all choices of d 0 and d 1 . If we consider, in a quantum field theory setting, the expansion (47) as an expansion with respect to some inverse power of the volume, the moments M 2n are then suppressed by these powers.
Convergence
For high orders N 0 , the coefficients γ in the definition (62) of the advanced moments M 2k can become very large. In this section, we will assume that for functions ρ(s) arising in a quantum field theory setting the moments remain within bounds. This occurs due to cancellations between simple moments s 2i , as we will show below. In this case, the expansion (61) of the phase factor expectation value in terms of the advanced moments is dictated by behaviour of the coefficients α 2k for large k. These coefficients are universal: they do not depend on the underlying theory, i.e., ρ(s). They arise from the solution of the linear system (55), which reads in a shorthand notation and it is this linear system that we are going to study in greater detail. Since the matrix A in (52) is symmetric and positive, we perform a Cholesky decomposition and solve for k: where L is a lower triangular matrix. Note that if the system Ly = b is solved at order N 0 and if subsequently the order N 0 is increased, the first N 0 components of the solution y are unaffected by the increase due to the triangular form of L. The same is true for the matrix L: increasing the order from N 0 to N 0 + 1 does not affect the first N 0 rows and columns. We are interested in the N 0 dependence of the last component of k: The Cholesky decomposition gives We have solved this iteration analytically for values N 0 up to 30. We find that for large n the data is well described by We find that very quickly L nn reaches an asymptotic regime which is well describe by see Figure 6. Asymptotically, we therefore find the exponential increase: In a next step, we studied the asymptotic behaviour of the solution y of the linear system L y = I. We find numerical evidence (see Figure 7) that y n converges quickly to a constant This suggest that the asymptotic N 0 dependence of the desired expansion coefficient is given by: Unfortunately, we could not prove any of these asymptotic behaviours analytically, but we have verified (85) by also solving the linear system L T k = y for k. Our analytical result for N 0 = 2 to N 0 = 32 is shown in Figure 8. We find the remarkable result that the expansion coefficients α 2N0 are exponentially decreasing with N 0 suggesting a rapid convergence of the Advanced Moment expansion as long as the moments M 2n are bounded.
Application to HDQCD
In essence, the Advanced Moments approach from section 5 is an efficient numerical method to evaluate the Fourier transform (14) for sufficiently smooth integrands ρ(s). In this section, we test the method in the quantum field theory context of QCD at finite densities of heavy quarks (HDQCD). Our preliminary results have been reported in [25].
Here we are interested in the strong sign problem region (in which µ ∼ 1.3): in Figure 3, we show that the density is almost constant whereas for µ ∼ 1 and µ ∼ 1.4, the density has variation of order 1 (see Figures 1 and 2). Hence, we expect that the Advanced Moment expansion will have a better convergence in the strong sign problem regime.
From now on, we focus on the severe sign problem region, µ = 1.2921. Once the density is known, we can compute the elementary moments (again using our fit results and semi-analytic integration). They are reported in Table 3. By virtue of the LLR method, they are extracted with a very good statistical precision. We also observe that going from s 2 to s 8 , the relative error increases very slowly. We turn now to the advanced moments: since all the elementary moments are positive, the relative signs in (88)-(94) imply that important cancellations occur. At leading order (LO), we have = −0. 000 015 9(23) , and at next-to-leading order (NLO) we find: where for next-to-next-to leading order (NNLO), we obtain: = −0. 000 003 5 (5) .
As expected, strong cancellations between the simple moments occur making it mandatory to determine the simple moments with high precision. The analysis has been carried out using the bootstrap resampling method, and we point out that strong correlations are at work to obtain the Advanced Moments at the level of precision reported here. The numerical values are also reported in Table 4. One should note that the overall sign of the advanced moments oscillate, however α i M i is a positive quantity, as can be seen in (61), or in the numerical values.
The phase factor expectation value (61) is then given by e iφ = 10 −6 × 1.45 (21) LO + 0.67(10) NLO + 0.068(10) NNLO When the order of the expansion increases, the statistical error decreases and that the results converges quickly to the "exact" answer obtained by fitting the extensive density ρ E and by carrying out the Fourier transform using the fit, as in [16].
(In the latter we quote 2.37(21) × 10 −6 , the small difference in the central value comes from the fact that we use a different δ s ). We observe a rapid convergence here.
Since the phase factor is a small number, it is useful to look at the logarithm of this quantity. We find log e iφ P Q = −13.032 ± 0.152 (Full) . It is remarkable that not only the central value but also the variance is very well approximated by our expansions. Indeed for this value of µ, the full (relative) variance is already given by the first order. Of course the quality of the approximation depends on the variation of ρ (and therefore on the strength of the sign problem). We now vary the value of µ in the range 1 < µ < 1.4 and compare the results of the phase factor expectation value obtained in [16] with the method proposed here. It is interesting to note that even in the weak sign-problem region, in which the density ρ fluctuates between 0 and 1, the NLO and NNLO approximations already yield decent approximations. This is illustrated in Figures 9 and 10. Our numerical results can be found in Table 5. We quote the "full answer" as obtained in [16] and the relative difference with the method presented here, for the first three orders. (Here we implement the Advanced Moments method with the same δ s as in [16].) The NLO approximation works at the percent level over the full available range, even in the weak-sign problem region. Relative difference between the moment approximation and the full answer. As expected, the approximation works better in the strong sign problem regime
Conclusions
There are two main possibilities in addressing finite density quantum field theory: (i) facing the large cancellations that give rise to the smallness of the partition function or (ii) to reformulate to an equivalent theory say by dualisation [6] or by a complexfication of the fields [5]. Method (ii) would be preferred if the approach exists and if exactness can be guaranteed. The appeal of method (i) is that it is universally applicable if a way is found to control the cancellations. A first success for direction (i) emerged with the advent of Wang-Landau type techniques and, most notably, the LLR method [11]: due to the feature of exponential error suppression of the LLR approach [12], high precision data for the density-of-states ρ(s) of finding a particular phase s over many orders of magnitude has become available. The partition function now emerges as Fourier transform of ρ(s). Due to large cancellations, this Fourier transform is a challenge in its own right. The recent success reported in [15] and in [16] hinge on the ability to find a fit function for ln ρ(s) that well represents hundreds of numerical data points with relatively few fit parameters. This situation is unsatisfactory since the quest for this fit function might not be always successful.
The present paper explores three methods to perform the Fourier transform: • The Gaussian approximation of the extensive densityof-states ρ E is most easily implemented, but hard to improve in a systematic way. For the example of HDQCD, we found this approximation yields the right order of magnitude through out and only misses the exact phase factor by a factor of two when the sign problem is strongest. • The telegraphic approximation yields the phase factor through an alternating (discrete) sum of the extensive density-of-states ρ E . The relative systematic error is of the order of the phase factor itself, which makes the approximation excellent in the strong sign-problem regime. • The advanced moment approach is a systematic expansion of this Fourier transform with respect to the deviations of ρ(s) from uniformity. The expansion therefore works best in the strong-sign problem regime. The expansion is independent of the quantum field theory setting an can be applied to the Fourier transform of any sufficiently smooth function ρ(s), s ∈ [−π, π]. At the heart of expansion are the so-called Advanced Moments. We have thoroughly derived these moments and the theory independent expansion coefficients α. We found evidence that the expansion coefficients decrease exponentially with increasing order, thus guaranteeing rapid convergence if ρ(s) admits moments M that are bounded. We have tested and validated the Advanced Moment expansion in the context of HDQCD: we have confirmed that the expansion converges very quickly. It works best in the strong-sign problem region as expected, although at third order the results agree with the "full" answer at the subpercent level even in the weak sign problem regime. | 7,197.4 | 2017-03-14T00:00:00.000 | [
"Physics"
] |
Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems, piecewise constant policy timestepping reduces the problem to nonlocal semi-linear equations with different control parameters, uncoupled over individual time steps, which we solve by fully implicit monotone approximations to the controlled diffusion and the nonlocal term, and specifically the Lax-Friedrichs scheme for the nonlinearity in the gradient. We establish a comparison principle for the switching system and demonstrate the convergence of the schemes, which subsequently gives a constructive proof for the existence of a solution to the switching system. Numerical experiments are presented for a recursive utility maximization problem to demonstrate the effectiveness of the new schemes.
Introduction
Classical Markovian mixed optimal stopping and control problems, where the target is to maximise the (linear) expectation of a payoff on a finite time horizon T , are defined as u(t, x) = sup τ sup α E t,x τ t e −r(s−t) f (α s , X α,t,x s ) ds + e −r(τ −t) ξ(τ, X α,t,x τ ) , (1.1) Such nonlinear expectations arise naturally in financial mathematics, for instance as models for American options in a market with constrained portfolios [20], from recursive utility optimization problems [7], and for robust pricing and risk measures under probability model uncertainty [26]. It has been demonstrated in [15] that under suitable assumptions the value function u in (1.2) can be characterized by the viscosity solution to a more complicated HJBVI (1.3), which involves an extra nonlinearity resulting from the nonlinear expectation: with x = (t, x), nonlocal operators L α and B α , the driver f of the BSDE, and given functions ζ and g, which we will specify in Section 2. Particularly, in the case where the driver is additive in y and independent of z and k, i.e., f (α, x, y, z, k) ≡ f (α, x) − ry, the generalized control problem (1.2) reduces to the classical linear expectation case (1.1), and (1.3) reduces to an HJB obstacle problem. 1 As it is usually difficult to obtain analytic solutions of HJBVIs, it is necessary to design efficient and robust numerical methods for solving these fully nonlinear PIDEs.
We remark that, to the best of our knowledge, even for the case with linear expectations (i.e. f in the special form from above), there is no published numerical scheme covering the generality of (1.3). However, there is a vast literature on monotone approximations for local HJB equations (see, e.g., [10,2,11] and references therein) and a number of works covering specific extensions. For instance, monotone finite-difference quadrature schemes are proposed in [8,4,5,3] for nonlocal HJB equations. We refer the reader also to [12] for penalty approximations to nonlocal variational inequalities and to [28] for an application of policy iteration together with penalization to solve HJB obstacle problems. Probabilistic methods for solving HJB equations (without jumps and optimal stopping) can be found, for example, in [22].
However, this standard approach cannot be easily extended to nonlinear f which is only assumed to be Lipschitz (and generally is not semi-smooth [24]), which prevents a direct application of Newton-like solvers (see [29] for a special case of the discrete optimization problem with f (α, x, y, z, k) ≡ f (α, x, y) differentiable and concave in y, and A finite).
Moreover, at each step of policy iteration, one needs to identify the global optimal policy for each computational node. The nonlinear driver f and other PDE coefficients may have sufficiently complicate nonlinearities in the control variable such that the only way to construct a convergent algorithm is to discretize the admissible control set, and perform exhaustive search to determine the optimal policy at each node.
Another approach to solve (1.3) uses piecewise constant policy time stepping (PCPT) as in [25]. It is based explicitly on a discrete approximation of the admissible set by a finite set, say with J elements, and then defines a piecewise decoupled system of PDEs corresponding to these J (constant) controls. The information from the different solutions is assembled at the end of each timestep by taking the pointwise maximum.
As a specific scheme for these semi-linear PDEs, we propose an implicit Euler time discretization, monotone (semi-Lagrangian) approximations for local diffusions, a monotone quadraturebased scheme for the nonlocal terms, and the Lax-Friedrichs scheme for the nonlinearity in the gradient. The different solutions may be defined on different discretization grids by possibly high order monotonicity preserving interpolations. This approach not only avoids policy iteration, but also allows for an easier construction of convergent monotone schemes and an efficient parallel implementation of the individual semi-linear PDEs. Note that it is essential to obtain a monotone discretization, since it is well-known that non-monotone schemes may fail to converge or even converge to false "solutions" [11]. By Godunov's Theorem [18], in general, one can expect a monotone scheme to be at most first-order accurate.
The main contributions of our paper are: • We formulate our algorithm by approximating the solution of (1.3) by the solution to a switching system with small switching cost. We shall establish a comparison principle for the switching system and demonstrate that as the switching cost tends to zero, the solution of the switching system converges to the viscosity solution of (1.3), which extends the results in [4] to obstacle problems of switching systems and includes nonlinear drivers.
• We discretize the switching system piecewise in time by fully implicit monotone approximations. The convergence of the scheme is demonstrated, which subsequently gives a constructive proof for the existence of a viscosity solution to the switching system. Our results extend the one obtained in [25] from the case of standard control problems. In contrast to there, PCPT leads to coupled semi-linear PDEs rather than linear PDEs due to the nonlinear expectations. The optimal stopping right is treated as an additional control and included in the switching directly instead of the classical penalisation approach.
• By truncation of the singular jump measure, we obtain a stochastic control and optimal stopping problem whose value function is shown to converge to the value function of the initial problem and which satisfies a HJBVI equation. Our result extends earlier ones obtained only in the case of a linear expectation without control and optimal stopping (see e.g. [8]).
• For practical implementations, we propose a Picard-type iteration for the efficient numerical solution without the need to invert the dense matrices resulting from the nonlocal terms.
• Numerical examples for a recursive utility maximization problem are included to investigate the convergence order of the scheme with respect to different discretization parameters.
The remainder of this paper is organized as follows. In Section 2, we introduce the Markovian mixed optimal stopping and control problem with nonlinear expectations, and characterize its value function as the viscosity solution of a nonlocal HJBVI. We then derive numerical schemes in Section 3 by approximating the HJBVI with a switching system, PCPT, and ultimately fully discrete monotone schemes. Then we move on to the convergence analysis of our numerical schemes in Section 4. Numerical examples for a recursive utility maximization problem are presented in Section 5 to illustrate the effectiveness of our algorithms. In the Appendix, we include a rigorous proof of the comparison principle for the switching system and some complementary results that are used in this article.
Problem formulation and preliminaries
In this section, we formulate the mixed optimal stopping and control problem with nonlinear expectation and introduce the connection between such problems and HJBVIs, which is crucial for the subsequent developments. We start with some useful notation that is needed frequently in the rest of this work.
We write by T > 0 the terminal time, and by (Ω, F, P ) a complete probability space, in which two mutually independent processes, a d-dimensional Brownian motion W and a Poisson random measure N (dt, de) with compensator ν(de)dt, are defined. We assume ν is a σ-finite measure on E := R n \ {0} equipped with its Borel field B(E) and satisfies We denote by E the usual expectation operator with respect to the measure P . For any given t ∈ [0, T ], we define the t-translated Brownian motion W t := (W s − W t ) s≥t and the t-translated Poisson random measure N t := N (]t, s], ·) s≥t . We denote byÑ t (dt, de) = N t (dt, de) − ν(de)dt the compensated process of N t , and by F t = {F t s } s∈[t,T ] be the filtration generated by W t and N t augmented by the P -null sets.
Furthermore, we introduce several spaces: L 2 ν is the space of Borel functions l : We now proceed to introduce the control problem of interest. For each t ∈ [0, T ], let A t t be a set of admissible controls, which are F t -predictable processes (α s ) s∈[t,T ] valued in a compact set A, and T t t be the set of F t -stopping times which take values in [t, T ]. For any given initial state x ∈ R d , and control α ∈ A t t , we consider the controlled jump-diffusion process (X α,t,x s ) t≤s≤T satisfying the following SDE: for each s ∈ [t, T ], where b, η ∈ R d and σ ∈ R d×d are given measurable functions. We remark that although our analyses are performed only for jump-diffusion processes with time-homogenous coefficients, similar results are valid for controlled dynamics with time-dependent coefficients. The performance of the control problem, depending on α, is evaluated by a nonlinear expectation induced by a BSDE with a controlled driver f (α s , s, X α,t,x s , y, z, k). That is, for any given stopping time τ ∈ T t t and any bounded Borel function ξ, we define the nonlinear expectation where the process (Y α,τ,t,x s ) s≤τ is a solution in S 2 t of the following BSDE: for each s ∈ [t, τ ], and (Z α,t,x s,τ ), (K α,t,x s,τ ) are two associated processes, if they exist, lying in H t and H ν t , respectively. Now we are ready to state the generalized mixed optimal stopping and control problem. For each initial time t ∈ [0, T ] and initial state x ∈ R d , we consider the following value function: (2.4) subject to the controlled SDE (2.2), where ξ is the terminal position given by for some reward functions ζ and g. Note that the value function of our control problem is constant up to a P -null set. Throughout this work, we shall perform the analysis under the following standard assumptions on the coefficients: Assumption 1. The set of control values A is compact and the driver f is a measurable function of the form f (α, s, x, y, z, k) :=f (α, s, x, y, z, E k(e)γ(x, e) ν(de))1 s≥t for some functionsf and γ. Moreover, there exists a constant C > 0 such that for any α, is continuous in t and admits the properties: Assumption 1 is the same as that made in [16]. Note that under assumptions (1), (2), equation (2.2) admits a unique solution. Assumptions (3), (4.a), (4.c), (5) quarantee the existence and the uniqueness of the solution of equation (2.3). Consequently, the generalized mixed control problem is well-defined. For notational convenience, in the sequel, we will writef as f , and denote by ψ α a generic function ψ with control-dependence.
The rest of this section is devoted to the equivalence between the mixed control problem and a generalized nonlocal HJBVI. Specifically, we now consider a Hamilton-Jacobi-Bellman variational inequality of the following form: x) contains both the time t and the spatial coordinate x ∈ R d , and the nonlocal operators L α := A α + K α and B α satisfy, for φ ∈ C 1,2 (Q T ): where E = R n \ {0} is defined at the beginning of Section 2 and the nonlocal operators K α u and B α u are well-defined under Assumption 1.
We emphasize that since the matrix σ α (σ α ) T is only assumed to be nonnegative definite, both the diffusion coefficient σ α (σ α ) T and the jump intensity η of (2.5) are allowed to vanish at some points. Consequently, there is no Laplacian smoothing from the second-order differential operator nor fractional Laplacian smoothing from the nonlocal operator to this degenerate equation (2.5). Therefore, in general, this HJBVI will not admit classical solutions, and we shall interpret the equation in the following viscosity sense based on semi-continuous envelopes of the equation [1,25].
Definition 2.1 (Viscosity solution of HJBVI). An upper (resp. lower) semicontinuous function u is said to be a viscosity subsolution (resp. supersolution) of (2.5) if and only if for any point x 0 and for any φ ∈ C 1,2 (Q T ) such that φ(x 0 ) = u(x 0 ) and u − φ attains its global maximum (resp. minimum) at x 0 , one has A continuous function is a viscosity solution of the HJBVI (2.5) if it is both a a viscosity suband supersolution.
Under Assumption 1, the HJBVI (2.5) is well-posed in the class of bounded continuous functions (see [14,15]). The unique viscosity solution of (2.5) (after a change of time variable) can be further characterized as the optimal value function (2.4) of the mixed control problem. In other words, to obtain the optimal value function for all initial times t and initial states x, it is equivalent to design effective numerical schemes to solve (2.5).
Moreover, a strong comparison principle holds for the HJBVI (2.5), the proof of which is similar to that in [14] (without controls) and hence omitted. In particular, if U is a bounded viscosity subsolution and V is a bounded viscosity supersolution to (2.5)
Construction of numerical schemes
In this section, we will design numerical schemes for solving HJBVI (2.5). We carry out the following string of approximations to construct our numerical algorithm: • truncation of the singular jump measure (equation (3.3) and Appendix C); • approximation of the control set with a finite set (equation (3.4) and Theorem 4.2); • approximation of the discretized control problem with a switching system (equation (3.5) and Theorem 4.5); • discretization in time and space (equations (3.7, 3.8) and Theorem 4.6).
We start the derivations of our schemes by approximating the singular measure ν with a truncated non-singular measure and a modified diffusion coefficient as suggested in [8]. This can be done by introducing an approximative jump-diffusion dynamics and an approximative backward SDE (see Appendix C). More precisely, for any given ε > 0, let us define the truncated measure ν ε (de) = 1 |e|>ε ν(de) and the modified diffusion coefficientσ α (x) such thatσ α We further introduce the modified local operator A α ε as: (3.2) and truncated nonlocal operators K α ε and B α ε by replacing ν with ν ε in (2.7) and (2.8), respectively. With these operators in hand, we consider the following modified HJBVI: . These modified coefficients clearly satisfy Assumption 1, and hence (3.3) is well-posed in the viscosity sense. Remark 1. In Appendix C, we provide an alternative interpretation of the above approximation by identifying the viscosity solution of (3.3) as the value function of a mixed control problem in terms of modified SDE and BSDE. This characterization further enables us to establish the convergence of this approximation through a probabilistic argument.
We then approximate the admissible control set in (3.3) by a finite set. More precisely, for a finite subset A δ of the compact set A such that max α∈A miñ α∈A δ |α −α| < δ, we introduce the finite control HJBVI by where we denote for simplicity the nonlinear function f α ε [u] := f α (x, u δ , (σ α ) T Du δ , B α ε u δ ). Since (3.4) is a special case of (2.5) with a finite admissible set, it is clear that (3.4) admits a unique bounded viscosity solution.
Next, we approximate the finite control equation (3.4) by a switching system ( [2,4]). Suppose the finite control set is given by A δ = {α 1 , α 2 , . . . , α J }. We denote by U ε,δ,c j , j = 1, . . . , J the solution of the following system of HJB equations: where we define M j U := max k =j U k − c for any c > 0. The positive switching cost is needed for the well-posedness of the switching system (3.5).
We now proceed to introduce a discrete approximation to the switching system based on the idea of piecewise constant policy timestepping. Define a set of nodes {x j,i } and timesteps t n , with discretization parameters h and ∆t, i.e., By parameterizing the grid Ω j,h = {x j,i } i with the control index j, we are allowing the usage of different discretization grids for different controls. We denote by U n j,i the discrete approximation to U j at the point x n j,i = (t n , x j,i ), and extend it to the computational domain by interpolation. Let L α j ε,h and f α j ε,h be the discrete form of the operators L α j ε and f α j ε , respectively. We discretize (3.5) on the grid Ω j,h with the uniform time partition t n+1 − t n = ∆t by performing piecewise constant policy timestepping and applying the constraints at the beginning of a new timestep, whereŨ n k,i(j) is the value of the interpolant of {U n k,l } l∈Ω k,l at the i-th point of the grid Ω j,h . Now by rearranging the terms of (3.8), we obtain the following numerical scheme: for x n j,i ∈ Q T and j = 1, . . . , J, As seen from (3.9), performing switching at the beginning of a new timestep introduces two additional terms to both the switching part and the obstacle part of the equation, which will not appear in a straightforward discretization of the switching system (3.5). However, we will demonstrate in Section 4.4 that these terms vanish as ∆t, h → 0, and consequently our scheme (3.9) forms a consistent approximation to (3.5).
For notational simplicity, we label our approximations only by h and assume in the sequel that ∆t is a given function of h with ∆t → 0 as h → 0.
Remark 2.
To determine the optimal stopping strategy and the optimal controls, one can simply compare values of the obstacle and all components of the switching system at each grid point. As we will see in Section 4.2, each component of the switching system converges to the solution of the HJBVI (2.5) as the discretization parameters tend to 0; therefore, although we have no guarantee for the convergence of the control approximation, this numerically found control is close to optimal for the mixed control problem (2.4).
We now describe in detail how we perform spatial discretizations for L α ε and B α ε to construct a monotone discrete operator L α ε,h and f α ε,h , for a fixed control parameter α ∈ {α 1 , . . . , α J }. To simplify the presentation, we consider a piecewise linear or multilinear interpolation I h on a uniform spatial grid hZ d . That is, We start with the nonlocal terms. The definition of K α ε gives Then, by replacing the integrands by their monotone interpolants (c.f. [5]), we derive the following approximations for K α,1 ε and B α ε (where we have dropped the mesh index j in x for simplicity): with the coefficients which are well-defined and nonnegative, and consequently result in monotone approximations. These coefficients can be efficiently evaluated by using quadrature rules with positive weights, such as Gauss methods of appropriate order [5].
With these modified coefficients, we are ready to construct the following approximations of the local operators: for any k > 0, which, by using (3.10) and the fact that m ω m = 1, can be further written in the discrete monotone form with non-negative coefficients The approximation to the local operator A α ε falls into the class of semi-Lagrangian schemes (see e.g. [11]), and provides a consistent monotone approximation for possibly degenerate, non-diagonally dominant diffusion coefficients.
Before presenting our fully discrete scheme, we shall point out that by considering a truncated problem, one can without loss of generality assume that σ α is bounded, which consequently implies the Hamiltonianf is Lipschitz continuous with respect to p. Indeed, suppose σ α is unbounded, then for any given µ > 0, we define the cut-off function and consider a truncated HJBVI (3.4) by replacing σ α with the bounded diffusion coefficient . Using the fact that 1 − ξ µ → 0 uniformly on compact sets as µ → 0, one can easily prove this additional approximation is consistent with (3.4), and hence its viscosity solution converges to the solution to (3.4) uniformly on bounded sets.
The Lipschitz continuous Hamiltonian enables an approximation by the implicit Lax-Friedrichs numerical flux [10]. For each l = 1, . . . , d, we denote by ∆ (l) − U n j,i ) the one-step forward (resp. backward) difference operator along the l-th coordinate, and by ∆U n j,i = (∆ − U n j,i ) T the central difference operator at the grid point x n j,i . Then for any θ > 0, the Lax-Friedrichs numerical flux is given for any ( where we define λ = ∆t/h. A fully implicit time discretisation is finally given by Substituting (3.7) into (3.17), one can reformulate this implicit scheme in its equivalent form (3.9). We end this section with a remark about the implementation of the implicit scheme (3.17). To avoid solving linear systems with the dense matrices resulting from the discretization of the nonlocal operators, we write the solution to (3.17) as the fixed point of a sparse contraction mapping T , such that sufficient accuracy is achieved in practice by a few fixed point iterations.
Given bounded functions U n− 1 2 j and U n,(k) j , we define the following mapping T on ℓ ∞ (Z d ), i.e., the Banach space of bounded functions on hZ d employed with the sup-norm | · | 0 : It is clear that a fixed point U n j with T U n j = U n j is a solution to (3.17). Moreover, for any given functions U n,(k) j and V n,(k) j in ℓ ∞ (Z d ), we obtain from the Lipschitz continuity of f and the ℓ ∞ stability of the numerical fluxf (see Lemma 4.10) that Since we need h = o(ε) in general to achieve consistency of our scheme (see Lemma 4.8), it suffices to require ∆t ε 2 < 1 and 4dθ < 1 to ensure T is a contraction mapping on ℓ ∞ (Z d ). This establishes the well-posedness of (3.17) and enables us to solve the nonlinear equation (3.17) through Picard iterations by setting We emphasize that the criterion ∆t ε 2 < 1 is a sufficient condition in the worst case, but is often far from computationally optimal since we have used no information about the exact behavior of the singular measure ν around zero (see Remark 4 for details). For typical Lévy measures from finance [8], we only need ∆t = O(ε) (such as in the variance gamma case in our tests) or even ∆t independent of ε (for instance, for a Gaussian density) to guarantee T is a contraction mapping.
Moreover, since in practice we can evaluate the discrete nonlocal operators K α,1 ε,h U n j and B α ε,h U n j at all grid points in O(N log N ) operations using a FFT (see e.g. [12]), and in each iteration a sparse linear system is solved (in one dimension it is tridiagonal), the total complexity of the implicit scheme is still close to linear. It is also worth pointing out that even if we chose explicit approximations for the nonlocal operators, due to the nonlinearity of f , one still has to perform iterations to solve the resulting nonlinear equations. Because we only assume Lipschitz continuity but no higher regularity of f , we adopt the Picard iteration to solve for U n .
Convergence analysis
In this section, we establish the convergence of the numerical approximations in Section 3 to the viscosity solution of the HJBVI (2.5).
We start by outlining the convergence analysis of the truncation of singular measures. It is not difficult to see that (3.3) is a consistent approximation of (2.5) in the viscosity sense, such that the comparison principle of (2.5) enables us to conclude that the solution of (3.3) converges to that of (2.5) on compact sets as ε → 0. In Appendix C, we provide an alternative proof by identifying the viscosity solution of (3.3) as the value function of a modified control problem, and establish its convergence to the original value function (2.4) using a probabilistic argument.
The remainder of this section thus focuses on the convergence analysis for the control discretization, the approximation of HJBVIs with switching systems, and the discrete approximations of the switching systems.
To simplify the notation, we will occasionally drop the terms {K α u} α∈A and {B α u} α∈A in (3.3), (3.4) and (3.5), and simply denote hem by F (x, u, Du, D 2 u) = 0 in the sequel.
Approximation by finite control sets
In this section, we shall study approximations of HJBVI (2.5) with a finite control set. The following consistency result will be essential for our convergence analysis. The proof is similar to [25] (who consider the case without nonlocal term, obstacle, and nonlinear driver) and included in Appendix A for the convenience of the reader.
Now we are ready to conclude the convergence of our approximation with finite control sets.
The proof is a straightforward extension of the arguments in [25] and is hence omitted.
Approximation by switching systems
In this section, we study the approximation of (3.4) by switching systems. We adopt the following standard definition of a viscosity solution to switching systems of the form (3.5) (see [1,4,25] and references therein). Definition 4.3 (Viscosity solution of switching system). A R J -valued upper (resp. lower) semicontinuous function U is said to be a viscosity subsolution (resp. supersolution) of (3.5) if and only if for any point x 0 and for any φ ∈ C 1,2 (Q T ) such that U j − φ attains its global maximum (resp. minimum) at x 0 , one has A continuous function is a viscosity solution of the HJBVI (3.5) if it is both a a viscosity suband supersolution.
Note that in the definition of the viscosity solution of F j , the test function only replaces U j in the integrals and derivatives, while leaving the terms {U k } k =j unchanged. Now we present the comparison principle for bounded semicontinuous viscosity solutions of (3.5), which not only implies the uniqueness of bounded viscosity solutions of (3.5), but is also essential for our convergence analysis. The proof will be given in Appendix B. The following theorem demonstrates the convergence of the switching system to the finite control HJBVI (3.4) as the switching cost goes to 0. Convergence with order 1/3 is proved in [4] by a different technique, for nonlocal Bellman equations without obstacles and nonlinear source terms.
We momentarily assume the switching system (3.5) to admit a viscosity solution bounded independently of the (small enough) switching cost c. We give a constructive proof of existence through our numerical schemes in Section 4.3. ) and u ε,δ be the viscosity solution of (3.5) and (3.4), respectively. Then for fixed ε, δ > 0, we have for each j = 1, . . . , J that U ε,δ,c j → u ε,δ uniformly on compact sets as c → 0.
Proof. Since ε and δ are fixed for our analysis, we shall omit the dependence on ε and δ, and simply denote by U c the solution of (3.5). Consider a sequence of switching costs c m → 0 as m → ∞, and the corresponding viscosity solution U cm = (U cm 1 , . . . , U cm J ). We shall first prove by contradiction that U cm j (x) ≥ M j U cm , x ∈ Q T , j = 1, . . . , J.
Suppose the statement is false, then there would exist k = j and x 0 ∈ Q T such that U cm j (x 0 ) < U cm k (x 0 ) − c m . We then obtain from the continuity of U cm j and U cm k that there exists a nonempty open ball B around x 0 such that On the other hand, there exists a C 2 function φ such that U cm j − φ attains its minimum at some point in B, say x 1 . Hence we deduce from the fact that U cm j is a supersolution that which leads to a contradiction. We now introduce the following functions through a relaxed limit: for j = 1, . . . , J, Letting r → ∞ leads to the fact that U j ≥ U k for all j = k. The statement for {U j } can be shown similarly.
Since it is clear that U and U is bounded upper and lower semicontinuous, respectively, we now aim to show U and U is respectively a sub-and supersolution of (3.4). Then the strong comparision principle gives us U ≤ U , which implies U = U = U is the unique viscosity solution of (3.4). Uniform convergence on compact sets follows from a variation of Dini's theorem (See Remark 6.4 in [9]).
We start by showing U is a subsolution of (3.4). Let φ ∈ C 1,2 and U − φ have a strict global maximum atx 0 ∈Q T , then there will be a sequence c m → 0 such that for each j ∈ {1, . . . , J}, we havex j m →x 0 , U cm j (x j m ) → U (x 0 ), and U cm j − φ attains a global maximum atx j m . Since U cm j is a subsolution of (3.5) with c m , if we havex 0 ∈ {0} × R d , U cm j (x j m ) ≤ g(x j m ) for infinitly many m and a fixed j, then it is clear that U (x 0 ) ≤ g(x 0 ). Therefore, without loss of generality, we assume for all m and j that We have two cases. If there exists j ∈ {1, . . . , J} and a subsequence of c m such that U cm j (x j m )− ζ(x j m ) ≤ 0, then by passing to the limit m → ∞, we have U (x 0 ) − ζ(x 0 ) ≤ 0. Otherwise, by passing to subsequence, without loss of generality we can assume U cm j (x j m ) − ζ(x j m ) > 0 holds for all j and m. Then for each m ∈ N, we can choose j m ∈ {1, . . . , J} andx jm m such that and deduce from (4.4) that Our choice of j m implies (U cm jm −φ)(x jm m ) ≥ (U cm k −φ)(x jm m ) for all k = j m , and thus U cm jm (x jm m ) > M jm U cm (x jm m ). Consequently we obtain from (4.5) that Since we only have finite many choices of j m , by passing to a further subsequence if necessary, we can assume that j m → j 0 , then letting m → ∞ and using the continuity of the equation, we have Since α j 0 ∈ A δ is an admissible control, we obtain and conclude that U is a subsolution of (3.5).
We now proceed to show U is a supersolution. If φ ∈ C 1,2 and U − φ has a strict global mimimum atx 0 ∈Q T , then for any given j ∈ {1, . . . , J}, there will be sequences c m → 0, , and U cm j − φ attains a global mimimum atx m . Using the fact that U cm j is asupersolution to (3.5), we have (by ignoring the term U cm then passing m → ∞ enables us to conclude for any j ∈ {1, . . . , J}, which completes our proof.
General discrete approximation to the switching system
In this section, we establish the convergence of the piecewise constant policy approximation of (3.9) to the solution of the switching system (3.5). We will first summarize all the required conditions to guarantee the convergence, and perform the analysis under these assumptions. Then we will demonstrate in Section 4.4 that these conditions are in fact satisfied by the numerical scheme (3.17) proposed in Section 3 .
We assume the scheme (3.9) satisfies the following conditions introduced in [25]: (1) (Positive interpolation.) LetŨ n k,i(j) be the interpolant of the k-th grid onto the i-th point x n j,i of the j-th grid, and N k (j, i, n) be the neighbours 2 to the point x n j,i on the k-th grid Ω k,h . Then there exist weights {ω n k,i(j),a } a∈N k (j,i,n) satisfying ω n k,i(j),a ≥ 0 and a∈N k (j,i,n) ω n k,i(j),a = 1, such that we can writẽ U n k,i(j) = a∈N k (j,i,n) ω n k,i(j),a U n k,a . (4.6) (2) (Weak monotonicity.) The scheme (3.9) is monotone with respect to U n j,i andŨ n k,i(j) , i.e., if V n j,i ≥ U n j,i , ∀(i, j, n);Ṽ n k,i(j) ≥Ũ n k,i(j) , ∀(i, k, n), then we have (3) (ℓ ∞ stability.) The solution U n+1 j,i of the scheme (3.9) exists and is bounded uniformly in h and c.
Also note the contrast to the linear interpolant (3.10) used in (3.11) and (3.12) for the construction of a monotone approximation to the integral operators.
We now present the convergence of the discrete approximation to the switching system. The proof is essentially the same as that in [25] and is omitted. We remark that in the proof, we construct the solution of the switching system directly from the numerical solutions. Since the solution of the scheme (3.9) is uniformly bounded, Theorems 4.4 and 4.6 immediately give the existence and uniqueness of a bounded viscosity solution to the switching system (3.5).
A specific implicit scheme for the switching system
In this section, we analyze the implicit scheme (3.17) and demonstrate that it satisfies Condition 1, which subsequently implies its convergence to the switching system.
The following estimates are essential for our consistency and stability analysis.
Proof. We first derive the estimate for B α ε,h φ n+1 j,i . It follows from |η α | ≤ C and the definitions of B α ε,h φ and B α ε φ that We then infer from Taylor's theorem with an integral remainder that the truncation errors of the local terms can be bounded by for some function ω(x n+1 j,i , k) such that ω(·, k) → 0 as k → 0 uniformly on compact neighbourhoods of x n+1 j,i , which enables us to deduce that where κ α,n h,m,i , β α,n h,m,i , and d α,n h,k,m,i are defined in (3.13) and (3.15), respectively.
Proof. We shall only prove the estimate for κ α,n h,m,i , since the estimate for β α,n h,m,i follows from a similar argument, and the estimate for d α,n h,k,m,i follows directly from the fact that m ω m = 1. The definition of κ α,n h,m,i and the integrability property (2.1) of ν imply that Alternatively, it follows directly from the identity m∈Z d ω m (·; h) ≡ 1 that which leads us to the desired estimates.
Remark 4. Since we have not used any information on the exact behavior of the nonsingular measure ν around zero, the estimates for the nonlocal terms in Lemma 4.8 and 4.9 are not optimal for many specific cases. If one can estimate upper bounds of the density of the Lévy measure, or equivalently estimate the (pseudo-differential) orders of the nonlocal operators K α and B α , more precise results for the truncation error of the singular measure can be deduced ( [3]).
The next lemma presents some important properties of the Lax-Friedrichs numerical flux for Lipschitz continuous Hamiltonian, which are crucial for our subsequent analysis. We refer readers to [10] for a proof of these statements. Then the following hold: .16) and (x n j,i , u, k) ∈ Ω j,h × R × R, and suppose Assumption 1 and the condition θ > Cλ hold, where C is the Lipschitz constant of the Hamiltonianf .
(1) (Consistency.) For any test functions
(2) (Monotonicity.) If V n j,i ≥ U n j,i , for all i, j, n, then we have (3) (Stability.) For any bounded functions U and V , we have Proposition 4.11. Suppose Assumption 1, the positive interpolation property in Condition 1 and the condition θ > Cλ hold. Then we have the following: (1) There exists a unique bounded solution U n of the scheme (3.17).
Proof. We start to establish the existence and uniqueness of a bounded solution of (3.17) in (1) (3.17), it suffices to establish that for small enough ρ, the operator P is a contraction on ℓ ∞ (Z d ), i.e., the Banach space of bounded functions on hZ d employed with the sup-norm, which along with the contraction mapping theorem leads to the desired results.
(Similar contraction operators have been introduced in [5,11] to demonstrate the well-posedness of their numerical schemes.) For any bounded functions U n j and V n j , the definitions of P, A α ε,h,k and K α,1 ε,h give that It remains to estimate (4.9), (4.10) and (4.11). Lemma 4.10 (3) enables us to bound (4.11) by −ρ2dθ(U n j,i − V n j,i ) + ρ2dθ|U n j − V n j | 0 . We then derive upper bounds for (4.9) and (4.10) depending the Lipschitz continuity of f in y enables us to bound (4.9) by ρ∆tC|U n j,i − V n j,i | = −ρ∆tC(U n j,i − V n j,i ). We then discuss the sign of B α ε,h U n j,i − B α ε,h V n j,i . Suppose B α ε,h U n j,i − B α ε,h V n j,i < 0, then we obtain from the monotonicity of f in k that (4.10) ≤ 0. Consequently we obtain that On the other hand, if B α ε,h U n j,i − B α ε,h V n j,i > 0, the Lipschitz continuity of f in k enables us to bound (4.10) by C(B α ε,h U n j,i − B α ε,h V n j,i ), which along with (3.12) implies again (4.12) provided that the the following condition is satisfied: (κ α,n h,m,i + β α,n h,m,i ) + C > 0, (4.13) which holds for small enough ρ. This completes the proof that P is a contraction operator.
We now proceed to establish the ℓ ∞ stability of the scheme. Let {U n−1 j } J j=1 be the solutions to (3.17). By expressing the discrete operators A α ε,h,k and K α,1 ε,h in the monotone form (3.14) and (3.11), and substituting them into (3.17), we obtain that Using similar arguments as those for the upper bound of (4.9), we deduce that (4.14) is bounded above by −∆tCU n j,i independent of the sign of U n j,i . Suppose now B α ε,h U n j,i < 0, then we obtain from the monotonicity of f in k that (4.15) is nonpositive. Then the ℓ ∞ stability of the numerical flux and the boundedness of f α (x, 0, 0, 0) yield that Here C is the constant from Assumption 1 and C 1 > 0 is a large enough constant that we will choose later. On the other hand, if B α ε,h U n j,i > 0, the Lipschitz continuity of f in k enables us to bound (4.15) by CB α ε,h U n j,i , which along with (3.11) implies again (4.16). With the estimate (4.16) in hand, we are ready to derive a uniform bound for the solutions {U n j }, which is independent of h and c. The proof follows from an inductive argument. Let us introduce the notation |U n | 0 = max 1≤j≤J |U n j | 0 for each n and define the term a 0 = max(|g| 0 , |ζ| 0 ), then it is clear that a 0 ≥ max(|U 0 | 0 , |ζ| 0 ). Suppose we have a n−1 such that a n−1 ≥ max(|U n−1 | 0 , |ζ| 0 ).
Then the definition of U n− 1 2 j,i implies that |U n− 1 2 j | 0 ≤ max(|ζ| 0 , |U n−1 | 0 ) ≤ a n−1 . Define the term a n := 1 1 + ∆tC a n−1 + ∆tC 1 , with the same constants as those in (4.16), then we have |U n | 0 ≤ a n . To proceed by induction, we further require a n ≥ |ζ| 0 . Since a n−1 ≥ |ζ| 0 and C is fixed, it suffices to require C 1 ≥ C|ζ| 0 . In this way, we can construct a sequence {a n }, such that |U n | 0 ≤ a n , but a n is uniformly bounded independent of c, h and ∆t, and hence this completes the proof of ℓ ∞ stability. We now study the weak monotonicity of the scheme. Let V n j,i ≥ U n j,i andṼ n k,i(j) ≥Ũ n k,i(j) for all i, j, k, n, then we have V Moreover the monotonicity of f in k and the weak monotonicity off imply that is nondecreasing with {U b+1 j,a } (a, b) = (i, n) , which gives the weak monotonicity of the scheme (3.17).
Finally we study the consistency of the scheme. By using the Lipschitz continuity of x → min(x, a), it is clear that it suffices to bound which can be estimated by using Lemma 4.8, Lemma 4.10, and the Lipschitz continuity of f .
Remark 5.
The contraction operator P is introduced to demonstrate our scheme admits a unique solution for any given discretization parameters ∆t, h, k and ε. However, due to its low convergence rate, it is not advisable to implement this contraction mapping directly to solve the nonlinear equation (3.17). In fact, Lemma 4.9 and the stability condition (4.12) restrict the contraction constant of P to admit a lower bound depending on the spatial discretization of the diffusion operator. This undesirable dependence of ∆t on k can be avoided by considering the mapping T defined by (3.18), which is implicit in the local terms. It has been shown that for small enough h, the contraction constant of T is proportional to θ, which can be chosen to achieve a rapid convergence.
Numerical experiments
In this section, we present several numerical experiments to analyse the effectiveness of the numerical scheme proposed in Section 3. We shall investigate the convergence of numerical solutions with respect to the switching cost, timestep, and mesh size, and show that a relatively coarse discretization of the admissible control set already leads to an accurate approximation.
We consider a portfolio optimization problem over a time interval [0, T ], in a framework of recursive utility. An investor can control his wealth process X t,x,α through a selection of the control process α ∈ A t t , say his or her portfolio strategy, and can also choose the duration of the investment via a stopping time τ . If the agent chooses a strategy pair (α, τ ), then the associated terminal reward is given by ξ t,x,α τ = ζ(τ, X t,x,α τ )1 t≤τ <T + g(X t,x,α τ )1 τ =T for some utilities ζ and g, and where τ ∈ T t t , the set of F t -stopping times valued in [t, T ]. The performance of this investment is evaluated under a particular nonlinear expectation, called the recursive utility process (see e.g. [7]), which is associated with a BSDE (with Lipschitz continuous drivers). It generalizes the standard additive utilities by including a dependence on the future utility (corresponding to the future wealth). Roughly speaking, the recursive utility depends on the future utility through the dependance of the driver f on y, and can also depend on the "variability" or "volatility" of future utility through the dependance of f on z and k.
Let x be the wealth at the initial time t, (α, τ ) be the chosen strategy, E α,t,x [·] be a recursive utility function associated with the BSDE with driver f α . The aim of the investor is to maximize the utility of the investment: over all admissible choices of (α, τ ). Under Assumption 1, it can be shown that the value function u of this mixed optimization problem coincides with the unique bounded viscosity solution of the (backward) HJBVI (2.5).
For the numerical tests, we consider a financial market with a risk-free asset with an interest rate r and a risky asset whose price follows where W is a Brownian motion andÑ (dt, de) = N (dt, de) − ν(de)dt is a compensated jump measure. If we denote by α t the percentage of the portfolio held in the risky asset at time t, then the dynamics of the portfolio is given by The performance will be evaluated by the recursive utility function induced by the BSDE with the following driver: for some instantaneous reward function ψ. Recall that any concave utility function admits a dual representation via a set of probability measures absolutely continuous with respect to the original probability measure P (see e.g. [21]). This result allows us to interpret κ ≥ 0 as an ambiguity-aversion coefficient relative to the Brownian motion as suggested in [7,Section 3.3].
The value function of this control problem satisfies the following HJBVI: We then specify the choice of data for our numerical experiments. We use the exponential utility function ζ(t, x) = g(x) = (1 − e −x ) + , which determines both the intermediate and terminal payoff, and acts as the initial condition and the obstacle to the HJBVI. Moreover, we consider the tempered stable Lévy measure ν(de) = e −µ|e| |e| de on R with intensity η(e) = 1 ∧ |e| for the jump component (which is a special case of the variance Gamma model in [8]). For simplicity, we choose a zero interest rate, i.e., r = 0.
We further choose the function ψ(t, x) = 0.8 exp(−(T − t)) exp(−x/2) as the instantaneous reward. As we will see later, this choice of ψ implies that the optimal control α varies in the state space and evolves in time, and there can be non-trivial stopping. The resulting HJBVI will be localized to the domain (0, 2) with u(t, x) = g(x) for (t, x) ∈ (0, T ) × R \ (0, 2). The numerical values for the parameters used in the experiments are given in Table 1. Now we are ready to discuss the selection of the discretization parameters in detail. The density of the tempered stable measure ν enables us to improve the estimates in Lemma 4.9 to m =0 κ α,n h,m,i ≤ log(ε), and hence choosing ε = h and ∆t = O(h) leads us to a consistent approximation to the switching system (3.5). Moreover, choosing θ = 1 40 and ∆t = h 15 ensures the numerical flux is stable and the contraction constant of T in (3.18) is less than 1 10 . The coefficients of the nonlocal terms are evaluated by the midpoint quadrature formula, which is clearly monotone and consistent. We observe that for the control problem with the parameters as in Table 1, the optimal strategy α * will always be obtained at one of the endpoints of [0, 1]. In fact, using Taylor's theorem, we are able to approximate the nonlocal term K α u by at any given (t, x) for which the value function lies above the obstacle and is sufficiently smooth. Then we infer from the HJBVI (5.1) that the optimal control α * is the maximizer of a quadratic function on [0, 1], which is attained in the interior only if However, since we have b < σ, the above conditions can never hold for any x > 0. Consequently, we deduce that the admissible set is already finite, and replacing [0, 1] by A δ = {0, 1} in (5.1) will not introduce any discretiztion error. This has been confirmed with our numerical experiments. For the sake of simplicity, we discretise each component of the switching system on a single uniform mesh, thus Condition 1 (1) is trivially satisfied. Table 2 contains the numerical solutions to the last component of the switching system at the grid point (T, x 0 ) with different mesh size h and switching cost c. We examine the convergence of the numerical solutions, denoted as U h , in h for fixed c, as well as their convergence with respect to the cost c. For any fixed positive switching cost c, we infer from the lines (a) that the numerical solutions converge monotonically to the exact solution. Moreover, the lines (c) indicate the approximation error admits an asymptotic magnitude O(h) + O(∆t), which seems not to be affected by the size of the cost c. By considering the boldface values in Table 2 as an accurate approximation to the exact solution of the switching system with a given cost c, we can further conclude that the switching system is consistent to the HJBVI (5.1) with order 1. This follows from the approximate factor of four between the differences 0.00469, 0.00117, and 0.00029 between the last three pairs of values, proportional to the reduction in c. Therefore, by taking c = O(h) and ∆t = O(h), we can obtain a first-order scheme for the HJBVI.
We then proceed to analyze the effect of the control discretization. We pick the same parameters as those in Table 1, except that b = 0.25, which is chosen such that it is now possible that the optimal control is attained in the interior of (0, 1) (as seen from a similar argument as earlier). Computations are performed using Matlab R2016b on a 3.30GHz Intel Xeon ES-2667 16-Core processor with 256GB RAM to enable parallelization. Table 3 illustrates the numerical results for different control meshes (J = 1/δ + 1) with a fixed mesh size h = 0.005 and switching cost c = 1/2560, and also compares the runtime with or without parallelization.
We can clearly observe from line (a) second order convergence of the numerical solutions, and a relatively coarse control mesh has already yielded an accurate approximation with a negligible control discretization error.
Next, we discuss lines (b)-(f) which analyse the algorithm's parallel efficiency. Hereby, the implicit finite difference scheme for individual components of the switching system (i.e., (3.8), for different j) is solved independently on different processors, while the maximisation step (3.7) requires communication between processors.
The total execution time with and without parallelization are presented in line (b) and (c), respectively, which indicate a significant reduction of computational times. Moreover, by subtracting the communication time among clusters, as shown in line (d), from the total runtime, we can obtain the actual time spent on executing the numerical scheme (line (e)). The speed-up rate of the parallelization is shown in line (f), which grows with the number of controls, and remains stable at the number of cores. Therefore, together with parallelization, piecewise constant timestepping enables us to achieve a high accuracy in the control discretization without significantly increasing the computational time, which is an advantage over policy iterations, which do not parallelise naturally.
We finally examine the impact of the computational domain by performing computations on (0, 3) with h = 1/400, ∆t = h/20, c = 1/640 and the parameters as in Table 1. Compared to the results in Table 2, this larger domain leads to a relative difference of 7.53 · 10 −7 , which is negligible compared to the time and spatial discretization errors. The numerical value function and the corresponded feedback control strategy with J = 21 are presented in Figure 1, in which the white area represents the region where the obstacle is active, and otherwise the colour indicates the value of the optimal control, as shown in the panel on the right. The approximation to the optimal control pair (τ, α) was found from the numerical solution as follows (see also (3.7) and Remark 2), noting that in our tests x j,i = x k,i for all j, k, and therefore no interpolation is needed: where α n i = α i * n is an approximation to the optimal policy and {(t n , x 1,i ) : θ n i = 1} is an approximation to the stopping region.
Conclusions
This paper provides a PDE approximation scheme for the value function of a mixed stochastic control/optimal stopping problem with nonlinear expectations and infinite activity jumps, which is the unique viscosity solution of a nonlocal HJB variational inequality. The approach that we have adopted is based on piecewise constant policy time stepping (PCPT), which reduces the problem to a system of semi-linear PDEs, and a monotone approximation scheme. We prove the convergence of the numerical scheme and illustrate the theoretical results with some numerical examples in the case of a recursive utility maximisation problem.
To the best of our knowledge, this is the first paper which proposes a numerical approximation for a control problem in such a generality. Natural next steps would be to derive theoretical results on the convergence rate and to extend this approach to the case of Hamilton-Jacobi-Bellman-Isaac equations obtained in [6]. and consequently we obtain from the Lipschitz continuity of f that for a suitable defined ω 1 (x, δ) with the properties of ω 0 (x, δ). Therefore, using (A.1), (A.2) and the fact that A δ ⊂ A, we have which completes the proof of our desired result.
B Comparison principle for switching systems
In this section, we establish the comparison principle for switching system (3.5), cf. Theorem 4.4. We consider a slightly more general switching system with no truncation of the singular measure in K ε and B ε , which includes as a special case the switching system (3.5). We first use a classical no-loop argument to reduce the problem into scalar cases, and then analyze the scalar HJBVI by extending the results for continuous solutions in [14] to semicontinuous viscosity solutions. For simplicity, we denote by σ the modified diffusion coefficientσ α defined as (3.1).
Proof of Theorem 4.4. Set
It suffices to show that M ≤ 0. For any given ε, ρ > 0, we introduce the functions for each t, s ∈ [0, T ] and x, y ∈ R d , and define the quantity M ε,ρ := sup j,t,s,x,y ψ ε,ρ j (t, s, x, y).
We now divide our analysis into three cases to establish M ≤ 0. If there exists a subsequence of {t ρ } such that t ρ = 0 for all ρ, we then deduce M ≤ 0 along this subsequence by adapting the arguments in [14] to semicontinuous solutions.
On the other hand, if t ρ is different from 0 for all ρ, then for any fixed ρ and small enough ε, using Lemma B.2, which can be proved similarly as Lemma 4.1 in [4], we know there exists j ε,ρ 0 ∈ {1, . . . , J}, which for simplicity is still denoted as j ε,ρ , such that U j ε,ρ (t ε,ρ , x ε,ρ ) > M j ε,ρ U (t ε,ρ , x ε,ρ ). In other words, at the point (t ε,ρ , s ε,ρ , x ε,ρ , y ε,ρ ), by considering the j ε,ρ component of the switching system, we can without loss of generality ignore the term U j ε,ρ − M j ε,ρ U in the definition of subsolutions and get back to the scalar HJBVI.
Then noticing the estimates derived in [14] for each term on the right-hand side of the above expression are uniform in the control α j ρ , and successively passing δ, ε and ρ to 0, we deduce that 0 < M ≤ 0, which leads to a contradiction. Thus we conclude M ≤ 0 and complete the proof.
C Truncation of singular measures
A possible way to work with a nonsingular jump measure is to introduce a Backward SDE with a modified driver and an approximative jump-diffusion dynamics where the small jumps part has been substituted by a rescaled diffusion coefficient of the Brownian motion W .
More precisely, we adopt the same probability space as introduced in Section 2, which supports the Brownian motion process W and the independent Poisson measure N (dt, de). For a given jump truncation size ε > 0, we define a modified diffusion coefficientσ α as in (3.1), and also introduce a modified driver f ε (α, t, x, y, z, k) :=f (α, t, x, y, z, |e|≥ε k(e)γ(α, x, e)ν(de)), where the function f is given in Assumption 1.
For any given initial state x ∈ R d , control α ∈ A t t and τ ∈ T t t , we consider the modified controlled jump-diffusion process (X ε,α,t,x s ) t≤s≤T satisfying the following SDE: for each s ∈ [t, T ], (e)Ñ t (ds, de), Y ε,α,t,x τ,τ = ξ(τ, X ε,α,t,x τ ). (C. 2) The coefficients of the above SDE and BSDE satisfy Assumption 1, and therefore the equations are well-posed. Now we are ready to state the modified mixed optimal stopping and control problem. For each initial time t ∈ [0, T ] and initial state x ∈ R d , we consider the following value function: with κ(ε) := |e|≤ε (1 ∧ |e| 2 )ν(de) and C a constant independent of α and ε. | 13,937 | 2018-03-10T00:00:00.000 | [
"Mathematics"
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Ethical Analysis of Taiwanese Psychiatric Patient’s Autonomy: By Jonsen’s Decision Making Model and Confucianism
The autonomy of psychiatric patients has been a popular issue worthy of debate. Because of the cultural background of Taiwan, families often become involved in the autonomous implementation of psychiatric patients, resulting in ethical dilemmas. Regarding medical indications, psychiatric patients can implement autonomy when their decisions do not violate the goals of medical care. The implementation of patient autonomy is respectful not only to patient preferences but also their humanity. For patients, quality of life is subjective; respecting quality of life from patient preferences conforms to the principles of beneficence, nonmaleficence and autonomy. Regarding medical decision making, treatment decisions can affect the interest of families. Taiwanese are affected by Confucianism, which emphasizes the importance of family relations and the intimacy between patients and their families. Therefore, families play an essential role in clinical decision making. This study explores the ethical autonomy of Taiwanese psychiatric patients via Jonsen’s decision making model and the perspective of Confucianism to determine whether Jonsen’s ethical decision making model is adaptive in Taiwanese society. Journal of Clinical Research & Bioethics J o u r n a l o f C lin ical Resrch& Bioe t h i c s
involved in taking care of her, and suggested Hysterectomy (uterus excision).
But when Miss Wong returned to normal, she expressed the desire to have children and a family.
Autonomy refers to the ability of a rational individual to make decisions on his/her own without being influenced by external factors, such as manipulations and threats, resulting in spontaneous actions after rational thinking. believe that personal autonomy encompasses, at minimum, self-rule that is free from both the controlling interference of others and from certain limitations, such as an inadequate understanding that prevents meaningful choice [2].
According to Kant (1785) in "The Formula of Autonomy": The Idea of the will of every rational being as a will which makes universal law [3]. The meaning is that: the free will of every rational being is a universal law. Humans are rational and have free will; hence, we can establish and follow rules. With rationality, humans possess dignity and values. After psychiatric patients receive adaptive medical care, the symptoms of disease can be mitigated. When psychiatric patients have the capacity to express their own rational opinions, we must respect and adopt them. This is done out of respect to the patient's humanity. Respect for the patient's humanity, values, and dignity can have a positive impact on treatment results.
The assessment of the behavioral capacity of psychiatric patients and issues related to surrogate.
Not all psychiatric patients are incapable. Hence, we must respect the decisions made by capable patients. Regarding the assessment of capacity, introduced their "Rival Standards of Incompetence." The following schema expresses the range of inability currently required by competing standards of incompetence. These standards range progressively from one, requiring the least ability, to the other end of the spectrum [4].
(1) Inability to express or communicate a preference or choice.
(2) Inability to understand one's situation and its consequences.
(3) Inability to understand relevant information.
(4) Inability to give a reason.
(5) Inability to give a rational reason (though some supporting reasons may be given). (6) Inability to provide risk/benefit-related reasons (though some rational supporting reasons may be given). (7) Inability to reach a reasonable decision (as judged, for example, by a reasonable person standard).
In clinical practice, the MacArthur Competence Assessment Tool (MacCAT-T) can be used for assessing patient decision-making ability. When a patient is incapable, the patient's representative must make medical decisions based on the interest of the patient.
The medical decision made by the surrogate must be based on the principles of nonmaleficence and beneficence. According to
Medical Indications
Medical problem: (1) Patient has some psychotic symptoms.
(2) Non-Adherence to Medication (3) Treatment goals: the patient can return to his or her community.
Patient Preferences
After recovery, the patient expressed the desire to bear children and to have a family.
Quality of Life
Return to normal quality of life.
Contextual Features
Family complained of the enormous effort involved in taking care of her, and suggested a Hysterectomy (uterus excision).
The importance of patient autonomy 1. One ought not to inflict evil or harm.
2. One ought to prevent evil or harm.
3. One ought to remove evil or harm.
4. One ought to do or promote good.
When surrogate make medical decisions, they must consider the best interest and the risk-benefit analysis of the disease of patients. However, the decisions made by surrogate have limitations. When the rights and decision-making of patients are not consistent with the decisions made by families, and the right of patients is harmed, patients can ask for legal recourse, preserving the interests of patients. Buchanan and Brock (1990) stated the intervention principle: the family should be disqualified if the patient is abused or neglected, or if there is a serious conflict of interest likely to bias their decisions against the rights and interests of the patient. The medical chief of staff may rebut the authority of the family [6].
Ethical Issue Analysis using Jonsen's Ethical Decision Making Model
Medical indications (1) What is the patient's medical problem? (2) What are the goals of treatment? (3) In sum, how can this patient benefit from medical and nursing care, and how can harm be avoided?
The primary medical problem of the case subject is the nonadherence to medication, resulting in inconclusive treatment results. Therefore, medical staff should teach the research subject and families the importance of adherence to medication, the goal of treatment (return to their community), and the risk and side effects of nonadherence. Based on their professional medical background, physicians must give appropriate suggestions to patients. Therefore, patients (or families) can select treatments according to patient preferences and quality of life (for example, oral prescriptions for mental disorders can be replaced with long-acting anti-psychotics if patients cannot adhere to the medications). Physicians should consider the interest of patients to minimize harm.
Patient preferences
(1) Has the patient been informed of the benefits and risks, understood this information, and given consent? (2) Is the patient mentally capable and legally competent, and is there evidence of incapacity? (3) If mentally capable, what treatment preferences is the patient stating? (4) If incapacitated, has the patient previously expressed preferences? (5) Who is the appropriate surrogate to make decisions for the incapacitated patient?
When the families decided to conduct a uterus excision on the research subject, the subject was incapacitated due to the occurrence of mental disorder, and did not understand the risks and results of the operation. Moreover, when the subject's condition improved (nearly capable of communicating with others), she expressed a desire to get married and have a family. Therefore, physicians should explain the effects and risks of the operation, and respect the decision made by the subject while the subject is capable. The subject should be treated with dignity, as with all other humans. According to "The Formula of Ends" proposed by Kant (1785), "Act in such a way that you always treat humanity, whether in your own person or in the person of any other, never simply as a means, but as a means, but always at the same time as an end [7]." Most philosophers who find that" Kant's views attractive find them so because of the Humanity formulation of the CI (Categorical Imperative). This formulation states that we should never act in such a way that we treat Humanity, whether in ourselves or in others, as a means only but always as an end in itself. This is often seen as introducing the idea of "respect" for persons, for whatever it is that is essential to our Humanity [8].
According to the definition of "The Formula of Autonomy" proposed by Kant, each rational being can establish and follow rules through his or her own will, forming the realm of ends; namely, a person can be the one to both establish and follow rules at the same time. Regarding the definition of "the realm of ends," Kant stated that in the kingdom of ends: everything has either a price or a dignity. If it has a price, something else can be put in its place as an equivalent; if it is exalted above all price and so admits of no equivalent, then it has a dignity [9].
Kant believed that humans have values and dignity which cannot be exchanged for other things. The dignity of humans is not a tool or means, but it should be regarded as an end. According to the definition of "The Formula of Autonomy", the autonomy and right of actors deserve the respect of others. Physicians should explain the benefits and risk of treatments to patients through communication. Therefore, physicians can better understand the willingness of patients and adjust medical goals accordingly.
During the period when the patient exhibited optimal mental status and functions, her cognitive functions, reality testing, judgment abilities, and affect nearly reached the reference level. She could calculate the accounts, purchase goods, and interact with customers independently. However, regarding issues such as marriage and raising children for the patient, medical staff were required to counsel the patient and her family. The discussion content included the following: the obligations and responsibilities of marriage and raising children, the risks the drugs may pose to a fetus, the possible consequences of discontinuing or changing medicine because of pregnancy, the importance of regular medication consumption for improving her condition and overall satisfaction with life, the probability of schizophrenia inheritance, and the impact that recurrent conditions have on children and marriage. Caring for children and maintaining a marriage are stresses that can induce recurrent conditions. After discussing these issues with the patient, we understood the views and perceptions of the patient and her family. During the discussion, medical staff provided professional suggestions from an unbiased and uncritical role to avoid damaging the patient's self-esteem. (1) What are the prospects, with or without treatment, for the patient to a normal life; and what are the physical, mental, and social deficits the patient might experience even if treatment succeeds? (2) On what grounds can one judge that some quality of life would be undesirable for a patient who cannot make or express such a judgment? (3) Are there biases that might prejudice the provider's evaluation of the patient's quality of life?
Quality of life
Quality of life is subjective, and observation by others can produce bias. Clinicians must explain to patients the possible effects on life quality that different treatments or the lack of treatment will have. Physicians also have to understand the expectations of patients on life, whether patients decide to take treatment or not, and the patients' opinions on the physical, mental, and social influence treatments have on the patients. Hence, improving the patient's quality of life is based on the ethical perspectives of beneficence, nonmaleficence, and respect for autonomy. Other people subjectively assess patient life quality when patients lose the capacity to express their opinions and volition. People have their own beliefs and values. Therefore, the opinions of observers can be inconsistent with those of patients, which can produce bias. To avoid excessive bias, observers should be as neutral as possible, and assess patient life quality based on the desires and best interests of patients, such as through the dialogue of patients with their families and friends, and the patient's diaries.
During the period when the patient exhibited optimal mental status and functions, the patient's Global Assessment of Functioning (GAF)=81-90, according to Axis V of the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV): The patient exhibited absent or minimal symptoms (e.g., the patient exhibited slight anxiety before purchasing or importing goods when raising funds and urging manufacturers as required), good functioning in all areas, interested and involved in a wide range of activities, socially effective, and generally satisfied with life. In the assessment of the Axis IV--Psychosocial and Environmental Problems of DSM-IV, the primary factor influencing the relapse of recurrent conditions in patients is missed medication doses. The reason for the patient's previous hospitalization was that her family was sometimes too busy to remind the patient to take her medication. Additionally, the patient's family believed that she had recovered because she could work normally in the store and, thus, could discontinue her medication. Furthermore, when taking her medication, the patient was occasionally asked "What medicine are you taking?" "Why are you taking medicine?" Such questions caused discomfort in the patient because she was afraid of being considered a psychopath or crazy. Furthermore, the patient believed that if she could manage working and interpersonal relationships without problems, her condition was cured; thus, she autonomously discontinued her medication.
Contextual features
Are there parties other than clinicians and patients, such as family members, who have an interest in clinical decisions?
Humans are collective beings who interact with others, forming social networks. These social networks serve the functions of support and aid. Therefore, close family members can intervene in the medical decisions. However, most families can make decisions based on the best interests of patients (which are generally correct because families know the patient's preferences), and participate in the process of medical decision making along with physicians. Jonsen (2006) suggests that patients are located in a social context of other persons with whom they have various sorts of relationships and interactions. At times, the family's interests may conflict with those of the patient: financial concerns or interfamilial disputes may spill into clinical care. The cooperation of relatives should be sought and encouraged [10].
However, the participation of families in the process of medical decision making can also lead to negative effects. Sometimes, the decisions made by family members violate medication indications. Jonsen (2006) says that in these situations, "when family pose problems about the care of the patient, it is necessary to seek and understand the reasons for their behavior and to attempt conciliation, if possible. On rare occasions, resorting to legal steps may be necessary to protect the patient. The role of families often is defined quite differently in other culture, and ethical problems will sometimes occur [10]." In this case study, the family is frustrated with taking care of the patient, and wants the patient to receive uterine excision to prevent the patient from becoming pregnant. However, the decision made by the family obviously violates the rights of the patient. Based on the responsibilities and obligations of medical staff, when the decision of a family is inconsistent with the professional suggestions of medical staff and violates the rights of patients, medical staff must prevent the families from acting, and even appeal to legal authorities if necessary.
Clinical and literature studies have both shown that the families of psychiatric patients play the role of caregivers, bearing significant stress. When the patient returned home, her worry and anxiety increased. The patient continuously presented problems, and her family was required to cope with the consequences. Thus, a "burn out" was unavoidable. To address this situation, medical staff must interview and psychologically support (understand the perceptions of her family through empathy) to establish the patient's family's trust in the healthcare system. Communicating the importance of taking medication on time may prevent the patient's recurrent symptoms. Additionally, medical staff must inform the family that to prevent the same problem from occurring repeatedly, clinicians will establish certain strategies to manage the patient's problems and use this to ease the family's emotions. A number of hospitals even host family support groups to enable people to share their care giving experiences. During the interactive process with group members, positive attitudes were achieved to manage the stress of caring for patients.
Related Ethical Issue Analysis via the Perspective of Confucianism
In clinical practice in Taiwan, we find that even if patients are capable (not all patients were suffering from psychological disorders) of making medical decisions, families make decisions for them, particularly when facing ethical dilemmas. This is because of the traditional background of Confucianism, which emphasizes the relationship of family and familial ethics. In addition, because patients are sick and mentally incapable, the decision-making and thinking capacities of the patients are weakened. Therefore, the families and physicians of the patients discuss and make the most adaptive medical decisions for the patients. postulates: In many Asian countries that have been influenced by Confucianism, the family continues to play a central role in medical decision-making [11].
There are five human relationships in Confucianism, including the relations between ruler and subjects, father and son, husband and wife, elder and younger brother, and between friends. (the original from Mengzi-T'eng Wen Kung). Yang says "The five human relationships refer to the affectionate relationships between fathers and sons, the righteous relationships between sovereigns and ministers, the attention to separate the functions of husbands and wives, a proper order between old and young, and the fidelity relationships between friends [12]." The five human relationships begin from familial relationships and are gradually developed in political societies, forming a harmonious ethical relationship between family and society. In Taiwan, most families participate in the process of medical decision making. Based on the best interests of the patients, families discuss the benefits and risks of related treatments with physicians, and make the most appropriate medical decision.
Chen and Fan [13] believe that the Chinese family-based and harmony-oriented model of medical decision making is like as well as how it differs from the modern Western individual-based and autonomy-oriented model in health care practices. The roots of the Chinese model are in the Confucian account of the family and the Confucian view of harmony [13]. Fan [14] said that the focuses on the issue of surrogate decision making to illustrate the Confucian familygrounded communitarian bioethics. In Chinese bioethics, functions as a whole to provide consent for significant medical and surgical interventions when a patient has lost decision-making capacity. The Chinese model, as well as the Confucian communitarian life of families, engages a family autonomy that is supported by a Confucian understanding of moral autonomy, rather than individual autonomy. Finally, the issue of possible conflicts between patient and family interests in relation to a patient's past wishes in the Chinese model is addressed in light of the role of the physician [14].
Therefore, according to Confucian perspective it do not depends on the family's wishes over the patient's preference. If there is difference medical opinion between patient and family, then the medical staff may help them to make consistent decision. If the opinion still do not coordinate then it depends on the patient's wish, but it should not violate the best medical interest of patient.
The Application of Jonsen's Ethical Decision Making Model in Taiwan and Related Problems-A Family without Confucianism
Individualism is highly emphasized in western society. If a patient is capable, the patient's family must respect their decisions. However, Chinese society is highly influenced by Confucianism; the intimate relationship between the individual and the family is inseparable, resulting in the participation of families, patients, and physicians in the medical decision making process. However, sometimes, whether patients are capable or not, they are excluded from the decisionmaking process. Though Jonsen's decision making model considers the necessity of family intervention in medical decision making and its potential for error, the model neglects the fact that the meaning of family among Chinese is derived from Confucianism, and the importance of family intervention in medical decision making. In Chinese families, the intervention of family in medical decision making is a common phenomenon, which is also a unique to Chinese culture.
Li and Wen [15] write that the Confucian family-determination model has been applied in Chinese society for thousands of years. Based on summarizing the reasons supporting the model, this essay indicates that it is an integral part of the model that in emergency or special cases, the physician must take medical action to save the patient, without the need to secure the consent of a family member. Chinese physicians must cultivate the Confucian virtue of benevolence in their practice of taking care of patients in a virtuous way, along with the patients' families [15].
Lee [16] reports the following: The "ethical relational theory of autonomy" integrates the Confucian concept of a person, which asserts that our relations with others, and in particular our family, are part of our personal identity. This theory of autonomy also has an ethical component: it takes into account the Confucian insight into the nature of moral experience, which as Lee shows, is quite similar to Kantian notion of autonomy. Lee argues that an autonomous action is an action that (1) is circumscribed by the "moral mind" or what would Kant terms "practical reason" and (2) this moral mind must be oriented to the welfare of others because their wellbeing is closely linked to our own welling and identity. The second feature of this theory takes into account the family, because our moral practice begins with the wellbeing of family members as they are so integral to our own identity and wellbeing. Lee concludes by arguing such a theory requires that medical decision making be a collective affair that involves both patients and their families [16].
The author discusses family decision-making only in certain contexts, which indicates the inadequacy of the literature on family intervention. A Taiwanese family often involves four topics chart. This presents the differences between Western Individualism and Eastern Familialism in clinical ethical decision-making. For vulnerable parties, family decision-making sometimes is good, and sometimes bad (it doesn't always consider the best interests of the patient). Therefore, medical care personnel must protect the patient from harm. Application of the theory of Jonsen's decision-making model is too widespread. It does not provide explanations about representative decision-making. The cross-cultural discussion is insufficient. For example: the author does not consider Confucian, Family-Centered Decision. But they are very important for Asian's patient/family to make ethical decision.
Conclusion
Ambrosini and Crocker (2009) report that psychiatric advance directives (PADs) are grounded in the ethics of autonomy. PADs are legal documents that allow individuals with mental illnesses to record their preferences for treatment should they become incompetent in the future. Autonomy is the value that empowers individuals to work toward their recovery [17].
From the perspective of Kant's theory, humans are rational beings who can establish and follow moral principles, possess autonomy, and treat themselves and others as ends instead of means; therefore, humans have dignity and values. Kant (1785) stated: Man, and in general every rational being, exists as an end in himself, not merely as a means for arbitrary use by this or that will [18].
Regarding the case study in this research, the patient's decision was not aligned with that of the family; thus, medical staffs have the right to prevent the family from making a medical decision. In Chinese society, individuals and families are regarded as a whole, and families make medical decisions for patients; though in some cases, patients can be capable. However, medical staff should prevent families from making decisions when such decisions violate the best interests of patient.
Even if the patient had not expressed her wish, the hysterectomy (uterus excision) could not have been performed. The philosophy of Confucianism would not support performing the operation on the patient. In this case, there were no medical indications that could justify this operation. When the patient was capable, she expressed her preference; therefore, her opinions must be respected. Respect for patient autonomy is a manifestation of respect for humanity. Medical staff can prevent the decisions made by representatives when those decisions violate the preferences of patients. Medical staff can suggest that representatives discuss these decisions with patients when patients are capable of doing so. Therefore, according to the best interests of the patient, the hysterectomy could not be performed. The discussion of whether to perform a hysterectomy should be conducted by medical staff. Medical staff can suggest the families use an intrauterine contraceptive or contraceptive patch under the premise of protecting the patient.
Although the reason the patient discontinued her medication was that she "forgot to take the medicine," questions and problems were developed based on (1) perceived health leading to the discontinuation of medication consumption; (2) the fear of being considered a psychopath or crazy because of the consumption of medicine; and (3) the family's failure to remind the patient to consume her medication on time. Regarding this problem, we suggest that medical staff conduct the following procedures: (1) Provide health education regarding the importance of consuming medication on time to prevent a relapse for the patient and her family. (2) inform the patient and her family that her oral drugs could be replaced using long-acting antipsychotic drugs. If the drug efficacy is not ideal, medical staff must consider replacing drugs and adjusting the dosage and administration methods. After her condition improved, the patient was transferred to the Day Care Ward to facilitate observation of the efficacy of long-acting antipsychotic drugs and the patient's degree of recovery. (3) When the patient achieved remission of her condition, she was reclassified as a Home Visit case. Subsequently, medical staff let the patient return to the community for deinstitutionalization. (4) Medical staff were responsible for conducting regular home visits. The OPD nurses staff could follow up on her condition with phone interview or transfer the patient to a psychiatry case manager. These professionals can continuously monitor the patient's condition and conduct GAF Scale and Psychosocial and Environmental Problems assessments. If a problem is identified, adequate intervention can be provided to resolve the issue. These measures enable the patient's family to understand that other ways for ensuring the patient's drug compliance and return to normal life exist. The family also has a responsibility and obligation to urge the patient to take her medication. Adopting the extreme method of a hysterectomy is not required to resolve related problems. This treatment exemplifies a spiritual or performance of ethical meaning that balances beneficence, nonmaleficence, and justice to provide a treatment the patient deserves. | 6,067.6 | 2012-10-27T00:00:00.000 | [
"Medicine",
"Philosophy",
"Psychology"
] |
Dynamic analysis of the effect of mesh tension on the deployment process of loop antenna
In orbit deployment and profile maintenance are the most important functional requirements in the development of loop antenna If the antenna cannot be deployed in orbit, it will lose the signal transmission function, and the profile in orbit holding function is related to whether the antenna can stably transmit electromagnetic signals. The mesh tension (main mesh tension, rear mesh tension and tension arrays tension) is the key means to maintain the profile stability in orbit. At the same time, it is also closely related to the rod load and the maximum motor driving force in the process of antenna deployment. Based on the theory of flexible multi-body dynamics, the dynamic modeling of the deployment process of ten meter loop deployable antenna is established in this paper On this basis, the influence of mesh tension on the deployment dynamics of loop antenna is analyzed by using the control variable method, and its related variation law is obtained. This study can provide guidance for the tension adjustment in the profile adjustment stage of the ring antenna, so as to shorten the development cycle, and can also predict the deployment of the antenna in orbit.
Introduction
The loop deployable antenna is mainly composed of loop truss, main mesh, rear mesh, metal mesh and the tension arrays, as shown in Figure 1. The loop truss is mainly composed of quadrilateral units as shown in Figure 2. During the deployment process, the motor drives the driving rope running through the diagonal bars of the quadrilateral, so that the quadrilateral units are changed from the folded to the deployed state. The main mesh and the rear mesh are fixed on the hinges of the loop truss through the connecting devices. The main purpose of the loop deployable antenna is to send and receive electromagnetic information in space. Therefore, in order to ensure that the antenna can work normally in space, the main mesh, the rear mesh and tension arrays should satisfy certain tension requirements, so as to ensure that the antenna metal mesh can own certain rigidity to ensure the antenna has sufficient stability for sending and receiving electromagnetic signals. Through the ground test and simulation analysis, it is found that the tension of the mesh surface has a great influence on the deployment process of the loop deployable antenna. Therefore, revealing the dynamic influence of the mesh tension on the deployment process of the loop antenna not only has a predictive effect on the deployment of the antenna in space, but also has certain guiding significance for the adjustment of the mesh tension during the profile adjustment in the ground development process. In this paper, based on the flexible multi-body dynamics theory, the dynamic modeling and simulation of the ten-meter-level loop deployable antenna are carried out, influence on the deployment process of the loop antenna is described in this paper.
Dynamic modeling of the antenna deployment process
The deployment process of the loop antenna involves hundreds of flexible rods and thousands of flexible cables moving in a wide range, and the rods and cables are deformed in a large range during the movement. In terms of modeling flexible parts for large deformation and large-scale motion, the current mainstream directions include absolute nodal coordinate method [1] [2] and geometrically accurate beam theory [3][4][5] [6]. Tao Cheng et al. [7] analyzed the asynchrony of the loop antenna deployment based on the absolute node coordinate method, and Zhao Zhihua et al. [8] carried out dynamic modeling and simulation of the loop antenna based on the geometrically accurate beam theory. The above two modeling methods have their own advantages and disadvantages in terms of computational efficiency, singularity resolution, strain objectivity, and programming implementation [9]. In terms of programming, the absolute node coordinate method is easier to implement, but in terms of accuracy and calculation speed, the geometrically precise method is more dominant. For this reason, this paper adopts the geometrically accurate beam theory to carry out dynamic modeling of flexible members and cables .
The dynamic modeling of the loop antenna deployment process adopts the first type of Lagrangian equation as shown in Equation 1 as the system dynamics control equation: , 0 where T is the kinetic energy, q is the generalized coordinate, q is the generalized velocity, V is the elastic potential energy, Φ is the constraint equation, λ is the Lagrange multiplier, and Q is the generalized external force.
The modeling of flexible members, dynamic ropes and cable nets can be found in the literature, the modeling can be found in the literature [10] [11], and the constraint modeling can be found in the literature [12].
Analysis of the influence of mesh tension on the deployment dynamics
The most concerned factors in the deployment process of the loop antenna are the driving force of the motor and the maximum bending stress of the vertical rod (compared with the horizontal rod and the inclined rod, the vertical rod is most likely to be damaged), destruction of rope and bars will directly In the research process, the control variable method was used to analyze the average tension of the outer part cables of the main and rear mesh, and the average tension of the tension arrays. To compare and analyze the deployment driving force and the maximum bending stress of the longitudinal bar. Considering that for the loop antenna system, after its deployment is stable, the main mesh, rear mesh, and tension arrays satisfy a certain balance relationship, and their changes have a certain coupling phenomenon; therefore, when the simulation process analyzes the influence of a variable on the dynamics of the deployment process, other tension variables Changes will occur. In order to analyze effectively and reasonably, ensure that other forces do not change by more than 5%.
Analysis of the influence of outer part main mesh cables on the dynamics of the deployment process
When analyzing the influence of the average tension of the outer part cables of the main mesh on the deployment dynamics, the variation range of the average force of the rear mesh is 8.70Kg-8.90Kg, and the change rate is 2.3%; the average tension of the tension arrays vary from 2.98N to 3.12N, with the change rate of 4.6%. The influence of the average tension of the outer part cables of the main mesh on the maximum motor driving force is shown in Figure 3. The average tension of the outer part cables of the main mesh gradually increases, and the the maximum motor driving force increases too; the average tension of the outer part cables of the main mesh increases from 2.6Kg to 4.6 Kg, the maximum motor driving force is increased from 18.94Kg to 30.33Kg, and the maximum motor driving force is increased by 60.1%.
Analysis of the influence of outer part rear mesh cables on the dynamics of the deployment process
When analyzing the influence of the average tension of the outer part cables of the rear mesh on the deployment dynamics, the average force of the outer part cables of the rear mesh varies in the range of 3.75Kg-3.91Kg, and the change rate is 4.2%; the average tension of the tension arrays vary from 2.98N to 3.12N, with the change rate was 4.6%. The influence of the average tension of the outer part cables of the rear mesh on the maximum motor driving force is shown in Figure 5. As the average tension of the outer part cables of the rear mesh gradually increases, the maximum motor driving force increases and the increase is larger; the average tension of the outer part cables of the rear mesh increases from 7.8Kg to 10.8Kg, the maximum motor driving force is increased from 21.5Kg to 29.05Kg, and the rate is increased by 35.11%. Relationship between average tension of side rope of auxiliary mesh and maximum dynamic change of motor deployment The influence of the average tension of the outer part cables of the rear mesh on the maximum bending stress of the vertical rod is shown in Figure 6. The average tension of the outer part cables of the rear mesh has little effect on the maximum bending stress of the vertical rod. The average tension of the outer part cables of the rear mesh increases from 7.8Kg to 10.8Kg, the maximum bending stress of the vertical rod varies from 219.16MPa to 224.28MPa, and the maximum variation is only 2.3%. Fig. 6. Variation relationship between average tension of side rope of auxiliary mesh and maximum bending stress of vertical rod
Analysis of the influence of the tension arrays on the dynamics of the deployment process
When analyzing the influence of the average tension of the tension arrays on the deployment dynamics, the variation range of the average force of the outer part cables of the main mesh is 3.75Kg-3.91Kg, and the change rate is 4.2%; the average force of the outer part cables of the rear mesh is 8.68Kg-9.10Kg, The rate was 4.6%. The influence of the average tension of the tension arrays on the maximum motor driving force is shown in Figure 7. As the average tension of the tension array increases, the maximum motor driving force shows an overall upward trend, but the increase is small. When the average tension of the tension array increases from 3N to 4N, the maximum motor driving force increases from 24.43Kg to 27.98Kg, and rate is 14.53%. Relationship between average tension of tension array and maximum dynamic change of motor deployment The effect of the average tension of the tension array on the bending stress of the vertical rod is shown in Figure 8. The average tension of the tension arrays has little effect on the maximum bending stress of the vertical rod. The average tension of the tension array increases from 3N to 4N, the maximum bending stress of the vertical rod varies from 215.58MPa to 224.04MPa, and the maximum variation is only 3.9%.
4.Conclusion
During the development of the loop antenna, the profile adjustment work occupies a long period of time in the development cycle. Through the above research and analysis, it can be concluded that within a certain range, the mesh tension has little influence on the load of the rod. As for the maximum motor driving force, when the average tension of the tension arrays and the tension of the outer part cables of the rear mesh remain unchanged, increasing the tension of the outer part cables of the main mesh will also increase the deployment power, and the increase is obvious; when the average tension of the outer part cables of the main mesh and the tension arrays remain unchanged, increasing the tension of the outer part cables of the rear mesh, and the the maximum motor driving force will also increase; when the average tension of the outer part cables of the main mesh and the average tension of the outer part cables of the rear mesh remain unchanged, increasing the average tension of the tension arrays, and the maximum motor driving force will increase as a whole. trend, but the increase is small. | 2,605.4 | 2022-09-01T00:00:00.000 | [
"Engineering",
"Physics"
] |
Sustainable Glass Foams Produced from Glass Bottles and Tobacco Residue
In this work, discarded soda-lime-silica glass bottles and tobacco residue (after oil extraction to produce biodiesel) were prepared in different formulations to obtain glass foams. The formulated compositions were homogenized and uniaxially compacted at 40 MPa then fired at 850 °C and 900 °C for 60 min to investigate the effects of tobacco residue and temperature in thermal and mechanical properties of the glass foams. The results show that glass foams obtained are promising materials for applications where thermal insulation and mechanical strength are desired, with values of 0.087 W.m-1K-1 and 2.1 MPa, respectively for 45% of the tobacco residue that was added to the glass foam and fired at 850 °C. These characteristics occur through a suitable combination of thermal conductivity and compressive strength, showing advantageous properties for applications in sustainable constructions and industrial energy efficiency.
Introduction
In Brazil, around 980 thousand tons of glass bottles are produced annually, and only approximately 50% of this amount is recycled 1 .Glass is a material of high durability and is inert, which gives it a high reuse rate.The production of glass foams represents an excellent alternative for the reuse of glass waste.This waste is applied as glass foams mainly for thermal insulation due of its low density, high porosity (> 60%), 2 low thermal conductivity (0.04-0.08 W•m -1 •K -1 ) 3 , dimensional stability, and also because it is non-toxic, nonflammable, chemically inert and has compressive strength values ranging from 0.4-6 MPa 3 .In addition, glass waste has higher operating temperatures than conventional insulation materials (polymer foams).Other possible applications are their use as filters, supports for catalysts and lightweight structural materials [4][5] .Thermal insulators are an essential contribution to saving energy in buildings, such as in the control of the loss and gain of heat through walls.This contribution can be an important reason for increasing the use of glass waste.In this way, thermal insulators present a relevant role as a destination for this waste from an economic and environmental point of view.This is due to the fact that glass used for its manufacture is not always returnable or reused in the manufacture of new packaging.In addition, the development of studies aimed at the aggregation of agroindustrial residues as a pore-forming agent in the vitreous matrix can become an alternative capable of reducing the use of raw materials and lengthening the life cycles of elements in the anthroposphere.This reduces the need for extracting natural resources from the environment and reduces the final costs for the industrial sectors [6][7] .
Tobacco is valued mainly for its leaves which are used in the production of cigarettes and other tobacco products.Recently, alternative uses of tobacco have been proposed.One of which is energetic tobacco.This is a variety of Solaris tobacco which was developed in Italy.It is a type of genetically modified tobacco that has very low levels of nicotine and is useful as an alternative energy resource.
Various tests have been used on energetic tobacco planted in the Vale do Rio Pardo region, Rio Grande do Sul, in Brazil to assess the quality and possibility of planting it in the soil where previously traditional tobacco was cultivated [8][9] .The energetic tobacco seed, which is used for biodiesel extraction, generates approximately 40% oil 10 and appears to be a sustainable option for the production of biofuels 8,[11][12] .The process of extracting the oil from the tobacco seed produces tobacco residue as a byproduct (approximately 60%), which is a residue that does not yet have an adequate disposal destination 8 .Materials Research In this context, the objective of this work is to develop sustainable glass foams using tobacco residue as organic pore forming agents and glass powder obtained from glass bottles as a matrix.It is important to highlight the study's concern for a sustainable destination of waste in the environmental area, since this will provide added value to two significant types of industrial waste.
Materials and Methods
In this study, green glass bottles (the soda-lime type) and tobacco residue (T), (originating from oil extraction for biodiesel production,) were used as an alternative vitreous matrix and pore forming agents.
Samples of dried tobacco residue were milled (5 min in a in a ball mill (Servitech, CT-242) and subsequently sieved to ensure that the particle size was below 90 µm (170 Mesh).
The glass bottles were washed and dried at 110 ºC for 2 h.In a subsequent step, they were fragmented with a hammer and then milled for 120 min in a ball mill (Servitech, CT-242) until reaching an 80 mesh (177 microns) particle diameter.The glass powder was labeled GP.The chemical composition of glass powder was obtained by X-ray fluorescence (Philips, model PW 2400).The sample was prepared in pressed pellets.
To obtain the glass foams, different formulations were prepared (100% GP, 95% GP -5% T w/w, 85% GP -15% T w/w, 70% GP -30% T w/w and 55% GP -45% T w/w).The formulated compositions were homogenized and humidified with an additional 10% (w/w) of water for better conformation of the samples.The powders were compacted uniaxially at a pressure of 40 MPa in a hydraulic press (Nowak, PH30) to obtain glass foams with a size of (60x20x5) mm.The samples were fired at 850 ºC and 900 ºC at a heating rate of 10 ºC.min -1 for 60 min.True density ( ρ t ) of glass foams (crushed and milled cell walls) were determined using a helium pycnometer (AccuPyc 1340, Micromeritics).Apparent densities ( ρ a ) of glass foams were determined by relating their geometric dimensions (obtained using a caliper, model Mitotoyo) and their masses (obtained with analytical balance FA-2104N, Bioprecisa).Porosity (Ɛ) of glass foams was calculated from geometric measurements and true density was determined according to Equation 1: (1) Pore microstructure could be visualized from images of fracture surfaces of fired foams obtained in an optical microscope (Olympus, 3Z61).Mean pore size for the glass foams were determined by quantifications corresponding to the specified pore diameter ranges.This was based on the linear intercept method (ASTM E112-12 17 ) where the ratio between the average length string (t) and average sphere diameter (D) is determined by Equation 2 to better represent the measurement of a 3D unit (pore) by a 2D image (ASTM D3576−98R15 18 ). (2) In this case, five images of the fractured surfaces from each foam were used, and 200 measurements of each image, on average, were made with the aid of (ImageJ®) software.
The thermal conductivity of glass foams was determined in a TCi Thermal Conductivity Analyzer, C-THERM TECHNOLOGIES (0 to 100 W.m -1 .K -1 measurement range).
The compressive strength of glass foams was measured with nominal dimensions (10x10x10) mm in a universal test machine (EMIC, model DL 10000, cross speed 1.0 mm.min -1 ) according to ASTM C133 -97R15 (2015) 19 .Ethylene-vinyl acetate sheets were used on the samples for uniform charge distribution.
Results and Discussions
Table 1 shows the results of chemical analysis of the glass powder.It is mainly composed of silicon oxide, calcium oxide and sodium oxide.In addition to these oxides, the presence of aluminum oxide and magnesium oxide was also observed.These two oxides are typically found in soda-lime glass as a structural stabilizer which increases chemical durability 20 .When the amount of iron oxide varies between 0.1% and 0.8%, the clear glass turns green and brown.In this work, the glass bottles used were green, which justifies the iron oxide content.The chemical composition found for glass powders is typical of soda-lime glass 20 .
According to the approximate chemical analysis (Table 2), the T has 73.13% of volatile solids.This is due to degradation of hemicellulose, cellulose and lignin, which are constituents of the biomass.Volatiles are subdivided into gases, such as light hydrocarbons, carbon monoxide (traces), carbon dioxide and tar.After the degradation, fixed carbon (12.02%) and ashes (14.84%) remain.They have a significant amount of carbon that causes the formation of gases in temperatures between 600 and 1000 ºC.
By the chemical analysis of the tobacco residue it is possible to verify the main element present is silica, followed by potassium, calcium and magnesium.In addition, residual amounts of titanium, alumina, sodium and iron were observed.These compounds are commonly found in plants.The mass loss of the tobacco residue was 85%, corroborating with the results of approximate analysis, leaving ~ 15% ash.X-ray diffraction analysis of the ashes of this residue (Figure 1) shows that the crystalline phases present are quartz (JCPDS: 01-083-0539), potassium carbonate (JCPDS: 00-049-1093) and calcium carbonate (JCPDS:01-086-2343).The presence of the carbonates, together with the decomposition of fixed carbon with the increase in temperature, favors the formation of pores in the glass foams.
In order to produce glass foam, an adequat firing temperature is critical since it is directly related to the viscosity of the glass and its expansion caused by the release of gas from the decomposition of the pore forming agents.In this case, pores are formed in the vitreous matrix in temperatures up to 650 ºC.This is due to the gases released in degradation of hemicellulose, cellulose and lignin.These compounds act as a sacrificial material.These pores form but do not cause matrix expansion.They only occupy the place previously occupied by the tobacco powders.At temperatures above 600 ºC, the fixed carbon and ashes are responsible for an expansion of the vitreous matrix.This is due to the release of gases at a temperature which allows for suitable viscosity in the glass.The most convenient viscosity range for the expansion of glass foam production with maximum porosity corresponds to temperatures between 800-1000 ºC using sodalime glass [21][22] .The selected firing temperatures were based on previous work containing agroindustrial residues as pore forming agents [6][7]23 . In hese works, the best properties for the obtained glass foams were found at firing temperatures between 850 and 900 ºC.
Figure 2 shows the porosity of glass foams produced with different amounts of T fired at temperatures of 850 ºC and 900 ºC.The porosity of glass foams produced ranges from 36.7% to 83.5%.The increase in the amount of tobacco residue causes an increase in porosity mainly at the sintering temperature of 850 ºC.However, at 900 ºC, the glass foam containing 45% T obtained lower porosity values compared to glass foam containing 30% T. These results can also be observed in the optical microscopy images (Figure 3).This fact may be related to the high percentage of the porogenic agent added, which causes excess formation of gases that break the formed walls and consequently allows trapped air to escape.Teixeira, et al. 23 showed that with higher sintering temperatures there is a decrease in glass viscosity, which is not sufficient to maintain the cell structure, since 950 ºC, for example, is very close to the liquidus temperature of the glass (1000 ºC) 22 .The glass foams produced have similar porosity values as those found in other works and in commercial products processed under similar conditions 6-7,21,23-25 demonstrating the efficacy of the residues used to produce glass foams.
Figure 3 shows optical microscopy images of glass foams produced with different contents of tobacco and fired at 850 and 900 º C. It can be inferred that the samples are free of cracks, with uniformly distributed pores and closed porosity.Very similar microstructures are observed for all glass foams obtained.In addition, a variation in the porosity (pore quantity and size) is observed with the increase of tobacco residue, seen in Figure 2. At 850 ºC, the increase in the addition of tobacco residue results in greater porosity.At 900 ºC, similar behavior is observed, until additions of 30% residue.However, increasing the aggregation of residue, at this temperature, above 30%, a decrease in porosity occurs.This is possibly related to the escape of gases formed in large quantities which causes the breakage of cell walls.Research using glass residues and banana leaves as pore forming agents showed that the addition of an organic agent decreased the apparent density of glass foam with the increase in residue (0.31 and 1.03 g.cm -3 ), consequently increasing its porosity (58.5 to 87.5%) 6 .Glass foams produced from bottle glass residues by the emulsification method using vegetable oil as a porogenic agent presented similar behavior, with porosity varying between 74, 85 and 93% for additions of 50, 70 and 90% oil, respectively 26 .Table 3 shows the mean pore size of the glass foams produced containing 5, 15, 30 and 45% (mass) of tobacco residue and fired at 850 and 900 ºC.Pore sizes in the range of 0.16 to 0.25 mm can be observed for samples containing 5 and 15% T at the two firing temperatures.The small pores observed are mainly due to the low amount of pore forming agents.Furthermore, at 850 ºC an increase in pore size is observed with increases in the amounts of pore forming agent, up to 1.70.In this case the pore size can be controlled by the addition of pore forming agent since there is an expansion of the vitreous matrix as a result of more gases being released.On the other hand, at 900 ºC the increase in the amount of tobacco residue from 30 to 45% decreases the size of the pores, which reinforces the hypothesis that an escape of the formed gases is occurring.
Figure 4 shows XRD diffraction patterns of the amorphous structure of the glass powder (as prepared) and partially crystalline structure of the glass foams containing 45 vol.% of tobacco residue, fired at 850 and 900ºC.The main reflections were attributed to the crystalline phases of devitrite Na 2 Ca 3 Si 6 O 16 , (JCPDS-00-023-0671) and β-quartz (JCPDS-01-089-8949).Crystalline silica which comes from undissolved quartz still exists as the major crystal phase.As for devitrite, it is a typical devitrification product in commercial soda-lime-silica glass.
Crystallisation studies on soda-lime glass show that cristobalite is formed at 665-925 ºC and devitrite at 750-925 ºC in air atmosphere [27][28] due to the presence of CaCO 3 and K 2 CO 3 which could possibly work as nucleation sites in our soda-lime-silica glass, inducing crystallisation.However, in this work, only small amounts of these oxides are available which does not favor crystallization of cristobalite.
Previous works containing agroindustrial residues (banana leaf 6 ) show the formation of cristobalite and devitrite.In these cases, cracks observed in the microstructure of the samples were attributed to cristobalite crystallization.These cracks can be associated with both the heat treatment and the type of plant used (which may contain larger amounts of fluxing agents).
Figure 5 shows thermal conductivity results for glass foams produced after the addition of 5, 15, 30 and 45% of tobacco residue and fired at 850 ºC and 900 ºC.In general, thermal conductivity decreases as the porosity increases.This is the result of the contribution of a higher porosity, which reduces thermal conductivity, especially in cases where pores are closed and not interconnected.The behavior related to the increase of porosity with a decrease in thermal conductivity is related to the release of gas from the burning of organic material, generating spacings with thermal conductivity close to the air (0.023 W.m -1 .K -1 ).As sintering temperature increases from 850 ºC to 900 ºC, thermal conductivity decreases.In this case, although the porosities are relatively similar, there may be a greater contribution of the larger pores in the glass foams obtained at 900 ºC, as observed in Figure 3.The lower value of thermal conductivity obtained in this work is similar to the result of glass foams produced using organic waste as a foaming agent (ranging from 0.06 to 0.15 W.m -1 .K -1 ) 6 .Thermal conductivity values of glass foams obtained with organic porous agent were lower than traditional types of glass (1.00 W.m -1 .K -1 ) 29 and ranged from 0.72 to 0.087 W.m -1 .K -1 .These glass foams have similar characteristics to materials such as bricks and ceramic tiles (varying between 1.05 and 0.70 W.m -1 .K -1 , according to their density), concrete with expanded clay (1.05 and 0.17 W.m -1 .K -1 ) and fiber-cement (ranging from 0.95 to 0.65 W.m -1 .K -1 ) 29 .Glass foams produced from transparent glass bottles and dolomite presented thermal conductivity varying between 0.29 and 0.55 W.m -1 .K -1 30 . Figure 6 shows mechanical strength results obtained for the different formulations.It is possible to observe that mechanical resistance is strongly influenced by porosity, that is, the larger the porosity, the lower the mechanical resistance 6 .The glass foam with the highest porosity (30% tobacco residue fired at 900 ºC) has the lowest compressive strength (approximately 2.8 MPa).In addition, glass foam fired at 850 ºC, containing 45% T, which presented better thermal insulation characteristics, had a compressive strength of 2.1 MPa and the lowest resistance between the obtained foams.This is in agreement with values found in the literature [31][32] .
It is worth noting that, in the glass foams obtained with 30% tobacco residue fired at 850 ºC all have properties within the range of commercial foaming properties.That is, porosity above 60%, thermal conductivity of 0.08 and mechanical strength of approximately 2.8 MPa.The magnitude of the measured properties of the glass foams produced is adequate for a number of applications requiring low thermal conductivity.
Conclusions
Discarded glass bottles were converted into glass foams using tobacco residue (5-45% by mass) as a porogenic agent.Glass foams produced after sintering at 850 and 900 ºC have porosities between 36.7% -83.5%, mechanical strength between 34 MPa and 2.1 MPa and thermal conductivity between 0.72 and 0.087 W.m -1 K -1 .For the use as thermal insulation, glass foam containing 30% organic residue and fired at 850 ºC proved to be more efficient due to its low thermal conductivity (0.08 W.m -1 K -1 ), maintaining its main physical and mechanical characteristics with a compression ratio of 2.1 MPa.This glass foam synthesis process is relatively simple and does not require the use of any toxic additives.This combination provides advantageous properties for applications in sustainable constructions and energy efficiency.They contribute greatly to the sustainable life cycle of these materials and give additional value to tobacco residue.
Figure 4 .
Figure 4. XRD diffraction patterns of the amorphous structure of the glass powder (as prepared) and partially crystalline structure of the glass foams containing 45 vol.% of tobacco residue, fired at 850 and 900ºC.
Figure 5 .
Figure 5. Thermal conductivity for glass foams produced after addition of 5, 15, 30 and 45% (mass) of T and fired at 850 °C and 900 °C.
Table 1 .
Chemical composition of bottle glass powder and Tobacco residue.
Table 2 .
Proximate chemical and elemental analysis of tobacco residue samples.
Table 3 .
Mean pore size of the glass foams produced containing 5, 15, 30 and 45% (mass) of T and fired at 850 and 900 ° C. | 4,365.2 | 2018-12-03T00:00:00.000 | [
"Materials Science"
] |
Identification of Novel miRNAs and miRNA Dependent Developmental Shifts of Gene Expression in Arabidopsis thaliana
microRNAs (miRNAs) are small, endogenous RNAs of 20∼25 nucleotides, processed from stem-loop regions of longer RNA precursors. Plant miRNAs act as negative regulators of target mRNAs predominately by slicing target transcripts, and a number of miRNAs play important roles in development. We analyzed a number of published datasets from Arabidopsis thaliana to characterize novel miRNAs, novel miRNA targets, and miRNA-regulated developmental changes in gene expression. These data include microarray profiling data and small RNA (sRNA) deep sequencing data derived from miRNA biogenesis/transport mutants, microarray profiling data of mRNAs in a developmental series, and computational predictions of conserved genomic stem-loop structures. Our conservative analyses identified five novel mature miRNAs and seven miRNA targets, including one novel target gene. Two complementary miRNAs that target distinct mRNAs were encoded by one gene. We found that genes targeted by known miRNAs, and genes up-regulated or down-regulated in miRNA mutant inflorescences, are highly expressed in the wild type inflorescence. In addition, transcripts upregulated within the mutant inflorescences were abundant in wild type leaves and shoot meristems and low in pollen and seed. Downregulated transcripts were abundant in wild type pollen and seed and low in shoot meristems, roots and leaves. Thus, disrupting miRNA function causes the inflorescence transcriptome to resemble the leaf and meristem and to differ from pollen and seed. Applications of our computational approach to other species and the use of more liberal criteria than reported here will further expand the number of identified miRNAs and miRNA targets. Our findings suggest that miRNAs have a global role in promoting vegetative to reproductive transitions in A. thaliana.
Introduction
Plant microRNAs (miRNAs) are involved in multiple developmental and physiological processes and negatively regulate gene transcript abundance through post-transcriptional repression of mRNAs, primarily by target cleavage [1]. MiRNAs are generated from endogenous loci that produce transcripts with internal stem loop structures that are processed to 20,25nt small double stranded RNAs. Many proteins of the miRNA biogenesis pathway are known. RNA polymerase II generates pri-miRNAs which are stabilized by DAWDLE (DDL) [2]. Pri-miRNAs are converted to stem-loop pre-miRNAs by DICER-LIKE1 (DCL1) [3] which interacts with the double stranded RNA-binding protein HYPO-NASTIC LEAVES1 (HYL1) [4] and SERRATE (SE) [5]. The pre-miRNAs are processed either to 21 nt mature miRNA/ miRNA* duplexes by DCL1 [4] or to 24 nt mature miRNA duplexes by DCL3 [6]. The mature miRNA duplexes are methylated by the S-adenosyl methionine-dependent methyltransferase HUA ENHANCER1 (HEN1) [7]. HASTY (HST) is the plant homolog of mammalian EXPORTIN 5 which is known to export pre-miRNA [8]. One strand of the methylated miRNA/ miRNA* duplex is preferentially assembled with the ARGO-NAUTE1, AGO1 protein, which slices the mRNA targets at the miRNA target site [9]. Despite the existence of this core pathway, its mutants have different effects on miRNA abundance and miRNA target abundance. Hypomorphic dcl1 mutants have undetectable or very low levels of mature miRNAs [10], and miRNA accumulation is similarly undetectable or very weak in null hen1 and hyl1 mutants [11,12]. Although HST is frequently depicted as an exportin [1], its function has not been validated, and hst mutants fail to accumulate miRNAs in the nucleus [13]. In hst mutants, some miRNAs accumulate to wild-type levels, others have reduced abundance, and others are not detectable [13].
Over 184 Arabidopsis miRNAs have been identified (miRBASE release 10.0) [14]. miRNAs have been predicted to regulate the expression of more than 600 genes [15], and 225 genes are known targets [16]. miRNAs and their targets have been discovered using approaches including cloning and sequencing sRNAs [10,17], bioinformatic prediction from genomic sequences [18], and sequencing cleaved mRNAs by parallel analysis of RNA ends (PARE) [19]. Utilizing miRNA biogenesis/transport mutants for miRNA and miRNA target identification has not been widely employed. First, many miRNA target transcripts do not accumulate when their cognate miRNAs decrease. In one study of hen1 and dcl1 mutants, miRNA target abundances were greater than wild type in eight of eight known targets examined [12]; while in another study, five of ten transcripts were significantly upregulated [20]. Two of three miRNA targets accumulate within the hst-1 mutant [13], and five of eight target transcripts had higher abundance in the hyl1 mutant compared to wild-type [12]. Second, a large number of genes are misexpressed in individual mutants causing an abundance of upregulated genes that are not miRNA targets [21,22].
The core function of plant miRNAs is in the regulation of development [23]. Hypomorphic dcl1 mutants and null hyl1, hst, and hen1 mutants reveal both shared and distinct developmental defects that may represent misexecution of developmental transitions [24]. All canonical 21nt miRNA mutants (dcl1, hen1, hst, and hyl1) have a shorter stature, delayed vegetative to reproductive transitions, and reduced female fertility compared to wild type [5,12,25,26]. Hen1 mutants have defects in floral meristem identity, a trait also shared by dcl1 partial loss-of-function mutants [11,25], and the juvenile development phase of hst15 is shortened [26]. The effects of many individual misexpressed miRNA targets also highlight the role of miRNAs in plant development. Misexpression of miRNA target genes leads to plant developmental defects in meristems (HD-ZIPIII genes) [27], leaves (TCP) [28], flowers (AP2 genes; CORN-GRASS1) [29,30], and roots (NAC1) [31]. Misexpression of targets also affects plant vegetative phase changes [5,32]. Despite these phenotypic observations, to our knowledge it is unknown if disrupting plant miRNAs can cause one tissue's transcriptome to resemble that of a different tissue. For example, in animals, delivering miRNAs into cells can cause their transcriptomes to resemble the transcriptome of the tissue where the miRNA is preferentially expressed [33].
This study performs novel analyses on a number of published data sets to identify miRNAs and their targets and to identify miRNA dependent tissue biases within the transcriptome. We integrate data sets including microarray profiling and sRNA deep sequencing data from miRNA biogenesis/transport mutants, microarray profiling data of mRNAs in a developmental series, and computational predictions of conserved, genomic stem-loop structures. Our results show that known miRNA targets fail to explain transcriptome patterns amongst miRNA mutants. Interestingly, transcript changes in hyl1 and hst mutants greatly overlapped, suggesting a novel functional connection between HST and HYL. Transcript changes in dcl1 and hyl1 were surprisingly distinct, and dcl3 had little effect on the transcriptome. We identified novel miRNA targets and five mature miRNAs, four of which had high similarity to previously identified mature miRNAs. One miRNA gene encodes two complementary miRNAs that target distinct transcripts. These miRNAs target transcription factors, and a gene with 4-a-glucanotransferase activity, thereby expanding miRNA functionality in metabolism. Finally, we found that genes regulated by miRNAs show strong tissue-specific patterns of expression. miRNA regulated genes tend to be highly expressed in the inflorescence, and miRNAs cause the inflorescence transcriptome to both diverge from a meristem and leaf-like state and to acquire a pollen and seed-like state.
Results
Known miRNA targets do not explain miRNA-defective mutant transcriptome patterns We first analyzed ATH1 gene expression data from the inflorescences of the miRNA-defective mutants, dcl1-7, dcl3-1, hen1-1, hyl1-2 and hst15 [21,34] (Figure 1). The numbers of known, up-regulated miRNA targets and the levels to which known miRNA targets were up-regulated were both poorly correlated with the number of misexpressed transcripts across the canonical miRNA mutants. We found that probe sets homologous to 131 of 225 known miRNA targets are present on the ATH1 microarray, excluding cross hybridizing probe sets. The number of known, upregulated miRNA targets in hst15 (29) was less than the number in other canonical mutants (44 in dcl1; 37 in hyl1; and 38 in hen1; Figure S1), although 1,995 genes are upregulated in the hst15 mutant ( Figure 1). The log-fold change distributions of known miRNA targets were also very similar between mutants with large transcriptome changes and mutants with small transcriptome changes ( Figure S2). Differences and similarities of transcriptome changes between mutants were also not explained by known miRNA targets, as the number of known miRNA targets shared between two mutants was not correlated with the number of upregulated genes shared between two mutants. Of the 930 upregulated genes in hyl1-2, 65% of transcripts increased in hst15, 35% in dcl1-7, and 44% in hen1-1 ( Figure 2A). Of the 1,995 upregulated genes in hst15, 30% transcripts increased in hyl1-2, 17% in dcl1-7, and 12% in hen1-1 (Figure 2A). hst and hyl1 shared 18 known miRNA targets, the same number as hst15 and dcl1-7 and less than between hen1 and hyl1 (24) ( Figure S3). Likewise, dcl1 and hen1 have similar transcriptomes-of the 1,710 up-regulated genes in hen1-1, 49% of the transcripts increased in dcl1-7 (Figure 2A), and of the 4,238 up-regulated genes in dcl1-7, 20% of the transcripts increased in hen1-1 ( Figure 2A). However, the known targets' overlap between dcl1-7 and hen1-1 (22) was about as great as those between dcl1-7 and hyl1-2 (24), and only slightly more than the overlap between dcl1-7 and hst15 (18) ( Figure S3).
These analyses also revealed two unexpected results. First, the similarity of transcript abundance changes in hst15 and hyl1-2, and the differences between dcl1 and hyl1 were unexpected given the predicted miRNA biogenesis/transport pathway [1]. The high level of hst15 and hyl1-2 intersection was described above. In contrast, 35% of the transcripts that increased in hyl1 increased in dcl1-7, and 8% of the transcripts that increased in dcl1 also increased in hyl1 (Figure 2A). The down-regulated genes showed similar intersections ( Figure 2B). Second, disrupting 21nt miRNA biogenesis had a severe effect on the plant transcriptome; while disrupting long miRNA biogenesis and siRNA biogenesis had a small effect. The number of genes with transcript levels that increased relative to wild type controls ranged from 930 to 4,238 among the canonical 21nt miRNA biogenesis mutants dcl1-7, hen1-1, hst15, and hyl1-2 ( Figure 1). The number of transcripts that decreased ranged from 867 to 2,172. In contrast, 258 genes increased in abundance and 210 genes decreased in abundance in the dcl3-1 mutant (Figure 1).
Computational prediction of novel miRNAs and targets
Our results suggested that known miRNA targets fail to explain transcription patterns amongst miRNA mutants, and we devised a method to identify both novel miRNAs and miRNA targets. The ATH1 array contains approximately 22,750 probe sets representing 23,750 genes. We reasoned that the transcripts that changed within the mutants included mRNAs to which miRNAs bind and cleave and downstream transcripts influenced by these direct targets. To identify novel miRNAs and miRNA targets, we defined a core set of genes up-regulated across the dcl1-7, hen1-1, hyl1-2 and hst mutants. This set contains 117 genes (123 probe sets changed significantly across all mutants (Figure 2A), but six probe sets cross-hybridized with multiple genes and were removed).
Transcription factors are over-represented among known miRNA targets [35]. To infer if our core set likely contained target genes, we evaluated the frequency of GO SLIM gene ontology terms within the set. Transcription factors occurred twice as frequently as expected (12% vs. 6%), ( Figure S4; Table 1; Fisher's Exact Test P,0.001), and the biological process ''transcription'' was over-represented within the up-regulated genes (6% vs. 4%, Table S1). Interestingly, genes classified in the ''response to abiotic or biotic stimulus'' biological process were also more frequent within the up-regulated genes as compared to the non-upregulated genes (6% vs. 3%, Table S1), and genes with unknown molecular functions occurred at less than half the expected frequency among up-regulated genes (11% vs. 24%, Table 1). Genes without GO SLIM terms were not inherently less likely to change in abundance than genes with GO SLIM terms, because the number of genes with unknown molecular functions among down-regulated genes is similar to their genome proportion (Table 1). Among the 105 genes significantly down-regulated across the mutants, there was no evidence that molecular function classes or biological processes were over or under represented ( Table 1; Table S1; Fisher's Exact Test P.0.01).
The core set of 117 genes up-regulated across all four canonical miRNA biogenesis mutants represented a conservative starting point to identify novel miRNAs and targets. We searched for high complementarity between a set of 1,984 sRNA sequences generated by deep sequencing of sRNAs from the A. thaliana rdr2-1 mutant [10] and 158 predicted mRNAs derived from the 117 up-regulated genes, allowing for three or fewer mismatches. We identified 113 sRNAs complementary to 76 putative mRNAs that were derived from 56 of the 117 genes. We ran a BLAST analysis of the 113 sRNAs against 2,585 conserved Arabidopsis 20mers that have homology to conserved genomic loci that could generate a hairpin structure (AtSet3) [18]. Forty of the 113 sRNAs were perfectly matched by 20mers in AtSet3. Twenty-nine were previously characterized miRNAs. From the remaining eleven sRNAs, we identified five novel, mature miRNA sequences. Three of the five mature miRNAs (miRNAs 3, 4, and 5) are encoded by two MIR169 genes on chromosomes 3 and 5 ( Table 2). MiRNA 3 is novel. The other mature miRNAs differ from the mature miRNAs in miRBase entries MIR166a, MIR169a, MIR169b, MIR169f and MIR169g by between one or two nucleotides. All candidate miRNAs were expressed in the rdr2 mutant and were not present in sequenced sRNAs from the dcl1 mutant (Table 3). Only miRNA 2 was found in wild type. These miRNAs have low abundance (Table 3), but the abundance is not unusual relative to other known miRNAs. Lu et al. found that 65% (30 out of 46) of known miRNAs have a count equal or less than six out of 4,573 sRNAs sequenced in a 454 analysis of the rdr2 mutant inflorescence [10].
Pre-miRNA secondary structures were predicted by RNAfold [36] and evaluated by MIRcheck [18]. The predicted secondary structures are shown in Figure S5. Interestingly, miRNAs 3 and 4 have homology to complementary sequences in the same stem loop of MIR169a ( Figure 3). One miRNA has high complementarity with the disproportionating enzyme (DPE2; At2g40840), which has 4-a-glucanotransferase activity and is an essential component of the pathway from starch to sucrose in leaf cells [37]. At2g40840 is relatively highly abundant in leaves, meristems and developing siliques and less abundant in pollen, seeds, and siliques in late developmental stages. The other miRNA has high complementarity with two CCAAT-binding transcription factors (At1g17590, At1g54160). The mature miRNAs 1, 2, 4, and 5 have high complementarity to transcription factor encoding mRNAs targeted by MIR166 and MIR169 miRNAs [18,21] (Table 4); however mature miRNAs 2, 4 and 5 have predicted novel target cleavage sites within these transcripts. We also observed that the CCAAT binding transcription factor At1g54160 is targeted by different mature miRNAs (1, 4, and 5). These findings revealed that one miRNA can regulate multiple target genes, and one gene can be targeted by multiple miRNAs.
Tissue specific transcriptional patterns of miRNA regulated genes
We tested if genes mis-expressed in miRNA mutants have tissue-specific patterns of expression. To determine this, we computed the ranks of the genes up-regulated and down-regulated in the canonical miRNA mutant inflorescences across 23 tissues. Tissues included roots, meristems, leaves, flowers, siliques, seeds, and mature pollen [38]. If genes up-or down-regulated across mutants had high or low transcript abundances within a tissue, these genes had high or low ranks within that tissue, respectively. We also ranked the transcripts that did not change in abundance amongst the mutants in each of the 23 tissues to obtain the expected distribution of gene expression ranks within each tissue. Significant differences in rank distributions were tested using the Table 1. Goslim categories in molecular function (MF) of differentially expressed genes and non-differentially expressed genes in dcl1-7, hen1-1, hyl1-2 and hst15. Komolgorov-Smirnov (KS) test (see materials and methods). We found that up-regulated core set genes were significantly abundant in the inflorescence relative to other tissues ( Figure 4). This finding suggested that known miRNA targets would also be highly abundant within the inflorescence. Indeed, known targets were highly abundant within the inflorescence relative to other tissues ( Figure 4). Interestingly, the genes down-regulated in the mutants were also highly expressed in the inflorescence relative to other tissues ( Figure 4). We also investigated whether miRNAs could cause the transcriptome of one tissue to resemble the transcriptome of another tissue. Using the tissue corrected distributional bias test (see materials and methods), we found that the up-regulated genes in miRNA biogenesis mutant inflorescences were preferentially expressed in wild type leaves and meristems ( Figure 5A), and less expressed in pollen and seeds ( Figure 5B). The down-regulated genes in miRNA biogenesis mutants were preferentially expressed in wild-type pollen, siliques and seeds ( Figure 5B), and less expressed in roots, meristems and leaves ( Figure 5A). Thus mutations in miRNA biogenesis genes cause the inflorescence transcriptome to resemble the leaf and meristem transcriptomes. In addition, the mutations make the inflorescence transcriptome less similar to mature pollen and seed transcriptomes.
Discussion
Transcriptional patterns of 21nt and 24nt miRNAdefective mutants Across canonical miRNA biogenesis/transport mutants, the number of misexpressed, known miRNA targets did not correlate with the number of transcripts that changed in abundance. In addition, the number of known miRNA targets upregulated between mutants did not correlate with the number of mRNAs upregulated between mutants. Thus, we postulated that transcriptome differences amongst mutants are due to roles of the biogenesis proteins in processes outside of miRNA biogenesis and/ or that a number of miRNA targets have not been identified. We examined an intersection of four mutant transcriptomes to identify novel miRNAs and miRNA targets.
Analysis of the miRNA mutant transcriptomes also showed that the pattern of transcriptional changes amongst mutants was not always consistent with the current model for miRNA biogenesis/ transport [1], and that dcl3 had little effect on the transcriptome. Transcripts upregulated in both hyl1 and hst were the same almost two-times more often than the transcripts that changed in other hyl1 and hst comparisons, and a relatively low number of transcripts were shared between dcl1 and hyl1. Of the 930 transcripts upregulated in hyl1, 65% were upregulated in hst15, and of the 1,995 transcripts upregulated in hst15, 30% were found in hyl1 (Figure 2A-2B). In Arabidopsis, RISC loading may occur both in the nucleus and in the cytoplasm [39]. One could envision HYL1 shuttling a subset of mature miRNAs to HST for export while other miRNA duplexes are integrated into the nuclear RISC. However, of the 37 known miRNA targets up-regulated in hyl1 and of the 29 known miRNA targets upregulated in hst, 18 were shared ( Figure S3), a number similar to other mutant pairs. As mentioned above, the role of HST as an exportin involved for miRNA transport has not been confirmed [13,26]; we suggest that HYL may interact with HST in the nucleus to facilitate mature miRNA processing. In contrast, we had expected the highest overlap of transcript changes between dcl1 and hyl1 because miRNA targets accumulate less in hyl1 than dcl1 [12], and HYL1 interacts with DCL1 to promote the precise processing and efficient generation of miRNAs [4]. Only eight percent of dcl1 transcripts overlapped with hyl1, and only 35% of hyl1 transcripts overlapped with dcl1 ( Figure 2A). The hypomorphic dcl1 mutant used in this study, dcl1-7, has a mutation in the helicase domain [25]. We considered the possibility that dcl1-7 could still process HYL1 dependent miRNAs. However, dcl1-7 has been shown to fail to process miR163 which is impaired in hyl1 [3], and the number of shared known miRNA targets among up-regulated genes (24) is higher between dcl1 and hyl1 than between dcl1 and other mutants ( Figure S3). The function of HYL1 in miRNA biogenesis is thus likely DCL1-dependent, and the genes affected in the hyl1 mutant that did not overlap with dcl1 likely reflect other roles for this protein. HYL1 was recently shown to bind to short interspersed element (SINE element) RNA and influence a variety of cellular processes [40]. Future work could examine the relationship amongst SINEs and the gene transcript abundance changes in the HYL1 mutant. As expected, the dcl1 and hen1 mutants had a high number of shared transcript changes [3,41]. DCL3 generates 23 to 25nt miRNAs from a number of the same miRNA precursors processed by DCL1 and is also necessary to process a number of 23-to 25-nt repeat-associated siRNAs (ra-siRNA) associated with heterochromatin and DNA repeats [10,42]. The dcl3 mutant had a small effect on the transcriptome with 258 and 210 transcripts up-regulated and down-regulated, respectively. This result supports the hypothesis that long miRNAs processed by DCL3 are functionally inert [1], despite the fact they are developmentally regulated and conserved over time [6], and the result is consistent with the limited role of repeats in Arabidopsis gene regulation [43].
The discovery of novel miRNAs
We hypothesized that a core set of 123 genes up-regulated among all the canonical miRNA mutants (Figure 2) would contain a number of novel miRNA targets. Transcription factors are known preferential, direct targets for miRNAs [18], and among the core set of up-regulated transcripts, only the ''transcription factor activity'' GO molecular function term was highly overrepresented (Table 1). This result was consistent with the expectation that these genes contained a number of direct miRNA targets. Interestingly, only the ''unknown molecular functions'' term was significantly under-represented amongst up-regulated genes ( Table 1). The small number of upregulated genes with an unknown molecular function suggests that miRNAs regulate genes that have a noticeable mutant phenotype and thus have a high chance of experimental characterization and discovery. We had also anticipated that the 123 genes would contain downstream miRNA targets that were involved in specific molecular functions or biological processes. Because only transcription factors were over-represented, we conclude that miRNA regulated downstream genes have a range of molecular functions and are involved in a number of biological processes.
By integrating a number of lines of evidence, we identified five novel mature miRNAs. Four were highly similar to previously characterized miRNAs. The novel mature miRNAs met criteria for the annotation of plant microRNAs (Table 2) [44]. The mature 20,21 nt miRNAs are expressed ( Table 3). As expected, the miRNA precursors contain extensive base-pairing, stable and conserved stem-loop structures. No asymmetric bulges exist between the miRNA and the opposite stem-arm in the stem-loop ( Figure S5). The novel mature miRNAs have high complementarity with their predicted target sites and meet empirical sequence parameters for miRNA:target recognition such as no mismatches at position 10 and 11 of the 59 end of miRNAs and no more than one mismatch at positions 2-12 ( Figure S6) [45]. MiRNA 3 targets a novel mRNA. The other four mature miRNAs target mRNAs that are known targets of other miRNAs. Three of these four novel miRNAs direct mRNA cleavage at novel positions ( Figure S6). This study identified miRNAs using only inflorescence transcriptome data and conservative criteria: putative targets had to be misexpressed in all mutants, and targets and miRNAs could differ by at most three nucleotides. It is very likely that analyses of individual biogenesis mutants and other biogenesis mutant tissues using the same or more liberal criteria would identify additional novel miRNAs and miRNA targets.
As described above, miRNAs are processed from a miRNA duplex. Mature miRNAs guide RISC to silence target mRNAs, and the complementary miRNA* is gradually degraded [39,42]. Interestingly, one miRNA gene encodes miRNAs 3 and 4 from the same pre-miRNA stem loop (Table 2, Figure 3). One miRNA targets At2g40840, an enzyme involved in the starch to sucrose transition. The complement targets CCAAT-binding transcription factors. Xue et al. [46] suggested that high levels of a miRNA* may suppress the function of a miRNA. Because we identified miRNAs based on the reduction of putative targets, both miRNAs identified here very likely function to cleave target mRNAs. This discovery is similar to previous reports in mammals in which RISC was able to cleave the antisense of let-7 target genes when the Figure 4. Known miRNA targeted genes, and genes up or down-regulated across mutants were highly abundant within the inflorescence. The inflorescence expression ranks of genes within these groups were significantly higher than ranks of genes outside these groups. Log (base 10) P values are plotted for three inflorescence tissues (FL1, FL2, and FL3). The dashed line shows an a critical value of 0.01. doi:10.1371/journal.pone.0010157.g004 miRNA/miRNA* duplex was provided [47]. Both strands of miRNA can also suppress the expression of mouse transcripts [48].
miRNA regulated genes have tissue-biased expression
We found that both up-and down-regulated genes in the inflorescences of miRNA biogenesis mutants were highly expressed in wild-type inflorescences relative to other tissues ( Figure 4). This observation suggests that miRNAs as a class spatially restrict target transcripts within tissues and/or affect target transcripts at a specific developmental time rather than eliminate transcripts from whole tissues [1]. Co-expression of a miRNA and its target is consistent with this interpretation. miR171 and its targets SCL6-III and SCL6-IV are highly expressed in inflorescences [17]. In rice, osa-miR160, osa-miR164 and osa-miR172 are co-expressed with their targets in root, leaf, seedling, endosperm and embryo [46].
Using the distributional bias test, we also found that genes upregulated in the 21nt miRNA biogenesis mutants' inflorescences were preferentially expressed in leaves and meristems and less expressed in pollen and seeds ( Figure 5A). Genes down-regulated within the mutants' inflorescences are significantly abundant in wild type pollen and seed and significantly low in meristems, roots and leaves ( Figure 5B). Thus, miRNA mutants cause the inflorescence transcriptome to resemble leaf and meristem transcriptomes and to diverge from pollen and seed transcriptomes. A number of developmental and molecular observations are consistent with this observation. The dcl1 mutant displays defects in embryo development, floral meristem identity, and delayed flowering [25], and hen1 and hyl1 have similar developmental defects as dcl1 [11,12,25]. Meristem and auxin related genes accumulate in the hyl1 mutant inflorescences [12]. SE, along with DCL and HYL1 functions in primary microRNA processing [5]. Some siliques from F1 progeny of se and hyl1 contained the abortive seeds because the se hyl1 double mutant is embryonically lethal [5]. Finally, overexpression of an AP2 cDNA with mismatches to miR172 caused enlarged floral meristems and many whorls of petals or staminoid organs [29]. Despite these observations, it was not clear a priori that loss of miRNAs as a class would cause one tissue's transcriptome to resemble that of another because different miRNA:target interactions are known to have opposite functions. For example, overexpression of miRNA156 in maize prolongs juvenile development while expression of miR172 promotes the transition to the adult phase of growth [30,32]. It would be interesting to examine how miRNAs globally alter the transcriptomes in tissues other than the inflorescence.
In conclusion, analysis and integration of large mRNA profiling datasets, sRNA deep sequencing data, and computational predictions of conserved genomic stem-loop structures revealed novel mature miRNAs, novel miRNA targets, and miRNAregulated developmental changes in gene expression in the model plant Arabidopsis thaliana. miRNAs have been identified in the important crop species maize [49,50] and rice [46,51]. It would be interesting to see if miRNAs in these diverse agriculturally important species also promote reproductive transcriptome changes.
Materials and Methods
Evaluating transcript abundance changes and tissue-biased expression ATH1 microarray raw data (.cel files) from wild type and miRNA-defective mutants, dcl1-7, dcl3-1, hen1-1, hyl1-2 and hst15 were kindly provided by Dr. Carrington's lab. Plant growth conditions, RNA extractions, labeling and hybridization were described by Allen et al., [21]. Arrays were hybridized with cRNA derived from inflorescence RNA. We used data from three arrays from each mutant line and three wild type lines. We normalized data using gcRMA implemented in R [52]. The expression level of each gene was represented by the mean of the log2-transformed, normalized and median polished signal levels across each set of tissue replicates, and significant differences between mutant and wild type were determined using linear models in the Bioconductor LIMMA package with a Bayesian correction for standard error. Differences were deemed statistically significant with a false discovery rate (FDR) of 0.05. We defined core sets of genes as those genes whose transcript abundance was higher or lower across all the canonical miRNA mutants.
To determine the tissue abundance of genes that were misexpressed in miRNA mutants, we obtained Affymetrix ATH1 data described by Schmid et al. [38]. We selected expression data from 23 of 79 tissues excluding similar tissue types to avoid over-representation in statistical analyses. Tissue descriptions and abbreviations are given in Table S2. Each gene's expression levels were ranked over all 23 tissues. We determined if core sets of genes had high ranks or low ranks within a tissue compared to the ranks of a reference group, the genes not included within the core sets. A gene in a core set with a high rank within a tissue meant that the gene's transcript abundance was high in the tissue relative to other tissues.
The Komolgorov-Smirnov (KS) test was used to identify tissues in which core sets of up-regulated or down-regulated genes had significantly high or low abundances. The mutant transcripts were sampled from the inflorescence, and thus a priori may have had high ranks in tissues with transcriptomes more like the inflorescence than other tissues. To avoid this bias, we compared the abundance of miRNA-regulated genes across tissues with genes that have the same expression ranks in the inflorescence. We randomly chose sets of genes which had the same expression ranks as genes in the core sets in the inflorescence 1,000 times. For each gene set, we applied the KS test. The core sets' observed KS p values were compared with the KS p values from the permuted data set to determine the significance of the core set KS value. We named this approach the tissue corrected distributional bias test. A core set had significantly higher or lower transcript levels in the tissue of interest relative to other tissues if the P-value was less than 0.01.
Computational analyses were performed on a high performance computing ''cluster of clusters'', the Shared Hierarchical Academic Research Computing NETwork (SHARCNET). We utilized the cornfish, narwhal, and whale clusters each with 14, 1,074 and 3,082 processors respectively. SHARCNET enabled rapid computations and the execution of some analyses that required large memory configurations (up to 16GB per processor).
Identifying novel miRNAs and corresponding targets
Predicted A. thaliana genomic and mRNA sequences were retrieved from GenBank RefSeqs (accessions: NC_003070.6, NC_003071.4, NC_003074.5, NC_003075.4, and NC_003076.5). A set of 2,585 Arabidopsis 20mers (AtSet3) which are located in potential hairpin structures typical of miRNA precursors and are conserved in rice was kindly provided [18]. Putative miRNA sequences generated by 454 sequencing were downloaded from NCBI. This data set contained 1,984 unique sRNAs derived from rdr2 inflorescence tissue which is enriched for miRNAs [10]. We compared transcripts whose abundance increased among mutants to both the sRNAs and the AtSet3 list of sequences to identify direct miRNA targets. First, the 1,984 sRNAs were blasted against the mRNAs of up-regulated genes. Three or fewer mismatches between a sRNA and an mRNA were considered a hit. Second, we determined the presence of the matched sRNAs within AtSet3, allowing only perfect matches between the sRNAs and AtSet 3 sequences. To visualize hairpin structures, ,500 nt genomic sequences centred on each matched sRNA were retrieved from the GenBank RefSeq records. With those genomic sequences, RNAfold implemented in ViennaRNA-1.8.1 [36] was used to predict the secondary structure. The RNAfold-predicted secondary structure was tested for miRNA hairpins and evaluated for a miRNA and miRNA* duplex by MIRcheck. Figure S1 The frequency of known miRNA targets amongst genes up-and down-regulated in the miRNA biogenesis mutants. Known miRNA targets were highly represented amongst upregulated genes. Table S1 Goslim categories in biological process (BP) of differentially expressed genes and non-differentially expressed genes in dcl1-7, hen1-1, hyl1-2 and hst15. | 7,372.4 | 2010-04-13T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
Mitochondrial Dysfunction and the Aging Immune System
Mitochondria are ancient organelles that have co-evolved with their cellular hosts, developing a mutually beneficial arrangement. In addition to making energy, mitochondria are multifaceted, being involved in heat production, calcium storage, apoptosis, cell signaling, biosynthesis, and aging. Many of these mitochondrial functions decline with age, and are the basis for many diseases of aging. Despite the vast amount of research dedicated to this subject, the relationship between aging mitochondria and immune function is largely absent from the literature. In this review, three main issues facing the aging immune system are discussed: (1) inflamm-aging; (2) susceptibility to infection and (3) declining T-cell function. These issues are re-evaluated using the lens of mitochondrial dysfunction with aging. With the recent expansion of numerous profiling technologies, there has been a resurgence of interest in the role of metabolism in immunity, with mitochondria taking center stage. Building upon this recent accumulation of knowledge in immunometabolism, this review will advance the hypothesis that the decline in immunity and associated pathologies are partially related to the natural progression of mitochondrial dysfunction with aging.
Introduction
The ancestry of the mitochondrion originated~2.5 billion years ago within the bacterial phylum α-Proteobacteria, during the rise of eukaryotes [1]. The endosymbiotic theory, advanced with microbial evidence by Dr. Lynn Margulis in the 1960s, proposed that one prokaryote engulfed another resulting in a quid pro quo arrangement and survival advantage [2]. The ability of mitochondria to convert organic molecules from the environment to energy led to the persistence of this pact.
Since most cells contain mitochondria, the clinical effects of mitochondrial dysfunction are potentially multisystemic, and involve organs with large energy requirements [3]. In addition to making energy, the basis of life, mitochondria are also involved in heat production, calcium storage, apoptosis, cell signaling, biosynthesis, and aging-all important for cell survival and function [4][5][6][7]. A decline in mitochondrial function and oxidant production has been connected to normal aging and with the development of a variety of diseases of aging. These topics are explored more thoroughly in other articles in this special edition. While the human immune system undergoes dramatic changes during aging, eventually progressing to immunosenescence [8], the role of mitochondrial dysfunction in this process remains largely absent in the literature. Consequently, the purpose of this review is to highlight three important issues in the aging immune system: (1) inflammation with aging; (2) susceptibility to viral infections; (3) impaired T-cell immunity. These clinical phenotypes will be related to our current knowledge on the role of the mitochondria in immune function. As the associations discussed are largely speculative, it is hoped that this review will serve as a stimulus for further investigation into these issues. nuclear gene and key regulator of mtDNA transcription and replication, activates immune cells via receptors for advanced glycation end products (RAGE) and TLR9 [23,24]. Products of oxidative phosphorylation (OXPHOS) can also stimulate innate immune cells. Released from apoptotic or necrotic cells, ATP binds to purigenic receptors initiating inflammation [25], while mtROS modifies core immune signaling pathways involving hypoxia inducible factor 1 alpha (HIF1α) and nuclear factor kappa light chain enhancer of activated B-cells (NFkB) [26,27]. Mitochondrial damage associated molecular patterns (DAMPs). DAMPs derived from mitochondrial components may be released during cellular injury, apoptosis or necrosis. Once these mitochondrial components are released into the extracellular space, they can lead to the activation of innate and adaptive immune cells. The recognition of mitochondrial DAMPs involves toll-like receptors (TLR), formyl peptide receptors (FPR) and purigenic receptors (P2RX7). By binding their cognate ligands or by direct interaction (i.e., reactive oxygen species, ROS), intracellular signaling pathways such as NFkB and the NLRP3 inflammasome become activated resulting in a proinflammatory response. TLR4 = toll-like receptor 4, TLR9 = toll-like receptor 9, P2RX7 = purigenic receptor, FPR1 = formyl peptide receptor 1, NLRP3 = NLR Family Pyrin Domain Containing 3, fMet = N-formylmethionine, mtROS = mitochondrial reactive oxygen species, mtDNA = mitochondrial DNA, Tfam = transcription factor A, mitochondrial, RAGE = receptors for advanced glycation end-products, NFkB = nuclear factor kappa-light-chain-enhancer of activated B cells.
Is Increased Susceptibility to Viral Infections Related to Depressed Mitochondrial Anti-Viral Signaling Pathways?
In general, older adults are more susceptible to a variety of viral infections, especially respiratory viral infections, resulting in high morbidity and mortality. For example, adults over the age of 65 exhibit a vulnerability to influenza A virus (IAV), and account for ≥90% of IAV-related deaths annually [31,32]. Type I interferons (e.g., IFN-α and IFN-β) are essential cytokines involved in the host antiviral response. Secreted by numerous cell types such as lymphocytes, monocytes, macrophages, dendritic cells, fibroblasts, endothelial cells, osteoblasts and others, type I interferons: (1) limit viral spread by inducing antiviral states in infected and neighboring cells; (2) stimulate antigen presentation and natural killer cell function; and (3) promote antigen-specific T and B cell responses and immunological memory. Interestingly, mitochondria play a major part in innate immune signaling against viruses and the production of type I interferons and will be discussed further.
RLRs (e.g., RIG-I and MDA5) are cytosolic receptors that recognize viral RNA. Consequent to binding viral RNA, RIG-I and MDA5 mobilize the mitochondrial antiviral signaling protein (MAVS) [33,34]. MAVS is a 56 kDa protein which contains an N-terminal caspase recruitment domain (CARD), a proline-rich region and a C-terminal transmembrane domain. Anchored on the outer membrane of the mitochondria, peroxisomes and mitochondrial associated membranes (e.g., endoplasmic reticulum), MAVS assembles into prion-like aggregates following RIG-I or MDA5 binding ( Figure 2). MAVS aggregates serve as a scaffold to recruit various TNF receptor associated factors (TRAFs), resulting in phosphorylation and nuclear translocation of interferon regulatory factors (IRFs) [35]. Downstream of MAVS, IRF3, IRF5 and IRF7 bind to their cognate promoters, leading to the production of type I interferons [36]. The localization of MAVS to the outer mitochondrial membrane is not coincidental. MAVS activity has been found to be dependent upon intact mitochondrial membrane potential, and by extension OXPHOS function [37]. To date, studies addressing MAVS function during aging and its relationship to waning antiviral immunity are lacking. Decreased mitochondrial membrane potential, mitochondrial dysfunction and declining mitophagy occur in a variety of aging cell types [38,39], raising the question of whether MAVS dysfunction can occur due to mitochondrial failure with aging. Mitochondrial respiratory capacity is impaired in aging monocytes [40] as is phosphorylation of IRF3 and IRF7, suggesting a link with MAVS [41]. As a result, type I IFN synthesis is significantly lower in dendritic cells and monocytes from aging individuals [42,43]. In addition to a decline in mitochondrial respiration, oxidative stress, another consequence of aging, may also be involved in this process [43].
Is Impaired T-Cell Immunity in Aging Related to a Decline in Mitochondrial Function?
Aging-related decline in immune function (i.e., immunosenescence) renders older individuals more vulnerable to infectious diseases and cancer, resulting in increased morbidity and mortality. Besides increased susceptibility to infection, vaccine efficacy is significantly reduced in the elderly, limiting the utility of prophylaxis [44,45]. Undeniably, profound changes in T-cell function are evident in older individuals, and these changes may be related to a decline in mitochondrial function.
T-cells play a central role in the coordination of adaptive immune responses and cell-mediated immunity. The ability of T-cells to fulfill this role is dependent upon rapid cellular proliferation and differentiation. In response to infection, T-cells proliferate every 4-6 h, generating >10 12 cells in one week [46,47]. This is accompanied by an increase in size, DNA remodeling, up-regulation of transcription factors and effector molecules, and increased expression of surface proteins [48,49], thus necessitating a large metabolic demand. To accomplish this task, metabolic fuels including fats, sugars and amino acids are actively transported across the cell membrane to feed the increase in To date, studies addressing MAVS function during aging and its relationship to waning antiviral immunity are lacking. Decreased mitochondrial membrane potential, mitochondrial dysfunction and declining mitophagy occur in a variety of aging cell types [38,39], raising the question of whether MAVS dysfunction can occur due to mitochondrial failure with aging. Mitochondrial respiratory capacity is impaired in aging monocytes [40] as is phosphorylation of IRF3 and IRF7, suggesting a link with MAVS [41]. As a result, type I IFN synthesis is significantly lower in dendritic cells and monocytes from aging individuals [42,43]. In addition to a decline in mitochondrial respiration, oxidative stress, another consequence of aging, may also be involved in this process [43].
Is Impaired T-Cell Immunity in Aging Related to a Decline in Mitochondrial Function?
Aging-related decline in immune function (i.e., immunosenescence) renders older individuals more vulnerable to infectious diseases and cancer, resulting in increased morbidity and mortality. Besides increased susceptibility to infection, vaccine efficacy is significantly reduced in the elderly, limiting the utility of prophylaxis [44,45]. Undeniably, profound changes in T-cell function are evident in older individuals, and these changes may be related to a decline in mitochondrial function.
T-cells play a central role in the coordination of adaptive immune responses and cell-mediated immunity. The ability of T-cells to fulfill this role is dependent upon rapid cellular proliferation and differentiation. In response to infection, T-cells proliferate every 4-6 h, generating >10 12 cells in one week [46,47]. This is accompanied by an increase in size, DNA remodeling, up-regulation of transcription factors and effector molecules, and increased expression of surface proteins [48,49], thus necessitating a large metabolic demand. To accomplish this task, metabolic fuels including fats, sugars and amino acids are actively transported across the cell membrane to feed the increase in energetic demands [50,51]. Along with this increased transport, T-cells undergo metabolic reprogramming during their transition from a naïve state to activated and differentiated cell types (e.g., effector, regulatory and memory cells).
The diverse roles played by mitochondria in T-cell activation emphasizes the potential mechanisms by which aging-related mitochondrial decline may contribute to immune dysfunction. Following stimulation of the T-cell receptor, T-cells undergo substantial changes in intermediary metabolism including an increase in glycolysis and OXPHOS [52][53][54][55][56][57]. In the presence of oxygen, pyruvate produced via glycolysis is fully oxidized in the mitochondria for energy in many cell types [58,59]. In T-cells, a significant proportion of glucose is not oxidized, but rather fermented to lactate from pyruvate via lactate dehydrogenase. This is done despite the presence of oxygen, and is termed aerobic glycolysis or Warburg metabolism [50,56,60]. Although Warburg metabolism is viewed as energetically inefficient, the rate of glycolysis is 10-100 times faster than glucose oxidation by the mitochondria, yielding equivalent amounts of ATP [61]. The additional payoff of Warburg metabolism lies in pathways that are branch points off of glycolysis (e.g., pentose phosphate pathway) which yield reducing equivalents for biosynthesis and nucleotides. Despite this adoption of the Warburg phenotype, OXPHOS is still required for T-cell activation [57]. ATP derived from the mitochondrial respiration promotes enhanced glycolysis as well as the initiation of proliferation in activated T-cells [62]. While pyruvate is mostly diverted to lactate rather than acetyl-CoA via pyruvate dehydrogenase, TCA function and the generation of reducing equivalents in highly proliferating cells is still maintained through anapleurosis: glutamine is converted to α-ketoglutarate via glutaminolysis [63,64]. Bioenergetic studies of aging tissues are consistent with a progressive decline in mitochondrial respiratory function due to a decrease in respiratory complex activity, mitochondrial membrane potential, and impaired mitophagy [39,65]. As a result, impaired OXPHOS results in reduced ATP production, thus potentially limiting glycolysis, biosynthesis and the attainment of biomass during T-cell activation and proliferation.
Besides engaging in bioenergetics, mitochondria also function in T-cell activation by modulating secondary messengers including calcium (Ca 2+ ) and reactive oxygen species (ROS). In activated T-cells, mitochondria localize to the immune synapse, and where they regulate Ca 2+ flux [5,6]. In response to this calcium flux, ROS production via complex III of the respiratory chain is amplified, leading to nuclear factor of activated T-cells (NFAT) activation and subsequent interleukin-2 (IL-2) production [66].
Aged T-cells show reduced Ca 2+ signaling, which could be partly due to deficits in Ca 2+ regulation found in mitochondria of aged cells [67,68], theoretically yielding perturbations at the immune synapse causing diminished T-cell signaling and activation.
Depending on the cytokine milieu, helper T-cells (Th), marked by the surface expression of CD4, differentiate into various effector subsets comprising T-helper 1 (Th1), T-helper 2 (Th2), T-helper 17 (Th17), regulatory T-cells (Treg). Each of these T-cell subsets are unique in their responsibilities and are identified by their cytokine signatures. Accompanying these functional distinctions are differences in metabolic reprogramming (Figure 3). For example, for T-cells subsets involved in inflammation (e.g., Th1 and Th17), the Warburg metabolism instituted at T-cell activation persists [69]. Despite this primary use of glycolysis, intact OXPHOS is still necessary for their function [57]. The effects of mitochondrial dysfunction may be more readily seen in regulatory (Treg) and memory (Tmem) T-cells. Tregs, which serve to modulate the immune system and maintain tolerance, revert back to OXPHOS as their main pathway for generating energy upon differentiation [69]. Tmem follow a similar metabolic path. Tmem are critical for adaptive immune responses characterized by robust responses to secondary immune challenges. Unlike effector T-cells, Tmem do not undergo extensive proliferation and produce little or no cytokines. As such, the metabolic profile of Tmem are essentially catabolic, relying on OXPHOS and fatty acid oxidation [70,71]. Therefore, it is not surprising to find that CD8 + cytotoxic memory T-cells have high respiratory capacity and increased mitochondrial mass, which allows them to rapidly reactivate upon re-exposure to their cognate antigens [62,72]. Given the age-related decline in mitochondrial function as described above, T-cell subsets which are critical for immunosurveillance and the clearance of invading pathogens could be functionally impaired and may partially explain the vulnerability to infection and cancer with aging [57]. Emerging data also suggest that aging significantly affects Treg frequencies, subsets and function [73], potentially leading to the increased incidence of autoimmunity, oftentimes seen with aging [74]. As noted above, Tmem also rely heavily on OXPHOS. Therefore, aging-related deficiencies in Tmem may also be traced to declining OXPHOS, manifesting as impaired immune memory to novel antigens and suboptimal boosts to existing memory [75]. function [73], potentially leading to the increased incidence of autoimmunity, oftentimes seen with aging [74]. As noted above, Tmem also rely heavily on OXPHOS. Therefore, aging-related deficiencies in Tmem may also be traced to declining OXPHOS, manifesting as impaired immune memory to novel antigens and suboptimal boosts to existing memory [75].
Conclusions
Virtually every country in the world is experiencing the challenges associated with accelerated growth in the aging population. With this graying of the population comes an increased incidence in diseases of aging, many of which have an immune component. As a result, understanding the pathophysiology of diseases of aging is now more important than ever. In this review, three main immune issues prevalent in the aging population were addressed: (1) inflamm-aging; (2) increased vulnerability to infection; and (3) declining T-cell immunity. The role of the mitochondria in inflammation and immunity, combined with the knowledge of a decline in mitochondrial function with aging, has been synthesized in this review in an effort to partially explain the immune phenotype associated with aging. However, further examination of this relationship is needed. As the methods of inquiry into mitochondrial biology continue to expand, so will investigations into the relationship between this ancient organelle and immunity in the aging population.
Funding: This work was supported by the intramural research program of the National Institutes of Health (HG200381-03).
Conflicts of Interest:
The author declares no conflict of interest. Figure 3. T-cell activation and differentiation involved metabolic reprogramming. At rest, naïve T-cells primarily use OXPHOS to derive their energy. Following activation, T-cells switch to Warburg metabolism and glutaminolysis to support their proliferative needs. Differentiation into T-helper subsets can involve either the maintenance of the Warburg phenotype (i.e., Th17, Th1, Th2), or the reversion to OXPHOS with FAO (i.e., Treg, Tm) as an important fuel. FAO = mitochondrial fatty acid oxidation, OXPHOS = oxidative phosphorylation, Th17 = T-helper cell 17, Th1 = T-helper cell 1, Th2 = T-helper cell 2, Treg = regulatory T-cells, Tm = memory T-cells.
Conclusions
Virtually every country in the world is experiencing the challenges associated with accelerated growth in the aging population. With this graying of the population comes an increased incidence in diseases of aging, many of which have an immune component. As a result, understanding the pathophysiology of diseases of aging is now more important than ever. In this review, three main immune issues prevalent in the aging population were addressed: (1) inflamm-aging; (2) increased vulnerability to infection; and (3) declining T-cell immunity. The role of the mitochondria in inflammation and immunity, combined with the knowledge of a decline in mitochondrial function with aging, has been synthesized in this review in an effort to partially explain the immune phenotype associated with aging. However, further examination of this relationship is needed. As the methods of inquiry into mitochondrial biology continue to expand, so will investigations into the relationship between this ancient organelle and immunity in the aging population. | 3,950.8 | 2019-05-11T00:00:00.000 | [
"Medicine",
"Biology"
] |